Purchasing this item will earn you 5395 reward points (Reward Points Rs. 539.50) !
Purchasing this item will earn you 5395 Rewards points (Rs. 539.50) !
Walden presents a very high quality standard at a very good price. Built in mahogany and designed with pickguard to avoid possible scratches by using pawl at the time of execution. The CS550CE G is an ideal guitar to play live and studio recording. Concorda 500 begins this solid top line with distinguishing elements such as its inlaid maple-mahogany rosette, a high gloss finish, and micro-dot finger board position markers. A tapered headstock with pearl Walden logo and chrome oil-sealed tuning machines complete this most affordable of Concorda line instruments. With Dreadnought, Orchestra, Grand Auditorium and cutaway-electric models available you are sure to find a Concorda 500 to suit your musical style.
CS550 CE is a 2012 novelty, and it is situated in the 500 series of the Concorda line of steel-stringed guitars. CS550CE comes with a concert shaped body made of rosewood back and sides and solid spruce top. This single cutaway steel-stringer features black binding around the top and tortoise shell pickguard on it. Sound hole is adorned with a double circle rosette. CS550CE comes in natural color with gloss finish. The bridge is made of rosewood and it features a belly shape, white string pins and white fossalite saddle. In the electronics department an under-saddle pickup and B-Band T35 preamp take care of amplification tasks. Preamp is equipped with a side-mounted control panel with three-band equalizer, volume knob and chromatic tuner. The neck is made of mahogany and equipped with a dovetail joint set at 14th fret. The fingerboard is made of rosewood and it has 20 frets with dot position inlays and 1-11/16 fossalite string nut. As with every Concorda 500 series guitar, the CG570 is fitted with a glass-fiber reinforced neck, two way truss rod and has a rosewood fingerboard and bridge.
It's hard to name that one person who's never played a guitar, or at least, wanted to. Hobbyists and occasional guitar players are in abundance, but those handful who are in dire need of a good acoustic guitar will certainly like what we've prepared.
This is more of a versus match between the best Guild Guitars than a regular review, but even so, these two models are some of the finest ever made, which will cut short your search substantially. Without any further ado, let's get straight to it.
Guild Guitar Company (often referred to as "GGC") is a world-class leader in the manufacturing of premium-quality guitars. They've been around since 1952 when they were founded by a certain Alfred Dronge. Some sources relate Dronge with George Mann, one of the executives of the Epiphone company, which speaks volumes about what kind of a calibre these guys are.
The GGC was bought off by Cordoba in 2014, but despite the legal technicalities behind this conjoining, the innovations brought by the new arrivals have resulted in exquisiteness. Let's take a look at what D-240E and OM-240CE can do for you.
Guild's D-240E is an outstanding acoustic guitar. Despite its simplicity, it hides quite a few secrets. At first glance, you could notice that it comes equipped with a number of plain, yet formidable features, such as the solid Sitka top, C-shaped neck, plain chrome machine heads, and more.
Just like the majority of top-tier guitars are made of mahogany and rosewood, the D-240E poses no exception. The sides, neck, and back are all made of premium-quality mahogany material while the fingerboard and bridge are made of rosewood.
This guitar numbers 20 gentle frets that allow for exquisite playability – even though this feature aims to help beginners learn the ropes, most professionals could benefit from it. What's more, the 25" scale suits beginners and veterans alike.
It's worthwhile mentioning that this guitar is only semi-acoustic. Namely, it features a marvellous hardware set which, when powered by an amplification device (guitar amp), boosts the volume, and perhaps, clarity, depending on which amp is being used. The Guild's own AP-1 active-acoustic Piezo pickups are "responsible" for unrivalled tonal qualities of the D-240E.
As for the matter of price, Guild's D-240E belongs to the "medium" price point category. It doesn't cost too much, let alone a fortune, but it certainly comes at a hefty price. Regardless, professionals seeking quality shouldn't pay too much regard for the couple hundred bucks extra on the price tag, so it's safe to say that this model is fairly valuable for the money.
Lastly, you'll not only get a beautiful, high-performance guitar should you choose this option – the brand offers a complementary gig bag for easy transport and storage as well. Even though this bonus feature isn't so rare, it's a welcome sight, to say the least.
Guild's OM D-240CE sounds a bit complex, but, in truth, it's as simple as it gets. This guitar is an exquisite piece of art – it looks ravishing, sounds amazing, and features some of the finest technologies and equipment known to the market of today.
Let's start off from the beginning. The OM D-240CE features a Solid Spruce top, mahogany back and sides, scalloped X brace, Pearloid ABS rosette, and a remarkable matte polyurethane finish. The neck was built from durable, high-resonance mahogany, the nut from bone.
Now, the bridge features a pre-compensated saddle which will certainly help you skip the dull setup part. Namely, the saddle heavily influences the intonation potential of each guitar, and a compensated one helps in many ways. Even though this guitar comes pre-strung with D'Addario's EXP 16 phosphor-coated strings, you can always upgrade if they're not to your liking.
Just like Guild's D-240E, this model is also a "semi-acoustic" guitar. It comes outfitted with Guild's AP-1 pickup which significantly boosts its overall performance, especially if you consider playing gigs somewhere in the future.
Even though there aren't any flaws concerning this model that are worth mentioning, the only think most people don't particularly like is that you don't get to choose any other colour. The "Natural" is all you could hope of getting, as the brand didn't make any other variations. Regardless, even in the most natural form, this guitar is as ravishing as it is elegant and beautiful.
Lastly, let's talk a bit about the price. Guild's OM-240CE belongs to the same price point category as Guild's D-240E, even though it's just tad more expensive. Regardless, this model is as good as the one we've previously reviewed, and it's up to you to determine which one suits you better.
People often choose between lesser evils – "this guitar is expensive, but worth the cash", or "this one's cheap, but sounds quite awful". The choices we make when we have to compensate for a fatal flaw with mediocre quality are often obvious, hence they don't fall too hard on us. However, choosing between "good" and "best" is a totally different story.
That's the reason why we've included only two guitars in this review. They both come from the same brand (which earned its fame throughout the decades of good work), and they're outfitted with a similar set of technologies and features. Since we start off with a presumption that you are a professional in need of a good guitar, simply choose the one which comes with a more convenient feature outfit.
Chords are, basically, several notes played simultaneously, resulting in a sort of harmony. Now, there are all kinds of chord types, from melancholic minors, over joyous majors, to heavy power chords. Whenever you strum several notes on your guitar (or hit two or more keys on your piano, or any other instrument), you're essentially playing a chord.
Imagining chords as pieces, of sorts, is ideal for beginners who're not well-versed in the complex language of the music theory. These "pieces" are comprised of even smaller "parts", called notes, and assembling them in a string of consecutive sequences will be the object of our topic – chord progressions.
Plain and simple, each time you play several simultaneous chords, you're dabbling with "chord progression", just like you're making a chord each time you play several notes. Just like chords have "root notes" (or "key" notes), the basic principles of chord progression start with the "root" chord.
Harmony – playing multiple sound pitches result in a harmony. A great example of it is a "chord".
Chord - a chord represents a note group (minor, major, diminished, augmented).
Scale – A set of notes organized in a fundamental frequency.
How can you expand your knowledge of music with chord progression?
Even though this might have crossed your mind, you don't have to actually know what chord progression is in order to use it. In fact, you don't even need to know what chords are, for that matter, but there are several reasons that might make you feel otherwise.
For example, even the most immediate beginners are capable of accidentally playing certain chords. A great example of that is the Am (the "A minor") chord, which is often considered as one of the easiest chords to play. Now, here's the kicker – what then? Knowing which chords are compatible with other chords will yield a fine harmony, whereas the other option might not sound appealing at all.
This leads us to the following conclusion – knowing to recognize the scale in which a certain chord belongs in opens up the doors to successfully stringing good chord progressions. Even if it's not much, it's great to begin with.
Unless you're a fan of unconventional music genres, you should at least consider learning the basics of music theory, and starting with the scales will be greatly beneficial to your knowledge of chord progression.
There are a number of scales in the music theory, including the Major scale, the Natural Minor scale, the Harmonic Minor, the Melodic Minor, pentatonic, chromatic scale, and such. Learning more about them will give you a sort of a vantage point over the notes that are musically compatible with the root note you intended to begin with.
Now, how can you use this knowledge to further improve your chord progression skills? In a way, you'll narrow down the map of your fingerboard (if it's the guitar you're playing, we're using it as an example), giving you a clear view of the direction in which the note sequence will go.
After all, the chord progression represents a sequence of chords, and understanding the scales will undoubtedly help you with this matter.
Most people have seen roman numerals in music textbooks at the elementary school, and, in case you haven't been paying attention at that certain class when this was explained, let us clarify the issue.
First of all, let's remind ourselves that the chord progression is a sequence, and, just like any other, it has a certain order. The pattern in which the chords are played are governed by this order, thus each chord is given a number.
The idea of adding numerals instead of putting plain chord letters is quite simple, actually – it's easier to memorize the numbers than letters due to the fact that some chords have more complex "names" (such as "A7", "Dm", and such). Further on that note, it's always easier to say "go one-two-four-two" than "go A-minor, diminished F, the A seven, and end with the G major".
Apart from sheer simplicity, there were other factors that motivated musicians to use numerals instead of letter combinations. Certain bands in modern music genres often transpose their songs to new keys frequently, so the numerals play a different role here - they serve as a "silent instructor" to new band members that don't have the time to prepare, especially during improvisation sessions.
The music theory is often hard to grasp head-on if you haven't any previous experience with it, and chord progression might appear tricky to some at start. The fact is, it's not – it only takes a while to understand how chords are built, and all you have to do is simply use this knowledge to make something bigger – a complete sequence of note combinations.
Essentially, learning how to use chord progressions can be beneficial for virtually every type of musician – composing songs will be easier, learning new ones will be a breeze, and improvising might feel more natural. All in all, this isn't nuclear science, and you're sure to catch up in no time. We wish you all the luck.
There is hardly a better instrument for beginners to take up than the acoustic guitar.
It's relatively easy to get a grip of, and anyone can easily learn a couple of chords and be able to play pretty much any popular song out there.
However, choosing the right one can be a difficult task. With so many different models on the market, it's easy to get confused, demotivated, and ultimately, give up.
Lucky for you, we have compiled a list of the 5 crucial things you should consider when buying an acoustic guitar. After reading this article, you will have a better understanding of acoustic guitars, and picking the perfect model for your needs will be way easier!
1. Body Size – Comfort is your priority!
Actually learning to play, and advancing, is very hard, if not impossible, if the instrument you practice with doesn't feel comfortable.
Various sizes also affect the sound, with different parts of the tonal range being more or less prominent.
(Grand) Concert – These come in at around 13" in terms of body size. Perfect for smaller musicians.
(Grand) Auditorium – Slightly bigger in size, offers a balanced sound as well as good volume.
Jumbo – Bigger than the Auditorium, great for country music.
Dreadnought – Stand at around 20", the best choice for bluegrass and similar genres.
Travel/ Mini – Varying in size, generally small and practical for traveling.
Your safest bet is to try out a friend's guitar, and see if it feels good in your hands. If not, ask them for the model, or simply measure the dimensions, and look for a smaller/ larger option for yourself!
So, the bigger the guitar, the more projection and volume it can offer. However, that isn't the only factor that defines the actual sound of an acoustic guitar.
Tonewood is the wood used for the body of an acoustic guitar. It gives different models various characteristics, both in terms of feel, build quality and sound.
Sapele – Fairly lightweight yet durable, very defined high range.
Maple – Similar to Sapele, Maple is rich with treble and easily cuts through the mix when played alongside other instruments.
Mahogany – Somewhere between Sapele and Maple, Mahogany makes for a strong and defined sound, with a slight boost in the highs.
Cedar – Compared to the other tonewood types, it's pretty soft. Just think flamenco in terms of the actual sound!
If you're a beginner, getting the "wrong" tonewood type for your first guitar won't really matter. But, in order to make a future-proof investment, try to make a rough sketch of the sound you're looking for and choose accordingly!
3. Steel or Nylon Strings? What's the Difference?
While many online guides suggest that beginner guitarists should go with nylon strings for their first acoustic guitar, there isn't really a rule to be followed.
The biggest differences between these two options are in the sound and feel.
Nylon strings feel much softer and won't wear out your fingertips that fast. The sound is also less bright and offers more warmth.
Steel strings, on the other hand, make longer practice sessions more painful, but contribute to higher volume levels and a crisp tone.
Listen to how both options sound on the internet, and go for what you find to be more appealing.
Just note that when you buy an acoustic guitar with steel strings, you can not put nylon strings on that model, and vice versa!
4. What About Acoustic-Electric Guitars?
Acoustic- electric guitars stand somewhere in the middle between regular acoustic and electric guitars. They have a pickup similar to those found on electric guitars, and give you the possibility to play through an amp!
Recording sessions and live performances are much easier if you play a guitar of this sort. So, if you plan on playing with other people in a band, or maybe even on the streets in the future, going with an acoustic-electric model is a great idea.
Just remember that you will have to spend a bit more money on this type of guitar!
5. How Much Money Do I Have to Spend?
It goes without saying that usually, the more you spend, the better the instrument is, at least to a certain point.
First of all, you should evaluate your skill level. Are you a beginner or a more advanced guitar player?
As an absolute newbie, you won't be able to tell the difference between cheap and more expensive models. Having that in mind, getting a $1000 acoustic guitar as your first instrument just doesn't make sense.
Look for popular brands such as Ibanez, Fender, Yamaha, Cort, or Taylor. Each of these brands offers a wide variety of great models with different price tags. It's better to spend a little more than you originally planned for a guitar that's proven itself worth the money, than going for an unknown, yet very cheap model.
For around $100, you can get a pretty decent beginner acoustic guitar.
If you feel like you need something a bit better, going up to $500 tops makes sense in most cases.
Anything more than that is generally a waste of money unless your life goal is to become a professional guitarist.
So, think about the type of music you want to play, the size that feels the most comfortable, and the sound you find most appealing. If needed, save up some extra money, and start playing!
We hope that you found this article helpful and that you learned something new about acoustic guitars!
As always, thank you for reading, and we will see you in the next one!
What would you possibly question, if I tell you about Spanish Guitar Company making Spanish guitars with Spanish craftsmen and founded by Spanish luthier? Yeah, this is a real deal.
What would you possibly question, if I tell you about Spanish Guitar Company making Spanish guitars with Spanish craftsmen and founded by Spanish luthier? Yeah, this is a real deal. The history of Rodríguez guitars is as rich as the wood from which they are crafted. Manuel Rodríguez — grandson of flamenco guitarist Manuel Rodriguez Perez Marequi and son of classical luthier Manuel Rodríguez Perez — learned the art of constructing a guitar firsthand. His apprenticeship began at the age of 13 in Madrid, where he also began exporting his finely crafted instruments to France, the United Kingdom, and the U.S. Fast forward to 1959, Manuel Sr. opened a shop Los Angeles, making classical guitars for a myriad of professional players, teachers, students, and even the Hollywood elite. He and his son moved back to Madrid in 1973 where Rodríguez guitars have been designed and built ever since. His son, Manuel Jr, continues on with the family tradition of crafting exquisite instruments with the fire and passion he learned from his heritage. Using only the finest tonewoods and expert craftsmanship, Manuel Rodríguez develops distinctive guitars fit for the world's preeminent artists. Each instrument is as unique and individual as the musicians who play them. Embodying the skills he learned as an apprentice to the master luthiers of Spain, Manuel Jr. ensures each guitar is a work of art to be treasured for generations.
"If that which cannot be repeated is art, then our guitars are also an artistic instrument. It is even more so when each artist constructs his guitar by creating exclusive ornamentation, using precious and unique woods, creating a mosaic, which distinguishes this soundhole from all the other soundholes. It is like a feather; a purfling that will never be repeated as far as color, thickness and taste are concern. We are therefore talking about an art piece that has a life of its own, produces elegant sound, and provides the guitarist with their own one-of-a-kind instrument to express their musical skill and harmonic knowledge. It is held in the hands and close to the body; it is an art piece of precious natural materials built to the luthier's taste and woodworking skills; it is your trade, personality, and dignity in doing a good job." — Manuel Rodríguez Jr.
Let me present Caballero 11 or Gentleman 11(Caballero in English).
Featuring a carefully chosen, solid Canadian cedar top and laminated bubinga back and sides, the Caballero 11 classical guitar is a beauty to behold and play. The headstock and fretboard are made of Indian rosewood. Nickel-plated tuners and Silver-plated frets are installed to last a lifetime. The body binding and wood rosette is exquisite.
The Rodriguez Guitar is hand crafted and glued to create precise balances. From the invisible careful sanding, even inside the body, that ensures the finished instrument's purity of tone, to the beautifully unique rosette inlays around the soundhole and on the back of the neck, each guitar is a credit to its luthier and worthy of being handed down from one generation to another.
The tone, resonance and beauty of fine guitars are all dependent upon the wood from which they are made. The wood used in the construction of Rodriguez guitars is carefully chosen and aged to guarantee the highest quality. No wood is purchased before the tree has been cut down, and at least 2 years must elapse before the tree is turned into lumber. The wood has to be well cut from the log. The grain must be close and absolutely vertical.
The Rodriguez Caballero 11 guitar features a multi-coloured wood rosette, as exquisite as the sounds that issue from it. Their intricacy and beauty signify the attention to detail that characterizes every Rodriguez guitar. This classical guitar has a look that can only be provided by Bubinga, as natural finish. With a top made of Cedar, the most impressive feature of this piece is its back side finish, a natural deep brown. For C11 model, all Bubinga back and sides are mated to a solid cedar top for a rich tone with a roundness and warmth seldom found on instruments in this price range. The beautiful figuring of the Bubinga adds to the overall aesthetics. A mahogany neck combined with the rosewood fingerboard will make sure the neck stays straight and true, and the wood rosette and binding will ensure great looks accompany your incredible sound. These woods give the instrument a rarely seen colour, because it is not commonly used.
How about if we discuss more about its tone woods?
Woods such as Bubinga are used by custom guitar-makers, but don't feature highly in mass-production guitars. These are mostly hard, dense woods with distinctive grain patterns. The colours can be appealing in their natural states, and they are usually used as one ingredient of many in a multi-wood body.
Cedar ranges in colour from honey brown to light chocolate. It has a quickness of sound that exceeds any of the spruces, a higher overtone content, lower fundamental content, and lower stiffness along the grain. Additionally, cedar tops require a significantly shorter break-in period than spruce tops, a phenomenon that a few dealers of new guitars are beginning to pick up on. Cedar has been used extensively by makers of classical guitars. Cedar-topped guitars are characteristically lush, dark-toned, and bursting with flavour. They are often less powerful in projection than their spruce cousins, however, and they tend to lose clarity near the top of their dynamic range. Having enough bottom end is never a problem for a cedar guitar, although preventing the sound from getting muddy sometimes is. Because of its pronounced weakness along the grain, I find cedar to be used to its best advantage in smaller-bodied guitars or with non-scalloped braces.
The second most common guitar-neck wood after maple, mahogany is most often coupled with a solid mahogany or mahogany/maple-topped body. This more porous, open wood doesn't quite have maple's hardness, strength, or stability, however, and it isn't suitable as a fretboard material. Mahogany has a warm, mellow tone with good presence in the lower mids. The mahogany/rosewood pairing contributes to complex highs, thick and creamy lows, and an appealing midrange that isn't honky or excessively punchy.
All in all this is the perfect guitar for all the classical gentlemen out there, who are looking for an excellent setup to begin their musical journey!
The Grail guitars are Top Range Guitars…with their series; be it Grail AG Cutaway or CG Series, specifically for beginners, professionals and/or both…Learn more about the Grail guitars; the sound output, appearance, features, models…and whenever you want to buy Grail Guitars online, you are sure to make an informed choice.
The name 'Grail' totally justifies this brand. Because every musician eagerly pursues to buy such kind of a guitar which has a better money-value in terms of quality than what the artist is paying for and Grail guitars give you the same.
The chronicle of the Holy Grail is one of the most enduring in Western European art and literature. However; in today's modern time, the meaning of Grail/ Holy Grail is a thing which is eagerly pursued or sought after. And you know what; the name 'Grail' totally justifies this brand. Because every musician eagerly pursues to buy such kind of a guitar which has a better money-value in terms of quality than what the artist is paying for and Grail guitars give you the same. Grail guitars have a reputation to deliver better quality than product's cost.
The designing of this piece of art is done in Taiwan and manufactured to specifications that offer superior sound and features at a price that is affordable. To achieve deep warm sound, Grail manufacturers use different combinations of tonewood. These guitars are designed and built in such a fashion that its sound will fit perfectly in any genre. Plus the body of guitar too, it's built for overall comfort. Grail guitars are committed to developing products at a value, which is irresistible.
Well what about the looks and design? Grail guitars are enhanced with inlays, designed pickguards and glossy finishes which make the guitars look great.
To help you understand better, I will now explain each product in a little bit of detail.
The Grail D110 is a dreadnought guitar with a deep resonance and warm tonal frequency suiting both Beginners and Musicians alike. Tonewoods used in the Guitar amplify the sound and make it sound larger than it looks. The slim neck allows for an easier playing experience. The action is precisely configured to make it easier on the fingers and facilitates longer playing. The D'addario phosphor bronze strings give it a rich and well-balanced tone and enhanced playability. Quality die cast machine heads ensure stable and reliable tuning.
The guitar is finished with high quality lacquer, which will keep your guitar in good condition for years to come.
The Spruce top and other Tonewoods used in this Guitar give it a rich clarity and resonance that is similar to much higher priced guitars to suit both beginners and musicians alike. The slim neck allows for an easier playing experience. The action is precisely configured to make it easier on the fingers and facilitates longer playing. The D'addario phosphor bronze strings renowned for its rich and well balanced tone and enhanced playability elevates the guitar playing experience. Amped up with quality die cast machine heads; ensures stable and reliable tuning. The guitar is finished with high quality and long lasting lacquer.
The D120 is a guitar that looks and sounds like a thoroughbred.
The Grail A190 proves that a 39" guitar can look snazzy and sound good. Right from the abalone like inlays to the fan pick guard; this guitar has all the features that will make you want to own it. The A190 is made of basswood with a glossy lacquer finish and ABS binding. It has individual machine heads for stable tuning.
This is the perfect guitar for students who want a convenient size without compromising on design and sound.
The Grail CG-910 is a Classical guitar that every beginner will love. The neck is easy to hold and the strings and action are designed for comfort picking. The Guitar has a Spruce Top and a multi colour Rosette giving it a contemporary look. The CG -910 has a warm tone and resonance and is a delight to play with.
Are you in need of a solid foundation for your electronic guitar experience? The Fender CD-60CE Electro Acoustic Guitar is one of the best options to opt for…Features are uniquely packed to help you learn the necessity… Plus, this classic dreadnought is very cost effective and durable.
The excellence and quality that you receive for that much money is dazzling. However, this is not the usual beginner guitar that you will see people chatting about. What is even more vital; the playability and the ease of use that this model present makes it one of the best starter guitars that you can think of. I am standing firm behind my words and I know that once you try this splendour you will share my opinion.
Here is the majestic beginner acoustic-electric guitar Fender cd60ce and by the way Fender recently announced that this model is one of their acoustic bestsellers. Why? Because this classic dreadnought comes with a laminated spruce top and mahogany back and sides. This reasonable masterwork comes with a rosewood fingerboard attached to a nato neck and 20 frets. The nut is a standard 1.69″ length and made out of synthetic bone. The rosewood bridge comes with a compensated graph saddle.
The headstock is radiating with style, and the die cast tuning machine pegs and the chrome finish of this guitar is splendid. This model features some unique Fender electronics that guarantee quality and full control of the sound. The CD60-CE features built in tuner, volume, mid, bass and treble controls.
This one sounds exactly like a good acoustic guitar. Cd60ce is good for a lot of music styles, but let's not overlook that we are talking about Fender, the king of versatility. Plug it into an amp, and you can do some heavy metal stuff too, just do not forget to lower the settings, because this monster can get really loud sometimes. Bassy lows and nice highs complete the picture. Everything that a beginner can come up with, this axe will handle.
Even if you are not just starting out, but you have couple years behind you, you will still love the CD60CE. It is affordable and with a few good upgrades you can easily lift the quality of the sound to a much superior level. The built-in tuner itself is good enough reason to go with this model and never look back.
All in all if you are looking for the best guitar to learn on, this Fender might as well be it. It sounds great, doesn't cost that much and offers plenty of value for money.
Perfect Method of Changing guitar strings.
We often consider the outward appearance of the guitar without even noticing how vital the strings can be. The strings should be cared for during routine and regular maintenance…Learn the effective ways to change your guitar string…dealing with old strings… and stretching, installing, cleaning of the other parts and strings….
In my decade of guitar playing experience (not bragging, just trying to explain you something!) I got efficient in something which is related to guitar playing; the most important part of guitar assembly, yet the most overlooked factor nevertheless, is changing the string(s).
Now I know that most of you guys will be like "Yeah like it's the most complicated thing in the world eh? Pffft... Changing the strings!" No it's not the most COMPLICATED thing in the world, but yea there are some things which can complicate the process. Counter Productive? Well, it takes time and effort but gives your guitar strings a longer life and of course to your guitar too while giving you a great deal of satisfaction when you play, a clean, fresh bright sounding guitar. Plus, you save money which you hand out for something you can do at the comfort of your home.
With a string winder, and starting from the low E string, unwind the string, until you are able to loosen it from the hole in the machine head. Work across the guitar repeating this method. This will put the smallest amount of pressure on your neck and body. Do not plainly cut the strings using wire cutter. This manner is dangerous, and gives an unexpected stress release within the guitar neck. It also makes for twice the sum of wire to dispose of. then, carefully pull out each string's peg, keeping track of which peg, came from which string. Wrap up each string back into a circle, and lock loop with one end. Try to make the circle small enough to fit into the envelope that your new strings will be disconnected from. In this way, everything is nice and neat, and there is less change of damage.
Now use your guitar polish, and clean your instrument, especially around the sound hole. This is also the time to decide, weather your fret board needs conditioning or not. There are many good polishes and fret board conditioners on the market. Personally, I like to remove any dirt and grease that has built up behind the frets. I find that trying to remove all traces of build up is needless and can lead to damage the neck. Harsh chemicals will dry out the wood, and water tends to swell the wood. So, just use a clean cloth and gently remove most of the grease, using the fret board conditioner. Leaving a little grease behind isn't going to hurt anything. If you get to aggressive and trying to remove all of it, you may do more harm than good.
Get a lead pencil. Before replacing your strings, take the sharp lead pencil, and rub the lead into the string slots on the top nut. This will put in a little graphite, and help to release uneven tension when you tune the guitar. Your guitar will stay in tune better.
Starting with the bass E string, place the end ball back into the saddle, and adjust the slot in the peg to fit the string. Press the peg all the way down while placing a little tension on the string, with the other hand. You are trying to find the end of your string ball, while pressing the peg into the hole. Take the other end, being careful, wind it around the machine head's pole 2-3 times, rotating counter clock wise, on the bass side and clock wise on the treble side. After placing the end of the wire through the hole, pull it tight. Now, begin twisting the machine head, placing more stress on the string. No string should be entangled with another. Check to see that the 2-3 windings are holding, and look correctly. Do this with all 6 strings. Using a tuner, slowly bring the bass string up to full note tension. Do this with all 6 strings. Don't waste your time trying to tune each string. Relative pitch will work for now. If your G string is a wrapped, be slow to bring it up to tone. It contains the thinnest core wire within the set and is the easiest to break. Worry about the G string, and then the top E string. Bring all of your strings up to tune, working your way from the bass to the treble. Use a good pair of small wire cutters, cut off the excess wire.
Your new strings will not stay in tune, until they have had time to stretch out. If you don't plan to play, tune it up, and leave it for a day or two, re-tuning when you have a chance. I have rarely done this, as I usually want to start playing. Additionally, I want my guitar to stay in tune, without constantly retuning… Here is a way, to help remove most of the built in slippage from your strings. Care must be taken, or you will break strings. As the strings become thinner, you must use less pressure. With your guitar fully tuned to E, place it horizontally on a padded table top, and/or your lap with the bass string adjacent to you. Grasp the bass E string with both hands. The wire should be between your four fingers and your thumbs. Hands spread apart, with approx. a half an inch space between your two thumbs, start bending the string. Pull with your fingers, while bending in the opposite direction. Do this moving up and down the neck. You are working the bindings. You should be very careful bending your G string, especially if it has an outer wrapping. This is the string, which will always break first, until you learn this technique. Turn your guitar around now, and do the same thing in the opposite direction, starting from high E to low E. Once you have learned this technique, you will be likely use it, as it makes a huge difference in the time it takes to keep your guitar in tune. It might be wise, to purchase an extra single G and E string. In the beginning, your G, B, and high E, are the strings that break most frequently.
Why quality guitars are better than the low cost ones?
"Well, playing guitar is my hobby, I don't want to invest that kind of money in it!" etc. Are the first few questions that pop up in our minds when we find out that economical equipments look expensive because at times the price tag looks much bigger than the future with that instrument! And then we go ahead and buy the cheap ones.
Well, that seems ok in the beginning until the pain kicks in. In 5 to 6 months the tone starts wearing off, in an year or so the fret board stars to bend, the cheap metal frets starts damaging and tearing your finger tips, a lot of strength is needed to play simple pieces (especially barred chords) and eventually, playing guitar becomes a chore and not something that you love to do.
Option A- Dropping the dream! It's a no-no! I don't even want to talk about it.
Option B- If it's a minor tweak; yea why not? But if it's something related with fret board; that's what I want to talk about. You see; the brands that are able to provide low cost goods can do so because they use inferior raw material, inexpensive craftsmanship and in general- a cheap job. So, let's say you see bend in the fret board. You go to the local guitar shop only to find out that the spare parts and labor work costs you as equal to the new cheap guitar. So what are you going to do now? Mend the old one or buy a new one?
Option C- After some months of experience, you will eventually find out that budget guitar is the best option because it plays well and definitely softer, and the tone is crisp and bright. Plus the lifespan of that instrument is really long; you can see and feel the better craftsmanship considering its look and playability when compared with the low cost ones.
The best motto is; Buy once-buy the best.


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Nose: Stewed apples, polished wood, hints of raisins, toffee, cinnamon, nutmeg anf hints of cloves.
Palate: Apple strudel with custard, creme caramel, nutmeg and hints of pepper and a touch of dry wood.
Overall: Unusual apple aromas can be found in this sherried dram, a very fine whisky indeed, with just enough wood influence to be noticeable.


This is a blog about the staggering (and fun) implications of that future.
The implications of a connected neocortex are quite literally unfathomable. As such, any list I can come up with will pale in comparison to reality… But here are a few thoughts to get the ball rolling.
This will deliver a new level of human intimacy, where you can truly know what your lover, friend or child is feeling. Intimacy far beyond what we experience today by mere human conversation. Forget email, texting, phone calls, and so on – you'll be able to send your thoughts to someone simply by thinking them.
Just imagine that you're in a bind and you need to solve a problem (quickly). In this future world, you'll be able to scale up the computational power of your brain on demand, 10x or 1,000x… in much the same way that algorithms today can spool up 1,000 processor cores on Amazon Web Servers.
If our brains can truly connect at high bandwidth, you will be able to bypass our current sensory organs (eyes, ears, touch) to the point where brain's perception of reality can be driven completely by a gaming engine – a virtual world. Likewise, the connections would exist in the motor cortex of your brain as well. When you move your limbs, imagine a corresponding set of virtual limbs (your avatar) moving perfectly in the virtual world. This is about creation of The Matrix x 1,000.
Remember the scene in The Matrix where Trinity needs to learn how to fly a helicopter, and Tank downloads a program teaching her how to do it? We'll be able to do this. Need to perform emergency surgery? Just download the ER doctor program. Need to learn a new language? Download it. Want to cook the perfect meal? Download the chef module. In fact, you probably won't even need to download it (which takes up memory), you'll probably just "stream" expertise from the cloud.
While this future may sound fanciful to many, let's remember that exponential technologies are initially deceptive, before they become disruptive.
And today, there are many labs around the world working on molecular machinery, CRISPR/Cas9 systems that allow us to edit our own genome, and brain-computer interfaces (through cortical implants and the field of optogenetics).
Kurzweil is a brilliant guy, but the Singularity theory is flawed. Our understanding of "consciousness," "intelligence," "perception" — and most other mysteries of the human mind — is still highly theoretical. In other words, we have yet to develop even the most basic grasp on the /mechanics/ of the "mind," which is, in itself, simply an abstract theoretical construct, a made-up concept — just a word, really. This kitchen-sink "mind" concept encapsulates a multitudinous mess of disparate neurological, biological, chemical, and physical processes which we would probably need to fully uncover and understand in order to engineer the kind of artificial intelligence Kurzweil is suggesting. And though some interesting progress continues to be made in neuroscience, genetics, etc., the irrationally deep complexities of our mental processes have persisted in eluding us, with little indication of an approaching change in course.
Furthermore, the Singularity is at least partly postulated by extrapolating from Moore's Law, which was first stated in 1965, an observation that "the number of transistors in a dense integrated circuit doubles approximately every two years." The assumption is that this trend would continue indefinitely into the future forever, guaranteeing a certain technological threshold being reached, apparently around 2030. However, in recent years this trend has slowed considerably, and even more importantly, there are basic physical limits intrinsic to the materials (such as silicon) used to produce the circuitry and processors; therefore, their size and speed cannot be improved indefinitely. Eventually, a maximum is reached, and the decelerating pace of trends associated with Moore's Law over the past several years would seem to suggest that we have begun to approach it.
That being said, he certainly does offer an enticing transhumanist, utopian vision of the future. Though I do believe it's far too good to be true, for the reasons above, as well as others, I still certainly hope he turns out to be right, after all, as he has supposedly been for those other hundred or so prophecies of his.
I appreciate your thoughtful comment, Dylan.


text:
\section{INTRODUCTION}

Spin-dependent transport in quantum dots is a subject of intense
study nowdays due to its relevance to the new generation of proposed
spintronic devices that encompasses, for instance, the Datta-Das
transistor,\cite{dattadas} memory devices\cite{sc02,mk04} and as
an ultimate goal quantum
computers.\cite{dda02} In
particular, the recent progress in the coherent control of
electron spins in quantum dots
\cite{jme04,acj05,fhlk06} has
stimulated even further the research in this field, for possible
applications in quantum computation and quantum information
processing.\cite{man00} In addition to these fascinating technological
applications, quantum dots constitute a unique well-controllable
system to study fundamental physical aspects of transport in the
strong Coulomb-correlated regime, and its interplay with
spin-dependent effects.

A common geometry used for transport studies in quantum dots consists of two leads
weakly coupled to a quantum dot (QD) via tunneling barriers. Spin-dependent effects such as spin accumulation
and spin-polarized transport can occur in these systems when both leads are (or at least one of them is) ferromagnetic (FM).
The junction FM-QD-FM resembles the standard TMR \cite{mj75,jsm95} and
GMR \cite{mnb88} geometries composed of an insulator layer
sandwiched by two ferromagnetic metallic leads, except for the
quantum dot replacing the insulator layer. This system (dot coupled to FM leads) was recently
experimentally realized in the context of semiconductor quantum dots\cite{kh07_1,kh07_2} and molecules.\cite{anp04,ss05,cam07}
A wealth of novel spin-dependent effects has been observed in this system
due to the interplay of quantum confinement, Coulomb correlations,
Pauli principle and lead-polarization alignments. For instance, novel
effects such as spin-accumulation,\cite{iw06,iw05} spin-diode,\cite{fms07_1,commentNina} spin-blockade,\cite{fe06,ac04,ac04_2,mp03}
spin-current ringing,\cite{fms07_3,ep08} negative differential
conductance and negative TMR,\cite{fe06,iw06} and so on, arise in
this context. In order to obtain additional information, not
contained in the average current, shot noise has also been analyzed in several
spintronic systems. A few exemples include shot noise in
spin-valve junctions\cite{brb99,yt01,egm03,mz05} and quantum dots attached to
ferromagnetic leads.\cite{rl03,fms02,du07}

Here we apply the Keldysh non-equilibrium technique to study
spin-polarized transport (current and shot noise) in a FM-QD-FM
system (Fig. 1). Both parallel (P) and antiparallel (AP) lead
magnetization alignments are considered. The left and the right
lead materials are taken to be different, thus resulting in additional
effects, not seen for leads with the same material. We analyze
both the current and the shot noise in the presence of Coulomb
interaction and spin-flip in the dot. We find an
interplay between spin accumulation and Coulomb interaction that
gives rise to a bias dependent current polarization $\wp$. More
specifically, $\wp$ can be suppressed or enhanced and have its
sign changed, depending on the magnetic alignment and the bias
voltage. We also note that the spin-flip can switch the current
polarization as it flows from the emitter to the collector lead.
In particular, it is possible to have an unpolarized
emitter-current and a polarized collector-current. For the shot noise, we find that spin-flip
can suppress it (in the AP case) with Fano factors reaching well
below 1/2.

The outline of our paper is as follows. In Sec. II we describe in
detail our model Hamiltonian. In Sec. III we present the
current and the noise calculations, respectively, including
general formulas for these quantities. In Sec. IV we present and
discuss numerical results for the current and the shot noise.
We summarize our conclusions in Sec. V. Technical details of our
calculation are described in the appendixes A-D.

\begin{figure}[tbp]
\par
\begin{center}
\epsfig{file=fig1.eps, width=0.35\textwidth}
\end{center}
\caption{Schematic of the system studied: a quantum dot coupled to
two ferromagnetic leads. On the forward bias the electrons tunnel
from the left lead to the right lead via the
quantum dot. We consider configurations in which the FM leads are
parallel (P) or antiparallel (AP). The dot has a single orbital
level and can hold at most two electrons of opposite spins. Intradot Coulomb
interaction and spin-flip are considered.} \label{fig1}
\end{figure}

\section{Model system and Hamiltonian}

Our system consists of a quantum dot with one quantized level
coupled to two ferromagnetic leads via tunneling barriers. While the
electrons in the leads are noninteracting, the electrons in the dot
experience Coulomb repulsion and spin-flip scattering. The system
Hamiltonian is
\begin{equation}\label{H}
H=H_L+H_R+H_D+H_T.
\end{equation}
The first three terms in (\ref{H}) correspond to the three different
regions: left lead, right lead and dot. The last term $H_T$
hybridizes these three regions thus allowing electrons to tunnel
from one region to the other. This term gives rise to current in the
presence of a bias voltage.

More explicitly, we have for the ferromagnetic leads
\begin{equation}
H_\eta=\sum_{k\sigma}
\epsilon_{k\sigma\eta}c_{k\sigma\eta}^\dagger c_{k\sigma\eta},
\end{equation}
where $\epsilon_{k\sigma\eta}=\epsilon_{k \eta}+ (-1)^{\delta_{\sigma \downarrow}} \Delta$
(Stoner Model) is the spin-dependent energy of the electron in
lead $\eta=(L,R)$, with the band spin splitting $\Delta$, $\sigma=\uparrow,\downarrow$ and $\delta_{\uparrow \uparrow (\downarrow \downarrow)}=1$, $\delta_{\downarrow \uparrow (\uparrow \downarrow)}=0$. The operator $c_{k \sigma\eta}$ $(c_{k \sigma\eta}^\dagger)$ destroys (creates) an electron with wave vector $k$ and spin $\sigma$ in lead $\eta$. The dot Hamiltonian is
\begin{equation}\label{hd}
H_D=\sum_\sigma \epsilon_\sigma d_\sigma^\dagger d_\sigma+ U n_\uparrow
n_\downarrow +R (d_\uparrow^\dagger d_\downarrow
+d_\downarrow^\dagger d_\uparrow), \label{HD}
\end{equation}
where $\epsilon_\sigma$ is the dot level and $d_\sigma$ $(d_\sigma^\dagger)$
annihilates (creates) an electron in the dot with spin $\sigma$.
Our model assumes a single spin-degenerate orbital level in the
dot, $\epsilon_{\uparrow}=\epsilon_{\downarrow}=\epsilon$. More
specifically, our dot can be singly occupied by an electron with
spin up or down or doubly occupied by two electrons with opposite
spins. We account for the Coulomb interaction in the dot via the
Hubbard term with correlation parameter $U$. We assume a linear
voltage drop across the system: $\epsilon=\epsilon_0-\frac{eV}{2}$, where $ e>0$, $V$ is the
applied voltage and $\epsilon_0$ is the dot level for $V=0$. The left $\mu_L$ and the right $\mu_R$ chemical
potentials are related by $\mu_L-\mu_R=eV$. Here we assume that $\mu_L$
is constant and defines the origin of the energy. For
positive bias ($ \mu_L>\mu_R$) the left lead is the electron
emitter and the right lead is the collector. The last term in (\ref{hd})
accounts for a coherent spin-flip in the dot.\cite{footR} This term can represent, e.g.,
a local transverse magnetic field that coherently rotates the electron spin,
which can be experimentaly realized via ESR techniques\cite{he01}
or by the Hanle effect.\cite{hanle,mb05}

Instead of carrying out the calculations with the Hamiltonian
(\ref{HD}), we perform the following canonical
transformation,
\begin{equation}\label{canonical}
d_{\sigma}=\frac{1}{\sqrt{2}}\sum_{i=1,2}
(-1)^{i\delta_{\sigma\downarrow}}d_i.
\end{equation}
With (\ref{canonical}), the dot Hamiltonian becomes
\begin{equation}  \label{HD_transformed}
H_D=\sum_{i=1,2} [\epsilon_0+(-1)^{i}R] d_i^{\dagger} d_i +U n_1 n_2,
\end{equation}
where $n_i=d_i^\dagger d_i$. Note that in (\ref{HD_transformed}) the dot level
is split into two levels; $\epsilon_1=\epsilon_0-R$ and
$\epsilon_2=\epsilon_0+R$. We note that this canonical transformation rotates the
spin quantization axis (e.g., to the direction of a local transverse magnetic field),
thus replacing the spin-flip term by a diagonal term with a split level.

The tunneling Hamiltonian in (\ref{H}) is
\begin{equation}  \label{HT}
H_T=\sum_{k\sigma\eta} (t_{k\sigma}c_{k\sigma\eta}^\dagger d_\sigma +
t_{k\sigma}^* d_\sigma^\dagger c_{k\sigma\eta}),
\end{equation}
where the matrix element $t_{k\sigma}$ connects an electronic state in lead $%
\eta$ to one in the dot. Observe that the hopping process between
the leads and the dot is spin conserving, i.e., $t_{k\sigma}$ does
not mix different spin components. Applying the transformation
(\ref {canonical}) in (\ref{HT}) we find

\begin{equation}
H_T=\sum_{k\sigma\eta i}\frac{(-1)^{i\delta_{\sigma\downarrow}}}{\sqrt{2}}%
\{t_{k\sigma}^* d_i^\dagger
c_{k \sigma \eta}+t_{k\eta\sigma}c_{k \sigma \eta}^\dagger d_i\}.
\end{equation}

Next we calculate current and noise for the model described above.

\section{Current and Noise}
\label{avg-cur}

The current is calculated in the standard way from the
definition $I_L(t)=\langle \hat{I}_L(t) \rangle$ where
$\widehat{I} _L(t)=-e \dot{N}_L $ is the current operator, with
$N_L=\sum_{k\sigma}
c_{k\sigma L}^\dagger c_{k\sigma L}$ being the total number operator, and $%
\langle ... \rangle$ is a thermodynamic average. From the Heisenberg equation $\dot{N_L}=i[H,N_L]$, we find
\begin{equation}\label{curroper}
 \hat{I}_L(t)=i e \sum_{k \sigma} [ t_{k \sigma} c_{k \sigma \eta}^\dagger (t) d_\sigma(t) - t_{k \sigma}^* d_\sigma^\dagger(t) c_{k \sigma \eta}(t) ],
\end{equation}
which results in the following current expression\cite{ym92,apj94}
\begin{equation}\label{curr1}
I_L(t)=2e\mathrm{Re} \sum_{k\sigma} t_{k\sigma} i \langle
c_{kL\sigma}^\dagger (t) d_\sigma (t) \rangle.
\end{equation}

A similar expression holds for the right lead current $I_R=-e\langle \dot{N}%
_R \rangle$. Since we are in stationary regime we have simply $I_L=-I_R$. Using the canonical transformation in Eq. (\ref{curr1}) we obtain
\begin{equation}  \label{curr2}
I_L=2e\mathrm{Re} \sum_{k\sigma i} t_{k \sigma} \frac{%
(-1)^{i\delta_{\sigma\downarrow}}}{\sqrt{2}} G_{ik \sigma L}^<(t,t),
\end{equation}
where $G_{i k \sigma L}^<(t,t)=i\langle c_{kL\sigma}^\dagger (t) d_i
(t)\rangle$ is the lesser Green function, which is calculated via the Keldysh nonequilibrium technique.\cite{lvk65,hh96}

As a starting point we construct the complex time Green function
$G_{i k\sigma L}(\tau,\tau^{\prime})=-i\langle T_c d_i(\tau)
c_{k\sigma L}^\dagger (\tau^{\prime})\rangle$, where $T_c$ is the
contour time-ordering operator and $\tau$ and $\tau^{\prime}$ are
complex times running along a complex contour.\cite{lvk65,hh96}
Then we go from the Heisenberg to the interaction picture, by introducing the
$S$-matrix operator $S=e^{-i\int_c d\tau \widetilde{H}_T (\tau)}$.
Here the tilde means that $H_T$ is in the interaction
picture. After expanding $S$ we find,\cite{apj94}

\begin{eqnarray}  \label{GsksLtautau'}
&&G_{i k\sigma L} (\tau,\tau^{\prime})=t_{k\sigma}^* \sum_j \frac{%
(-1)^{j\delta_{\sigma\downarrow}}}{\sqrt{2}}
\nonumber\\&&\phantom{xxxxxxxx}\times\int_c d\tau_1
G_{ij}(\tau,\tau_1)g_{k\sigma L}(\tau_1,\tau^{\prime}),
\end{eqnarray}
where $G_{ij}(\tau,\tau_1)=-i\langle T_c d_i(\tau)
d_j^\dagger(\tau_1)\rangle $ and $g_{k\sigma
L}(\tau_1,\tau^{\prime})=-i\langle T_c \widetilde{c}_{k\sigma
L}(\tau_1) \widetilde{c}_{k\sigma L}^\dagger (\tau^{\prime})
\rangle$. Note that while $G_{ij}(\tau,\tau_1)$ is in the
Heisenberg picture, $g_{k \sigma L}(\tau_1,\tau')$ is in the interaction picture (denoted by the tilded operators). This
``separability'' of the interaction and Heisenberg pictures follows
from the assumption of noninteracting electrons in the leads. This allows us to put
the ``difficult'' part of the analysis entirely in the dot Green
functions, which contain the Coulomb interaction, the spin-flip
and the coupling to leads.

The next step is to apply Langreth's analytical continuation rules
\cite{hh96}
to (\ref{GsksLtautau'}), to find the lesser Green function appearing in (\ref{curr2}). This yields
\begin{eqnarray}
&&G_{ik \sigma L}^< (t,t^{\prime})=t_{kL\sigma}^* \sum_j \frac{%
(-1)^{j\delta_{\sigma\downarrow}}}{\sqrt{2}} \int dt_1\times  \nonumber \\
&&\{G_{ij}^r(t,t_1)g_{k \sigma L}^<(t_1,t^{\prime})+G_{ij}^<(t,t_1)
g_{k \sigma L}^a(t_1,t^{\prime})\},
\end{eqnarray}
where the labels $r$, $a$ and $<$ mean retarded, greater and
lesser, respectively. The calculation of the retarded $G_{ij}^r$, and lesser $%
G_{ij}^<$ dot Green functions is presented in the Appendix A.

Using this result in (\ref{curr2}) we arrive at
\begin{eqnarray}
I_L&=& 2e \mathrm{Re} \sum_{ij} \int dt_1  \nonumber \\
&\times&\{G_{ij}^r(t,t_1) \Sigma_{ji}^<(t_1,t) + G_{ij}^<(t,t_1)
\Sigma_{ji}^a(t_1,t) \}
\end{eqnarray}
where $\Sigma_{ji}^{L(<,a)}(t_1,t)$=$\frac{1}{2}\sum_{k\sigma}|t_{k%
\sigma}|^2 (-1)^{(i+j)\delta_{\sigma\downarrow}}$ $g_{k\sigma
L}^{(<,a)}(t_1,t)$, with the lesser Green function $g^<_{k\sigma
L}(t_1,t)=i\langle \widetilde{c}_{k\sigma L}^\dagger (t) \widetilde{c}%
_{k\sigma L}(t_1)\rangle$, and the advanced one $g_{k\sigma
L}^a(t_1,t)=i \theta(t-t_1) \langle \{\widetilde{c}_{k\sigma L}(t_1),
\widetilde{c}_{k\sigma L}^\dagger (t)\}\rangle$, here the curly
brackets denote an anticommutator.

In the steady state regime the Fourier transforms of the Green
functions result in single frequency Green functions. Since this
is the regime of interest here, we state for later use the Fourier
transform of the leads Green functions,
\begin{eqnarray}
g_{k\sigma \eta}^{a}(\epsilon)&=&g_{k \sigma \eta}^{r^*}(\epsilon)=\frac{1}{\epsilon-\epsilon_{k\sigma \eta}- i\delta},\\
g_{k\sigma \eta}^<(\epsilon)&=&2\pi i n_\eta(\epsilon)\delta(\epsilon-\epsilon_{k\sigma \eta}),
\end{eqnarray}
where $n_\eta$ is the Fermi distribution function of lead $\eta$.

\subsection{Average current in the stationary regime}

In a stationary regime all of the Green functions depend on only
$t-t_{1}$, yielding the Fourier transform
\begin{eqnarray}
I_{L}&=&2e\mathrm{Re}\int \frac{d\epsilon }{2\pi }\sum_{ij}\{G_{ij}^{r}(\epsilon
)\Sigma _{ji}^{L<}(\epsilon )+G_{ij}^{<}(\epsilon )\Sigma _{ji}^{La}(\epsilon)\},\nonumber\\
&=&ie\int \frac{d\epsilon }{2\pi }\mathrm{Tr}\{\mathbf{\Gamma }^{L}[(\mathbf{G}^{r}-\mathbf{G}^{a})n_{L}+\mathbf{G}^{<}]\},
\label{ILwrearranged}
\end{eqnarray}
with
\begin{equation}
\mathbf{\Gamma }^{L}=\frac{1}{2}\left(
\begin{array}{cc}
\Gamma _{\uparrow }^{L}+\Gamma _{\downarrow }^{L} & \Gamma
_{\uparrow
}^{L}-\Gamma _{\downarrow }^{L} \\
\Gamma _{\uparrow }^{L}-\Gamma _{\downarrow }^{L} & \Gamma
_{\uparrow
}^{L}+\Gamma _{\downarrow }^{L}%
\end{array}%
\right) ,  \label{GammaL}
\end{equation}%
where $\Gamma_{\sigma}^{L}=2\pi \sum_{k}|t_{k\sigma }|^{2}\delta
(\epsilon -\epsilon _{k\sigma L})$ is the linewidth function. In what follows we neglect the energy-dependence
of $\Gamma_\sigma^\eta$ (wideband limit), which will be taken as a constant phenomenological parameter.

\subsection{Spin-resolved currents}

From Eqs. (\ref{ILwrearranged}) and (\ref{GammaL}) we can also
determine the spin-resolved components of the average current
\begin{eqnarray}\label{ILs}
I_{L}^{\sigma} &=&ie\int \frac{d\epsilon }{2\pi }\mathrm{Tr}\{\frac{%
\Gamma _{\sigma}^{L}}{2}\left(
\begin{array}{cc}
1 & (-1)^{\delta _{\sigma \downarrow }} \\
(-1)^{\delta _{\sigma \downarrow }} & 1%
\end{array}
\right)  \nonumber \\
&\times &[n_{L}(\mathbf{G}^{r}-\mathbf{G}^{a})+\mathbf{G}^{<}]\}.
\end{eqnarray}
A similar result holds for $I_R^\sigma$. Equation (\ref{ILs}) gives the spin-polarized current components
with their polarization axes defined along the magnetic moment of the leads. In the present study no spin-torque
is considered, which makes the projected current the relevant quantity to investigate. In the presence of spin-torque more general
definitions for spin-resolved charge currents and spin-currents should be used. A general expression for the spin-current in the presence of
spin transfer was recently derived in Ref. [\onlinecite{mb05_2}].

\subsection{Noise definition}

Fluctuations of the current are interesting because they can give additional information about the
system beyond that provided by the average current
alone.\cite{ymb00} Here we derive an expression
for the current fluctuations, which include both thermal and shot
noise. The \textit{thermal noise} is related to fluctuations in
the occupations of the leads due to thermal excitation, and it vanishes at zero temperature.
\textit{Shot noise} is an unavoidable temporal fluctuation
of the current due to the granularity of the electron charge. It
is nonzero only for finite bias, i.e., it is a nonequilibrium
property. In the linear response regime the
fluctuation-dissipation theorem holds, yielding the relation
$S(\omega)=4k_B T G(\omega)$, where $G(\omega)$ is the
conductance.\cite{ymb00} Hence, in equilibrium the noise contains the same
information as the conductance. Away from equilibrium this
relation is no longer valid and the noise spectrum can provide
additional information.

We define noise via $S_{\eta\eta^{\prime}}=\langle \{\delta
\widehat{I}_\eta(t),\delta
\widehat{I}_{\eta^{\prime}}(t^{\prime})\}\rangle$, where $ \delta
\widehat{I}_\eta (t)=\widehat{I}_{\eta}(t)-I_{\eta}$ is the current
fluctuation at a time $t$ in lead $\eta$. Equivalently,
\begin{equation}  \label{Sdefinition}
S_{\eta\eta^{\prime}}(t,t^{\prime})=\langle \{\hat{I}_\eta(t),\hat{I}%
_{\eta^{\prime}}(t^{\prime})\}\rangle-2I_\eta^2,
\end{equation}
where we use the fact that $I_{\eta}=\langle \widehat{I}_\eta
(t)\rangle=\langle \widehat{I}_{\eta^{\prime}}(t^{\prime})\rangle$
in the stationary regime. Using the current operator
$\widehat{I}_\eta$ [Eq. (\ref{curroper})] and Eq. (\ref{canonical}) in Eq. (\ref{Sdefinition}), we obtain
\begin{eqnarray}  \label{Setaeta'operators}
S_{\eta\eta^{\prime}}(t,t^{\prime})&=&(ie)^2\sum_{kk^{\prime}\sigma\sigma^{%
\prime}ij} \frac{1}{2} (-1)^{i\delta_{\sigma\downarrow}}(-1)^{j\delta_{%
\sigma^{\prime}\downarrow}}  \nonumber \\
&&\{ t_{k\sigma} t_{k^{\prime}\sigma^{\prime}}\langle
c_{k\sigma\eta}^\dagger(t)
d_i(t)c_{k^{\prime}\sigma^{\prime}\eta^{\prime}}^\dagger(t^{\prime})
d_j(t^{\prime})\rangle  \nonumber \\
&& -t_{k\sigma} t_{k^{\prime}\sigma^{\prime}}^* \langle
c_{k\sigma\eta}^\dagger(t) d_i(t) d_j^\dagger(t^{\prime})
c_{k^{\prime}\sigma^{\prime}\eta^{\prime}}(t^{\prime})\rangle  \nonumber \\
&& - t_{k\sigma}^* t_{k^{\prime}\sigma^{\prime}} \langle
d_i^\dagger(t) c_{k\sigma\eta}(t)
c_{k^{\prime}\sigma^{\prime}\eta^{\prime}}^\dagger(t^{\prime})d_j(t^{%
\prime})\rangle  \nonumber \\
&& + t_{k\sigma}^* t_{k^{\prime}\sigma^{\prime}}^*\langle
d_i^\dagger(t) c_{k\sigma\eta}(t) d_j^\dagger(t^{\prime})
c_{k^{\prime}\sigma^{\prime}\eta^{\prime}}(t^{\prime})\rangle\}  \nonumber \\
&&+h.c.-2I_\eta^2.
\end{eqnarray}

\subsection{Noise in terms of Green functions}

Each $\langle ... \rangle$ term in (\ref{Setaeta'operators}) can
be expressed in terms of a Green function. Defining the two particle Green functions,
\begin{eqnarray}
g^{(2)}_1(\tau,\tau^{\prime})&=&i^2 \langle T_c
c_{k\sigma\eta}^{\dagger}(\tau)d_i(\tau)c_{k^{\prime}\sigma^{\prime}\eta^{
\prime}}^{\dagger}(\tau^{\prime})d_j(\tau^{\prime})\rangle  \nonumber \\
g^{(2)}_2(\tau,\tau^{\prime})&=&i^2 \langle T_c
c_{k\sigma\eta}^{\dagger}(\tau)d_i(\tau)d_j^\dagger(\tau^{\prime})c_{k^{
\prime}\sigma^{\prime}\eta^{\prime}}(\tau^{\prime})\rangle  \nonumber \\
g^{(2)}_3(\tau,\tau^{\prime})&=&i^2 \langle T_c
d_i^\dagger(\tau)c_{k\sigma\eta}(\tau)
c_{k^{\prime}\sigma^{\prime}\eta^{\prime}}^{\dagger}(\tau^{\prime})d_j(
\tau^{\prime}) \rangle  \nonumber \\
g^{(2)}_4(\tau,\tau^{\prime})&=&i^2\langle T_c
d_i^\dagger(\tau)c_{k\sigma\eta}(\tau)d_j^\dagger(\tau^{\prime})c_{k^{
\prime}\sigma^{\prime}\eta^{\prime}}(\tau^{\prime})\rangle,
\nonumber
\end{eqnarray}
we can write (\ref{Setaeta'operators}) as
\begin{eqnarray}  \label{Setaeta'middle}
S_{\eta\eta^{\prime}}(t,t^{\prime})&=&
e^2\sum_{kk^{\prime}\sigma\sigma^{\prime}i j} \frac{1}{2}
(-1)^{i\delta_{
\sigma\downarrow}}(-1)^{j\delta_{\sigma^{\prime}\downarrow}}  \nonumber \\
&&\{ t_{k\sigma}
t_{k^{\prime}\sigma^{\prime}}g^{(2)>}_1(t,t^{\prime})
\nonumber \\
&& -t_{k\sigma} t_{k^{\prime}\sigma^{\prime}}^*
g^{(2)>}_2(t,t^{\prime})
\nonumber \\
&& - t_{k\sigma}^* t_{k^{\prime}\sigma^{\prime}}
g^{(2)>}_3(t,t^{\prime})
\nonumber \\
&& + t_{k\sigma}^* t_{k^{\prime}\sigma^{\prime}}^*
g^{(2)>}_4(t,t^{\prime})\}
\nonumber \\
&&+h.c.-2I_\eta^2,
\end{eqnarray}
where $g_{i}^{(2)>} (t,t^{\prime})$ is obtained from the complex time
Green function $g^{(2)}_i (\tau,\tau^{\prime})$ via analytical
continuation. Similarly to the current calculation where we
develop an \textit{S}-matrix
expansions in $G_{\sigma k\sigma L}(\tau,\tau^{\prime})$ to obtain $%
G^<_{\sigma k\sigma L}(t,t^{\prime})$, here we expand the $S$-matrix in $%
g^{(2)}_i (\tau,\tau^{\prime})$ and then obtain $g^{(2)>}_i
(t,t^{\prime})$. This procedure follows the standard calculations proposed in Ref. [\onlinecite{apj94}] to derive the
current equation. The details of this \textit{S}-matrix expansion
are presented in Appendix B; here we simply state the results,
\begin{eqnarray}\label{g1}
&&g^{(2)}_1(\tau,\tau^{\prime})=\frac{1}{2}\sum_{i_1,i_2=1,2}(-1)^{i_1
\delta_{\sigma\downarrow}} (-1)^{i_2
\delta_{\sigma^{\prime}\downarrow}}
\nonumber \\
&& \times t_{k\sigma}^*t_{k^{\prime}\sigma^{\prime}}^* \int \int
d\tau_1 d\tau_2 g_{k\sigma\eta}(\tau_1,\tau)
g_{k^{\prime}\sigma^{\prime}\eta^{\prime}}(\tau_2,\tau^{\prime})
\nonumber
\\
&& \{G_{i i_1}(\tau,\tau_1)G_{j i_2}(\tau^{\prime},\tau_2)-G_{i
i_2}(\tau,\tau_2)G_{j i_1}(\tau^{\prime},\tau_1)\},\nonumber \\
&&
\end{eqnarray}
and
\begin{eqnarray}  \label{g2}
&&g^{(2)}_2(\tau,\tau^{\prime})=-\delta_{k\sigma\eta,k^{\prime}\sigma^{%
\prime}\eta^{\prime}}g_{k\sigma\eta}(\tau^{\prime},\tau)G_{ij}(\tau,\tau^{%
\prime})  \nonumber \\ && \phantom{xxx} + \frac{1}{2}\sum_{i_1,i_2=1,2}(-1)^{i_1
\delta_{\sigma\downarrow}} (-1)^{i_2
\delta_{\sigma^{\prime}\downarrow}}
\nonumber \\
&&  \times t_{k\sigma}^* t_{k^{\prime}\sigma^{\prime}}\int \int d\tau_1
d\tau_2 g_{k\sigma\eta}(\tau_1,\tau)
g_{k^{\prime}\sigma^{\prime}\eta^{\prime}}(\tau^{\prime},\tau_2)
\nonumber
\\
&&\{G_{i i_1}(\tau,\tau_1)G_{i_1 j}(\tau_2,
\tau^{\prime})-G_{i j}(\tau,\tau^{\prime})G_{i_2 i_1}(\tau_2,\tau_1)\}.  \nonumber \\
&&
\end{eqnarray}
Equations (\ref{g1}) and (\ref{g2}) hold on a Hartree-Fock or other mean-field theory (see details in Appendix B). The other two Green functions $g_3^{(2)}$ and
$g_4^{(2)}$ are given by
\begin{equation}  \label{g3}
g^{(2)}_3(\tau,\tau^{\prime})=g^{(2)^*}_2(\tau,\tau^{\prime}),
\end{equation}
and
\begin{equation}  \label{g4}
g^{(2)}_4(\tau,\tau^{\prime})=g^{(2)^*}_1(\tau,\tau^{\prime}).
\end{equation}
From a diagrammatic point of view the terms in Eqs. (\ref{g1}) and (\ref%
{g2}) involving
\begin{equation}
G_{i i_1}(\tau,\tau_1) g_{k\sigma\eta}(\tau_1,\tau) G_{j
i_2}(\tau^{\prime},\tau_2)g_{k^{\prime}\sigma^{\prime}\eta^{\prime}}(\tau_2,\tau^{\prime}),
\end{equation}
and
\begin{equation}
G_{\sigma\sigma}(\tau,\tau_1)g_{k\sigma\eta}(\tau_1,\tau) g_{k^{\prime}\sigma^{\prime}\eta^{\prime}}(\tau^{\prime},\tau_2)G_{\sigma^{\prime}\sigma^{\prime}}(\tau_2,%
\tau^{\prime})
\end{equation}
are disconnected. These disconnected terms, together with similar
ones in the equations for $g^{(2)}_3(\tau,\tau^{\prime})$ and $g^{(2)}_4(\tau,\tau^{\prime})$, cancel identically the term
$2I_{\eta}^2$ in Eq. (\ref{Setaeta'middle}) (see Appendix C). So we can say that this corresponds to the linked cluster expansion to the noise.
The other terms in Eqs. (\ref{g1})-(\ref{g2}) give the connected diagrams and thus can give a
contribution to the noise. Substituting the connected terms of
Eqs.(\ref{g1})--(\ref{g4}) in Eq.(\ref{Setaeta'middle}) we find
\begin{eqnarray}  \label{Sttau}
&&S_{\eta\eta^{\prime}}(t,t^{\prime})=e^2\sum_{k\sigma}|t_{k\sigma}|^2\{%
\delta_{\eta,\eta^{\prime}} \sum_{ij}
(-1)^{(i+j)\delta_{\sigma\downarrow}}
\nonumber \\
&&\times[g_{k\sigma\eta}^>(t,t^{\prime})G_{ji}^<(t^{%
\prime},t)+G_{ij}^>(t,t^{\prime})g_{k\sigma\eta}^<(t^{\prime},t)]
\nonumber
\\
&&
-e^2\sum_{kk^{\prime}\sigma\sigma^{\prime}}|t_{k\sigma}|^2|t_{k^{\prime}%
\sigma^{\prime}}|^2\int_c \int_c d\tau_1 d\tau_2  \nonumber \\
&& \times \frac{1}{4} \sum_{i,j,i_1,i_2=1,2}
(-1)^{(i+i_1)\delta_{\sigma\downarrow}}
(-1)^{(j+i_2)\delta_{\sigma^{\prime}\downarrow}}  \nonumber \\
&& \times\{
G_{ii_2}(t,\tau_2)g_{k^{\prime}\sigma^{\prime}\eta^{\prime}}(\tau_2,t^{%
\prime})G_{ji_1}(t^{\prime},\tau_1)g_{k\sigma\eta}(\tau_1,t)  \nonumber \\
&&
-G_{ij}(t,t^{\prime})g_{k^{\prime}\sigma^{\prime}\eta^{\prime}}(t^{\prime},%
\tau_2)G_{i_2i_1}(\tau_2,\tau_1)g_{k\sigma\eta}(\tau_1,t)  \nonumber \\
&&
-g_{k\sigma\eta}(t,\tau_1)G_{i_1i_2}(\tau_1,\tau_2)g_{k^{\prime}\sigma^{%
\prime}\eta^{\prime}}(\tau_2,t^{\prime})G_{ji}(t^{\prime},t)  \nonumber \\
&&
+g_{k\sigma\eta}(t,\tau_1)G_{i_1j}(\tau_1,t^{\prime})g_{k^{\prime}\sigma^{%
\prime}\eta^{\prime}}(t^{\prime},t_2)G_{i_2i}(\tau_2,t)\}^{t>t^{\prime}}
\nonumber \\
&& \phantom{xxxxxxxxxxxxxxxxxxxxxxxxxx}+h.c.,
\end{eqnarray}
where the superscript $t>t^{\prime}$ means that
an analytical continuation should be performed by applying Langreth's rules.

\subsection{Zero-frequency shot noise}

The shot noise is defined as the Fourier transform of $S_{\eta\eta^{\prime}}(t-t^{\prime})$, which
in the stationary regime reads
\begin{equation}\label{noiseDefin}
S_{\eta\eta^{\prime}}(\omega)=\int_{-\infty}^{\infty}
d(t-t^{\prime})
e^{i\omega(t-t^{\prime})}S_{\eta\eta^{\prime}}(t-t^{\prime}).
\end{equation}
Using the analytical continuation of Eq. (\ref{Sttau}) into Eq.
(\ref{noiseDefin}) we find the following zero-frequency shot
noise,\cite{jxz03}
\begin{eqnarray} \label{SLL}
&&S_{LL}(\omega=0)=\frac{e^2}{\pi}\int d\epsilon \mathrm{Tr} \{i n_L\mathbf{%
\Gamma}^L\mathbf{G}^>  \nonumber \\
&-&i(1-n_L)\mathbf{\Gamma}^L \mathbf{G}^<+\mathbf{\Gamma}^L \mathbf{G}^>\mathbf{\Gamma}^L%
\mathbf{G}^< \nonumber \\
&+& \mathbf{\Gamma}^L (\mathbf{G}^r-\mathbf{G}^a)\mathbf{\Gamma}^L (n_L\mathbf{G}^>-(1-n_L)%
\mathbf{G}^<) \nonumber \\
&-&n_L(1-n_L)(\mathbf{G}^a\mathbf{\Gamma}^L\mathbf{G}^a\mathbf{\Gamma}^L+%
\mathbf{G}^r\mathbf{\Gamma}^L\mathbf{G}^r\mathbf{\Gamma}^L) \},
\end{eqnarray}
where $\mathbf{G}^>$ satisfies the identity $\mathbf{G}^>-\mathbf{G}^<=%
\mathbf{G}^r-\mathbf{G}^a$. All the Green functions in Eq.
(\ref{SLL}) are in the frequency domain. In our analysis we take
only the component $\eta=\eta'=L$. Since the $dc$ noise is
position independent, we have simply
$S_{LL}(0)=S_{RR}(0)=-S_{LR}(0)=-S_{RL}(0)$. Equation (\ref{SLL}) can be expressed in a standard form
as follow\cite{lesovik,mb90} (Appendix D),
\begin{eqnarray} \label{SLL_buttiker}
&&S_{LL}(\omega=0)=\frac{e^2}{\pi}\int d\epsilon
\nonumber\\&&\phantom{xxxx} \times \mathrm{Tr} \{
[n_L(1-n_L)+n_R(1-n_R)] \mathbf{T}(\epsilon)
\nonumber\\&&\phantom{xxxxxxxxx}+ (n_L-n_R)^2 \mathbf{T}(\epsilon)
[1-\mathbf{T}(\epsilon)] \},
\end{eqnarray}
with the transmission matrix $\mathbf{T}=\mathbf{\Gamma}^L\mathbf{G}^r\mathbf{\Gamma}^R
\mathbf{G}^a$. In the calculation leading to Eqs. (\ref{SLL}) or (\ref{SLL_buttiker}) we have truncated an S-matrix
expansion by breaking two-particle Green function into products of one-particle Green functions. This procedure holds
in a mean field theory. Thus for a consistent application of Eqs. (\ref{SLL})-(\ref{SLL_buttiker}) a similar
approximation (Hartree-Fock like) for the Green functions should be made (see Appendix A).
Some limitations imposed by this approximation are discussed in the end of Sec. \ref{results}.\cite{diagram}

\subsection{Model for the FM leads}

The ferromagnetism of the leads is considered via the spin-dependent parameter $\Gamma_\sigma^\eta$.
From the Stoner model, for instance, we can see that the density of states for spin up electrons of the lead is shifted with respect to that of
the spin down electrons. Since $\Gamma_\sigma^\eta$ contains information about the
spin-dependent density of states it is expected that $\Gamma_\uparrow^\eta \neq \Gamma_\downarrow^\eta$.\cite{fms04} Following
Ref. [\onlinecite{wr01}] we define $\Gamma_\sigma^L=\Gamma_0[1+(-1)^{\delta_{\sigma \downarrow}} p_L]$. The parameter $\Gamma_0$ gives
the strength of the lead-to-dot coupling and $p_L$ is a parameter
describing the degree of spin polarization of the left lead.\cite{expvalues} Note that $%
\Gamma_\uparrow^L > \Gamma_\downarrow^L$ for $p_L \neq 0$. This
means that the population for spin up around the Fermi energy in the
left lead is greater than the population for spin down. Similarly,
for the right ferromagnetic lead we assume $\Gamma_\sigma^R=\Gamma_0 [1 +
(-1)^{\delta_{\sigma \downarrow}} p_R]$ for the parallel (P) and $\Gamma_\sigma^R=\Gamma_0 [1 - (-1)^{\delta_{\sigma \downarrow}} p_R]$ for the antiparallel (AP) lead alignments. Note that for the P case we have $\Gamma_\sigma^L=\Gamma_\sigma^R$ and for the AP
configuration $\Gamma_\sigma^L=\Gamma_{\overline{\sigma}}^R$, with
$\overline{\sigma}$ being the opposite of $\sigma$. In the present work we mostly discuss the $p_L \neq p_R$ case, i.e.,
a geometry in which the left and right leads are composed of different
materials (Ni and Co, for instance).

\subsection{Numerical procedure}

The numerical results are obtained following a self-consistent procedure. We calculate the average
\begin{equation}
 \langle \hat{n}_{ij} \rangle = \langle d_i^\dagger d_j \rangle = \int \frac{d\epsilon}{2\pi i} G_{j i}^<(\epsilon),
\end{equation}
self-consistently with Eqs. (\ref{A9})-(\ref{A15}). When converged solutions for the expectation values $\langle d_i^\dagger d_j \rangle$
and dot Green functions are found, we determine the current [Eq. (\ref{ILs})] and the noise [Eq. (\ref{SLL})]. This iterative schema is performed for each bias voltage.

\section{RESULTS}\label{results}

\subsection{Spin resolved electronic occupations}

\emph{Occupations}. Figures \ref{fig2}(a)-(b) show the spin up and
spin down occupations of the dot for both parallel (P) and
antiparallel (AP) alignments. In the P case the dot has a net
spin-down polarization with $n_{\uparrow }<n_{\downarrow }$, while
in the AP configuration $n_{\uparrow }>n_{\downarrow }$. These
spin imbalances in the dot can be easily understood in terms of
the tunneling rates $\Gamma _{\sigma}^{\eta }$ adopted. The parameters
$p_L=0.23$ and $p_R=0.35$ used here\cite{parameters} yield the
following tunneling rates in the parallel case: $\Gamma _{\uparrow
}^{L}=12.3$ $\mu $eV, $\Gamma _{\downarrow }^{L}=7.7$ $\mu $eV,
$\Gamma
_{\uparrow }^{R}=13.5$ $\mu $eV and $\Gamma _{\downarrow }^{R}=6.5$ $\mu $%
eV. In the AP case the values of the tunneling rates to the right
lead are swapped ($\Gamma _{\uparrow }^{R}\rightleftarrows \Gamma
_{\downarrow }^{R}$). From these rates we conclude that in the P
case a spin up electron leaves the dot faster than it comes in.
The opposite happens for a spin down electron. The imbalance of
these in/out tunneling rates results in a larger spin down
occupation in the parallel case, i.e., $n_{\uparrow
}<n_{\downarrow }$, Fig. \ref{fig2}(a). By the same token, in the
AP alignment we have $n_{\uparrow }>n_{\downarrow }$ as seen in
Fig. \ref{fig2}(b).

\begin{figure}[tbp]
\begin{center}
\epsfig{file=fig2.eps, width=0.45\textwidth}
\end{center}
\caption{Spin-resolved occupations $n_\uparrow$ and $n_\downarrow$
and the spin accumulation, $m=n_\uparrow - n_\downarrow$, against
bias voltage in both parallel and antiparallel FM lead alignments.
In the P case $n_\uparrow < n_\downarrow$ while in the AP
alignment $n_\uparrow > n_\downarrow$. These imbalances give rise
to spin-dependent population suppressions in the bias range 1-3
meV. This translates into a tunable $m$ with the bias voltage. Parameters:
$p_L=0.23$, $p_R=0.35$, $k_B T=200$ $\mu$eV, $\Gamma_0=10$ $\mu$eV,
$\epsilon_0=0.5$ meV and $U=1$ meV.}\label{fig2}
\end{figure}

\emph{Spin accumulation}. In Fig. \ref{fig2}(c)-(d) we show the
spin accumulation ($m=n_\uparrow - n_\downarrow$) as a function of
the bias voltage. In the zero bias limit $m$ is essentially zero.
When the bias increases the spin accumulation in the P case assume
negative values. In contrast, in the AP alignment $m$ is enhanced. In
particular, in the bias range corresponding to a singly-occupied dot
(1-3 meV)\cite{singleocup} the additional suppression [Fig.
\ref{fig2}(c)] or the enhancement [Fig. \ref{fig2}(d)] of $m$ is
due to the {\it spin-dependent population suppression} that takes
place in the presence of Coulomb interaction and spin
accumulation. More specifically, in the AP case due to Coulomb
interaction $n_{\uparrow }$ tends to suppress more strongly
$n_{\downarrow }$ than otherwise. This translates into an enhancement
of $m$. In the P alignment the spin up occupation $n_\uparrow$ is
more suppressed than $n_\downarrow$, thus $m$ becomes more
negative [Fig. \ref{fig2}(c)]. We emphasize that this effect
happens for both the P and AP alignments because we assume $p_L
\neq p_R$. For equal leads we find $n_\uparrow = n_\downarrow$ in
the P case so that $m$ remains zero in this configuration.

\subsection{Current and its polarization}

\emph{Current}. Figures \ref{fig3}(a)-(b) show the current in the
P and AP cases for $U=1$ meV and $R=0$. Similarly to the
occupations, some features of the spin-up and spin down currents
can be understood in terms of the tunneling rates. For instance,
their saturation values (second plateau) can be easily calculated
from the standard expresssion\cite{standardeq}
\begin{equation}
I^{\sigma}_\eta=e\frac{\Gamma _{\sigma}^{L}\Gamma _{\sigma}^{R}}{%
\Gamma _{\sigma}^{L}+\Gamma _{\sigma}^{R}},  \label{Issimple}
\end{equation}%
which gives $I^{\uparrow }_\eta>I^{\downarrow}_\eta$ and $I^{\uparrow
}_\eta<I^{\downarrow}_\eta$ in the P and AP cases, respectively. For the
first plateau Eq. (\ref{Issimple}) is not valid and these
inequalities can change.\cite{at03}

In the P case [Fig. \ref{fig3}(c)] $I_\uparrow$ is more strongly suppressed than
$I_\downarrow$ due to the interplay of spin accumulation ($n_{\uparrow} < n_{\downarrow
}$) and Coulomb interaction. This results in a supression of the current polarization [$\wp =(I_{\uparrow
}-I_{\downarrow })/(I_{\uparrow }+I_{\downarrow})$] in the range 1-3 meV. On the other hand,
in the AP case [Fig. \ref{fig3}(d)] $I^\downarrow_\eta$ is more suppressed than $I^\uparrow_\eta$ due to
the inverted inequality $n_{\uparrow} > n_{\downarrow}$, thus resulting in an enhancement of $\wp$.

\begin{figure}[tbp]
\par
\begin{center}
\epsfig{file=fig3.eps, width=0.45\textwidth}
\end{center}
\caption{(a)-(b) Spin-resolved currents $I_\uparrow$ and
$I_\downarrow$ and (c)-(d) current polarization for both parallel
and antiparallel alignments. In the P case we find $I_\uparrow
> I_\downarrow$. In contrast, for AP alignment $I_\uparrow < I_\downarrow$ in the bias window $1-3$
meV (singly occupied regime) and $I_\uparrow > I_\downarrow$ when
the bias exceeds the charging energy above $3$ meV (doubly occupied
regime). Panels (c)-(d) reveal a suppression and an enhancement of
the current polarization in the singly occupied regime for the P
and AP cases, respectively. Parameters: $p_L=0.23$, $p_R=0.35$,
$k_B T=200$ $\mu$eV, $\Gamma_0=10$ $\mu$eV, $R=0$, $\epsilon_0=0.5$ meV and
$U=1$ meV.}\label{fig3}
\end{figure}

\emph{Spin-flip effects}. In figure (\ref{fig4}) we show the
current polarization against bias voltage for distinct spin-flip parameter $R$. The polarization is calculated for the left and right
leads, according to the formula
$\wp^\eta=(I^\uparrow_\eta-I^\downarrow_\eta)/(I^\uparrow_\eta+I^\downarrow_\eta)$,
where $\eta=L,R$. For $R=0$ (solid line) we have $\wp^L=\wp^R$ for
all biases. This curve is the same as seen in Fig. \ref{fig3}(d).
When $R \neq 0$ these two polarizations depart from each
other. The $\wp^L$ increases with $R$ tending to reach the left
lead polarization value $p_L=0.23$. In contrast, $\wp^R$ assume
negative values tending to $-p_R$ as $R$ increases. This shows that even though we have a constant total current along
the system ($I_L^\uparrow+I_L^\downarrow=I_R^\uparrow+I_R^\downarrow$), its
polarization can change across the system when $R \neq 0$, i.e., when there is  a transverse magnetic field applied on
the dot which coherently rotates the spin.

\begin{figure}[tbp]
\par
\begin{center}
\epsfig{file=fig4.eps, width=0.45\textwidth}
\end{center}
\caption{Current polarization against the bias voltage for differing
spin-flip rates in the AP alignment and in both left and right leads. For
$R=0$ the polarization is the same on both sides. When $R \neq 0$, though, the current polarization in the left side enhances,
tending to the left magnetization degree $p_L$.
In contrast, the current polarization in the right side assumes negative values, tending to
$-p_R$. Parameters: $p_L=0.23$, $p_R=0.35$, $k_B
T=200$ $\mu$eV, $\Gamma_0=10$ $\mu$eV, $\epsilon_0=0.5$ meV and U=1
meV.}\label{fig4}
\end{figure}

Figure \ref{fig5} shows $I_\eta^\sigma$ against $R$. For $R=0$,
$I^\uparrow_L=I^\uparrow_R$ and $I_L^\downarrow=I_R^\downarrow$ as
expected. For $R \neq 0$ these equalities disappear, with
$I_L^\uparrow$ and $I_R^\downarrow$ increasing and
$I_L^\downarrow$ and $I_R^\uparrow$ decreasing with $R$. This
leads to an enhancement of $\wp^L$ and $|\wp_R|$ as seen in Fig.
\ref{fig4}. Interestingly, there is a crossing point between
$I_L^\uparrow$ and $I_L^\downarrow$ around $R \approx \Gamma_0/4$. So
for this particular $R$ the total current becomes unpolarized in
the emitter (left) lead and relatively high polarized in the
collector (right) lead. This means that it is possible to change
the current polarization from emitter to collector lead by precessing
the electron spin in the quantum dot.

In the inset of Fig. \ref{fig5} we show the total current against $R$.
This curve resembles a typical Hanle resonance.\cite{hanle,mb05}
Similarly to Ref. [\onlinecite{mb05}], here we can say that in the AP configuration and positive bias (i.e., with left being the emitter)
the dot tends to be more up populated due to the majority up population in the emitter and the majority down population in the collector lead.
On average a transverse magnetic field tends to increase the spin down component in the dot along the down magnetization
of the collector lead. As a result the electron can more easily tunnel into the right ferromagnet and the current increases.

\begin{figure}[tbp]
\par
\begin{center}
\epsfig{file=fig5.eps, width=0.45\textwidth}
\end{center}
\caption{Spin-resolved currents versus $R$. For $R=0$
we have $I_L^\uparrow=I_R^\uparrow$ and
$I_L^\downarrow=I_R^\downarrow$ with $I_\eta^\uparrow$ and
$I_\eta^\downarrow$ being different from each other. For
increasing $R$, $I_L^\uparrow$ and $I_R^\downarrow$ grow while
$I_L^\downarrow$ and $I_R^\uparrow$ decreases. For a particular
$R$ there is a crossing between $I_L^\uparrow$ and
$I_L^\downarrow$, thus resulting simultaneously in a non-polarized
left-current and a polarized right-current. Parameters:
$p_L=0.23$, $p_R=0.35$, $k_B T=200$ $\mu$eV, $\Gamma_0=10$ $\mu$eV,
$\epsilon_0=0.5$ meV, U=1 meV and bias=4 meV.}\label{fig5}
\end{figure}

\subsection{Shot Noise}

Figure \ref{fig6} shows the Fano factor, $\gamma=S_{LL}/2eI_L$,
against $R$ in the AP configurations. The P alignment gives approximately
insensitive Fano factor with respect to $R$. In the AP
configuration, the Fano factor can be suppressed with $R$,
reaching values below 0.5. This suppression can be further
intensified by increasing the lead polarization parameters $p_L$
and $p_R$. In particular, for fully spin-polarized leads ($p=1$) AP aligned,
the Fano factor reaches values close to 0.3 when double occupancy is allowed (bias = 6 meV) and it attains
0.35 in the single occupancy regime (bias = 2 meV).\cite{fgb02} For fully polarized leads in the P configuration
the Fano factor remains at 0.5 independently of $R$.

A simple physical picture for this additional suppression of $\gamma$ is as follows. Consider an up spin sitting on the dot. A second up spin trying to hop onto it is Pauli blocked, till the first electron tunnel to the collector lead or undergo a coherent spin-flip. If the spin-flip is fast enough (faster than the into/out tunneling processes) the first electron can return to its original state (via another spin-flip), instead of tunneling out of the dot. This blocks additionally the second up spin, consequently suppressing even further the noise.

We note that for any $R$ when we go from the single (bias = 2 meV) to the double (bias = 6 meV) occupation regimes a reduction of the Fano factor is observed in both P and AP alignments (cf. solid black to solid gray lines and dashed black to dashed gray lines). This general feature was already predicted in Ref. [\onlinecite{mb06}], where a diagrammatic formulation for the noise is derived. It is valid to mention that in the present study we have performed an S-matrix expansion (Appendix B) to the noise which could in principle be mapped into a Feynman diagrammatic formulation. Comparing our results with previous findings in the literature we observe a difference between them in the single-occupancy regime.\cite{singleocup} Figure \ref{fig7} shows a comparison for the shot noise obtained from Eq. (\ref{SLL}) and from analytical results in Ref. [\onlinecite{at03}] (derived for $p_L=p_R=0$ and $R=0$). While the second plateau [II in Fig. (\ref{fig7})] coincides in both
numerical and analytical cases, the first plateaus (I in the plot) do not coincide.\cite{comparison}
This disagreement is related to the Hartree-Fock factorization underlying our calculation.

\begin{figure}[t]
\par
\begin{center}
\epsfig{file=fig6.eps, width=0.45\textwidth}
\end{center}
\caption{Fano factor against $R$ for two fixed bias voltages corresponding to single (bias = 2 meV)
and double occupancy (bias = 6 meV) in both P and AP alignments. In the P case the Fano factor is
approximatelly constante. In contrast, in the AP alignment the Fano factor can be suppressed
due to spin-flip, reaching values below 0.5. In particular, for fully polarized leads ($p_L=p_R=1$) the
Fano factor can be strongly suppressed, assuming values close to 0.3 when double occupancy is allowed. Parameters: $\epsilon_0=0.5$ meV, $U=1$ meV, $\Gamma_0=10$ $\mu$eV and $k_B T=200$
$\mu$eV.}\label{fig6}
\end{figure}

It is yet valid to note that without Coulomb interaction
($U=0$) and for fully spin polarized leads antiparallel aligned, the Fano factor is given by
\begin{equation}\label{fano_similar_mulburn}
\gamma=1-\frac{1}{2} \frac{\beta^2 (5+\beta^2)}{(1+\beta^2)^2},
\end{equation}
where $\beta=R/\Gamma_0$. Eq. (\ref{fano_similar_mulburn}) is also found for a three tunneling
barriers junction.\cite{hbs97} Hence, for fully spin-polarized AP
leads and non-vanishing spin-flip, the FM-QD-FM setup resembles a
three-barrier geometry.

\begin{figure}[h]
\par
\begin{center}
\epsfig{file=fig7.eps, width=0.45\textwidth}
\end{center}
\caption{Comparison of the shot noise for the present approach (numerical) and
the one derived in Ref. [\onlinecite{at03}] (analytical). While the second
plateau (II) coincides in both approaches, the first plateau (I) differs. We
attribute this contrast to the Hartree-Fock type approximation used in
our calculation. Parameters: $p_L=p_R=0$, $k_B T=50$ $\mu$eV,
$\Gamma_0=10$ $\mu$eV , $R=0$, $\epsilon_0=0.5$ meV and $U=1$
meV.}\label{fig7}
\end{figure}

\section{CONCLUSION}

Using the nonequilibrium Green-function technique we have studied
the transport properties of a quantum dot coupled to two
ferromagnetic leads. We consider both parallel (P) and
antiparallel (AP) alignments of the lead polarizations. Coulomb
interaction and coherent spin-flip are included in our model. We
find that for distinct ferromagnetic leads the interplay between
Coulomb interaction and spin accumulation translates into an
enhancement and a suppression of the current polarization $\wp$ in
AP and P cases, respectively, depending on the bias. We also
observe that the spin-flip can change the current polarization
when it flows from the emitter to the collector. It is even
possible to have a polarized current in the collector while it is
unpolarized in the emitter. We have derived an expression for
the noise [Eq. (\ref{SLL})] which exactly accounts for spin-flip but only approximately for Coulomb interaction.
Finally, we found a suppression of the Fano factor to values well below 1/2 due to spin-flip.

The authors acknowledge support for this work from the Brazilian agencies CNPq, CAPES, FAPESP and IBEM and
the FiDiPro program of the Finnish Academy. The authors thank J. K\"onig and J. Martinek for helpful discussions.

redpajama_set_name: RedPajamaArXiv


text:
Q: What is the difference between error handlers and the ErrorHandlerMiddleware in CakePHP? I know these questions aren't popular but I tried to ask on the CakePHP slack and got no response. I wanted to add the Crud CakePHP plugin to a project of mine. In order to handle errors the plugin may use a custom error handler:
//Crud ErrorHandler registration - simplified
(new ErrorHandler($exceptionRenderer))->register();

The error handler will however only be registered depending on the following check:
$appClass = Configure::read('App.namespace') . '\Application';

// If `App\Application` class exists it means Cake 3.3's PSR7 middleware
// implementation is used and it's too late to register new error handler.
if (!class_exists($appClass, false)) {
    $this->registerExceptionHandler();
}

When asked about the reasoning behind this check a Crud github repo member told me:

That's because middleware queue cannot be accessed from the ApiListener to setup the custom exception renderer. [...] You aren't supposed to register the error handler yourself. The error handler middleware handles that. You are bound to have problems by doing so.

Now I cannot quite figure out what the relationship between error handlers and the ErrorHandlerMiddleware is. In regards to the middleware the docs state the following:

Cake\Error\Middleware\ErrorHandlerMiddleware traps exceptions from the wrapped middleware and renders an error page using the Error & Exception Handling Exception handler

The first part of this description seems to imply that the ErrorHandlerMiddlewarecatches exceptions only from other middleware. From what I understand however the whole app is wrapped by them. The second part of the description states that the middleware uses an Exception handler to display errors. However looking through the source of the middleware I see no reference to an error handler, but an exception renderer which is something else. The only error handling done seems to be a simple try/catch statement which renders the exception using the renderer. This seems like a mistake in the docs to me as no handler instance is actually being used.
Lastly the middleware description above points to a doc page which states:

You can create an error handler out of any callback type. For example you could use a class called AppError to handle your errors. By extending the BaseErrorHandler you can supply custom logic for handling errors. An example would be:

// In config/bootstrap.php
use App\Error\AppError;
$errorHandler = new AppError();
$errorHandler->register();

But this gets me back to the start where the Crud github team member told me not to do this.
Questions:

*

*What is the relationship between ErrorHandlerMiddleware and a
custom error handler?

*What happens if I register multiple error handlers - do they override?

*What happens if my app uses the ErrorHandlerMiddleware but it also registers a custom error handler? Which catches what (for example exception in middleware vs exception in controller)?

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text:
Trecchina es una localidad italiana de la provincia de Potenza, región de Basilicata, con 2.413 habitantes.

En el 2009 esta ciudad fue una de las incluidas en el rodaje de la película Basilicata coast to coast. En ella se veía a una banda de músicos atravesar la región Basilicata desde Maratea hasta Scanzano Jonico. El film fue dirigido por Rocco Papaleo, quien además se desempeñó como actor junto a Alessandro Gassman, Max Gazzè y Giovanna Mezzogiorno.

Evolución demográfica

Referencias

Enlaces externos

Localidades de la provincia de Potenza

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