It was in 1987 that Ajahn Sucitto and I were stuck in a traffic jam on the M25. The Ajahn produced a tape recorder and interviewed me about the Hammer Woods at Chithurst. That interview appeared in the Forest Sangha Newsletter. I would now like to tell you a little about the work that has gone on since.
You may remember that the basis of the management plan was to change areas of non-native tree species to those that grew in the old English oak forests. This entailed getting rid of large areas of our commercial chestnut coppice and replanting.
All through the South, the old Woodland Management ways, which disappeared after the Second World War, are beginning to start up again.
We now have about sixty acres of chestnut remaining, which is just right for our needs. Apart from producing our firewood, it is an important industry in the local area. It provides work for a number of people, who make fence posts, tree stakes, bean poles and many other forest products.
I have been able to find local workers who are interested in the monastery, respect the woods and have a love of nature. These people are great to have around and very different from those who worked here when I first arrived. We even have a 'bodger' who makes besoms from the birch saplings that grow so vigorously and often swamp the trees that we plant.
We have plantations of non-native conifers, which consist of Japanese Larch, Douglas Fir, Western Hemlock and Spruce. This winter, a market has been found for such timber and many of these trees are being felled. The area of Japanese Larch has already been re-planted with native broad leaves, part of the over one thousand trees and shrubs that I alone will have planted this winter.
In the forestry world we are being told that a market is starting in Sussex for the products of hazel coppicing. Such a market has existed in Hampshire for the last few years and it is growing. We have an area of derelict hazel coppice and with the help of the local British Trust for Conservation Volunteers, I am getting this into working order once again.
All through the South, the old Woodland Management ways, which disappeared after the Second World War, are beginning to start up again. This is great for wildlife and the countryside.
We have various schemes to help wildlife, which I shall list at another time. Suffice to say now, that we have in general been successful and things are well in the Hammer Woods.
mother calls the children in.
a skyful of stars as dawn comes.
clattering softly on chestnut leaves.


text:
North Sydney Demonstration School (NSDS) is a primary school located in Waverton, New South Wales, Australia. It is one of only three demonstration schools in New South Wales.

Overview
Structured education levels provided at "North Sydney Dem" range from kindergarten to sixth grade. North Sydney Demonstration School is a school co-operating with the University of Sydney, in partnership the school and university foster and support the use of evidence based and innovative teaching practices to ensure a quality 21st century education for all. The school also actively participates in data collection for educational research projects and in the development of educational materials.
North Sydney Demonstration School is situated on the land which was owned by Lady Hay and Alexander Berry. Before the school was called North Sydney Public School, it was known as Greenwood's School.

References

Public primary schools in Sydney

redpajama_set_name: RedPajamaWikipedia


text:
Comics I Got in Brooklyn, part 5
I'm over the hump on these Brooklyn Comics and Graphics Festival reviews. If you've been reading all these, thanks! And for my usual readers who are looking for reviews of Houston area visual art, I haven't forgotten you! I'll have more reviews of art shows soon.
Noah Lyon, Retard Riot #24 cover, 2008
This is the smallest mini I got (4.5 x 2.5 inches, 16 pages). I picked it up because I liked the bleak hopeless cover. With a name like Retard Riot, one figures Noah Lyon is a punk cartoonist who values shock value highly. Think of Johnny Ryan, for example.
Noah Lyon, Retard Riot #24 pp. 8-9, 2008
He lacks Ryan's demented irony, though. This comic strikes me as unrelentingly dark, black humor with an extra helping of grim.
Jordan Crane, Smoke Signal #7 cover, December 2010
Smoke Signal is quarterly tabloid published by Desert Island Comics. (Here's a tangential Desert Island Comics story I heard last night, by the way. I was talking to a guy who used to live in that neighborhood. Now you may recall that Desert Island is located where a bakery used to be. They kept part of the old sign.
My friend used to go to that bakery frequently, but one day he was walking down that street--which is very busy--and saw that someone had been hit by a truck in front of it. It was the owner of the bakery. He recalled the horror of seeing her shoe in the road. I wonder how long after that did Desert Island take over the space? Did the bakery shut down because of her death? It seems like almost like a parable of gentrification. Old super-practical neighborhood business, owner dies, artsy hipster business takes its place.)
So anyway, Smoke Signal. It's a thick anthology where artists have one or two huge tabloid pages to work with. That said, lots of what is here are obviously just parts of longer stories, some which seem to be serialized in Smoke Signal, some I'm not sure of. So it can be a bit of a frustrating reading experience.
Tim Lane, detail from Belligerent Piano, 2010
One artist who used the large tabloid pages very effectively was Tim Lane. This image is just a small part of the page--the whole page has 37 tiny panels of unremitting psychological torture. At first, as I read it, I thought it was too much. OK, I get it--dude with the gun is a sadist and his victim is scared shitless. But the gunman's dialogue just keeps going, referencing Horishima and the Holocaust as examples of when guiltless people die. It's so intense that it ends up having a powerful cumulative effect. This effect is amplified by the constant change in perspective--looking up, looking down, looking up, looking down, etc.
Tim Hensley, Psycho & Vertigo, 2010
Tim Hensley does the back cover, a series of "Little Lulu"-like episodes from the life of Alfred Hitchcock. They're excellent little bits of minimalism. This approach is a surprisingly good way to paint a portrait of a real historical figure.
Sammy Harkham, Crickets #3 cover, 2010
Crickets #3 by Sammy Harkham was one of the big deals of the show. Apparently it was meant to be published by Drawn & Quarterly, but ended being self-published. Why? I don't exactly know. A review in Comics Comics mentions that in this issue, Harkham took a serious turn for a more literary style of comic making. Harkham is known as a splendid cartoonist but is perhaps best known for editing Kramers Ergot, which was really the most important "art comics" anthology. It really pushed forward the concept of non-literary comics. So Crickets #3 is kind of a dramatic switch.
It works, though. The first story, "The New Yorker Story" is about a man trying to write a story for The New Yorker. Ironically, the story itself could be a New Yorker story, and I mean that in the best way possible. It's a perfect little short story.
Sammy Harkham, "Blood of the Virgin" p. 28, 2010
The second story, "Blood of the Virgin", is set in the late 60s. Seymour is a film editor for Roger Corman-style B-movie studio. The story loops around his personal life and his life as part of this commercial enterprise, and it's an interesting, complex story. One aspect, which comes out on this page and elsewhere, is Seymour's disdain for (if not ressentiment of) anything arty, whether it be French films or even some of the work of his coworkers. This is something that's going to have echoes for lots of people working in creative fields. The mainstream comics worker who sniffs at the pretensions of art comics, or the comics creator of any stripe who resents the art world with its incomprehensible artwork and superior attitude. The examples are plentiful. And Seymour is contrasted in this regard to his colleague Oswald, who also turns out to be a professional rival.
John Mejias, Paping: The Teachers Edition, 2007
John Mejias' Paping: The Teachers Edition is a collection of stories about being a K-8 art teacher that were published in his minicomic Paping. Mejias taught in the Bronx and on Long Island. The stunning cover is probably the best part of this collection--the interior suffers from some indifferent production (bits of panels get cut off, for example) and extremely episodic story-telling--appropriate for minicomics, but less so for a large, integrated work.
That said, there is a lot to like here. When cartoonists do autobiographical work or realistic fiction, we often see a lot of lifestyles of the poor and hipsterish. People don't have jobs or they work as artists for a living. One ends up with a lot of comics about doing comics or other highly introspective works. This is not necessarily bad--see Gabrielle Bell's Diary, which is the next comic I'm reviewing--it's just that one hungers to see some other part of the world. Mejias' work is about himself, but it's also about his students and fellow teachers and the whole educational system.
John Mejias, The Teacher's Edition p. 7 (detail), 2007
Early on, you get a lot of bitterness about the weird world of New York City teaching. (The next chapter is called "No Good Deed Goes Unpunished.") And the insane explanations given for whitewashing Mejias's murals are certainly enough to make someone bitter. But fortunately, the rest of the book isn't like this. It's more observational, and while he deals a lot with his own state of mind, he gradually lets other characters take center stage--certain students, some colleagues, etc. Eventually, he brings in other voices, illustrating a story by fellow teacher Jody Buckles, and printing a story by Shawn Cheng about being a student in Taiwan and in New York. And Mejias incorporates some of the work of his students into his comics as in this story, where one of his colleagues, school psychologist Dr. "Doc" Adams, has died suddenly of a heart attack.
John Mejias, The Teacher's Edition p. 42 (detail), 2007
I loved this. I like the idea of incorporating student work into one's own work. I guess you have to be careful that you aren't exploiting them. In this case, Mejia was mourning his close friend, and his student managed to produce something highly moving that spoke to Mejia's own grief.
Gabrielle Bell, Diary cover, 2010
This is the second Gabrielle Bell reviewed in this spasm of reviews. Diary is drastically different from All My Dreams Come True. Diary is autobiographical and told with dense, wordy panels.
Gabrielle Bell, Diary p. 5, 2010
And as you would expect in a diary, Bell doesn't try to give you a big picture. These comics are relentlessly focused on what is happening to her, which could be deadly. But Bell is funny and self-deprecating, which makes them work.
Gabrielle Bell, Diary p. 18, 2010
This story, about Bell's attempt to adopt The S.C.U.M. Manifesto by Valerie Solanis, seems to be entirely fictional (although it's hard to tell). It's a story about over-promising, and hilariously builds a matryoshka doll of falsehoods--which doesn't even really unravel when she finally "comes clean" at the end.
Bell was selling original art at her table. I was struck by how tiny her originals were. In addition to selling finished pages, she was also selling individual panels. These were panels that she drew but ended up changing in the finished works. I bought one from the Valerie Solanis story.
Gabrielle Bell, untitled, 2010
If you compare this panel to the one that got printed, the only difference I can find is that Bell's mouth is open in the printed version and closed here. By the way, the size of this original panel is 2.75 inches square.
Labels: comics, Gabrielle Bell, John Mejias, Jordan Crane, Noah Lyon, Sammy Harkham, Tim Hensley, Tim Lane
Desert Island December 18, 2010 at 3:04 PM
The bakery which became Desert Island closed in 1996. At that time it remained closed for many months, and then became the art supply store Big Genius, which lasted about 4 years. Then a T-Mobile cell phone store moved in, which lasted about 5 years. My store replaced them, which is a much more positive change than the scenario you suggest above. Here's a picture of the glorious destruction of the T-Mobile store: http://www.flickr.com/photos/popopnits/2245983794/
Robert Boyd December 18, 2010 at 3:59 PM
That is less satisfying as a parable, but it's a better story. Replacing a T-Mobile store is unambiguously positive.
The guy who told me that story is an artist who moved with his wife from Brooklyn to Houston about two years ago. So I wasn't sure what the time-frame of his story was, except that it was at least two years ago...
People Who Died
The Year in Pan
Books I Got in Brooklyn--The End!
My Top 10 Houston Art Shows
Young Lions and New Character Parade
The Motel Art Improvement Service
This Has Always Cracked Me Up
Photo Tour: William Earl Kofmehl III at Lombard-Fr...
Photo Tour: Faile at Perry Rubenstein Gallery
Photo Tour: Omar Chacon at Margaret Thatcher Projects
Photo Tour: Anselm Kiefer at Gagosian Gallery
The Dinner Party by Judy Chicago
Comics in Art Museums
Photo Tour: Women Pop Artists at the Brooklyn Museum
Books I Got in Brooklyn, part 2
!Women Art Revolution!
Blast From the Past: In 2001, I predicted that Man...
Highwater Books and Me
A Modest Proposal For Immodest Artwork
The Warhol Foundation Plays Hardball
New Surfaces at Anya Tish
Can There Be Good Political Art?
Maria Smits at Lawndale
The Brooklyn Comics and Graphics Festival
Don't Forget to "Like" Pan on Facebook
Welcome to Williamsburg

redpajama_set_name: RedPajamaCommonCrawl


Take a retreat from your everyday life and come together in the tropical paradise of UNAWATUNA, where you will have the opportunity to explore and empower yourself and your life–mind, body, spirit—through yoga, meditation, coaching, adventure, journaling, and much more.
This retreat is all about coming back to yourself, re-harmonizing, and connecting with and rekindling your authentic, powerful, natural spirit. And we promise lots of laughter and fun!
All levels of yoga experience are welcome, even if you've never heard of, seen, or done a down dog! What happens in the retreat is also designed to help you plant seeds for intentional and positive change when you re-enter your life back home.


Cain comes clean to Moira by admitting that Holly tried to call her before she took her heroin overdose, but he deleted the message.
When Moira is out, Cain tells Holly to leave – insisting that she would be better off killing herself away from Moira. Can Moira stop Holly from leaving? And if she does intervene, will this be the final straw for Cain?
Meanwhile, Gabby and Liv film themselves smashing things at Gordon's and post the videos online to show the party is legit, but it doesn't take Bernice and Chas long to realise that the girls have lied about where they are. When they arrive at Gordon's house, Chas struggles to discipline Liv and later tells Aaron about the party. Aaron fears Liv's behaviour is all about Gordon.
Elsewhere, Nicola warns Dan not to tell Kerry that Ashley needs to be supervised.
Also today, Jimmy, Dan and Ashley settle down to watch a horror film at the pirate ship, but they frighten Arthur.


text:
\section{Introduction}

As it is well known, the Hamiltonian of a quantum mechanical system must be bounded from below due to stability requirements and, as a consequence, there is no self-adjoint time operator canonically conjugated to the Hamiltonian \cite{CNi68} (see, however, \cite{Olk09}), hence posing serious difficulties to define a meaningful time scale for quantum phenomena such as tunneling.

Several approaches have been considered to circumvent the above difficulty, leading to many definitions of quantum tunneling time, among which the dwell time and the phase time are the most prominent (see \cite{HSt89, LMa94, Win06-2, Win06-1} and references therein). However, the time scales proposed until now are generally plagued by difficulties which prevent their interpretation as a traversal time in the general case.  For instance, a serious controversy in the interpretation of many such time scales is related to the Hartman effect, which asserts that in the stationary case the time saturates for a static opaque potential \cite{Har62} (also see \cite{ORS02, LLB02} for a generalized version).

However, one cannot properly address the problem of quantum tunneling time in the stationary case because the very concept of a particle having a definite tunneling time requires that it be represented by a \textit{localized} wave packet (see, for example, \cite{FHa88}). With this in mind, in this work we reexamine the tunneling of a wave packet through a static potential by using the quantum clock formalism introduced by Salecker and Wigner \cite{SWi58} and further refined by Peres \cite{Per80}. Our main concern here is to scrutinize whether the Hartman effect, both in its original and generalized versions, emerges or not for a wave packet.

The Salecker-Wigner-Peres (SWP) clock \cite{SWi58,Per80} (see also \cite{Lea93,CLM09}) consists of a quantum rotor weakly coupled to the system (the tunneling particle), and it can be shown to be equivalent to the Larmor clock \cite{FHa88, But83, LAe89}, prepared and observed in a particular set of states, in the limit of large spin -- for a detailed treatment see \cite{SCo93}. In this framework a ``time operator" (not canonically conjugated to the Hamiltonian) can be defined \cite{Per80}, and the application of such an operator to quantum tunneling was extensively analyzed by Leavens and McKinnon \cite{LMc94}, who found that its expectation value only produces a meaningful result after a calibration procedure is adopted for the clock readings. Recently, Park \cite{Par09} considered the one-dimensional scattering of a wave packet by a rectangular potential barrier and found that the expectation value of that ``time operator" in the asymptotic final states gives the dwell time averaged with respect to the components of the initial wave packet, which, however, cannot be considered a traversal time because it does not distinguish between transmitted and reflected particles \cite{Par09}.

In this paper, instead of associating the clock readings to expectation values of such a ``time operator", we follow Peres' approach in the study of the time of flight \cite{Per80}. According to this method the transmission (reflection) time, which is obtained by following the peak of the clock's wave function, is given by the time derivative of the phase shift of the transmission (reflection) amplitude with respect to the perturbation potential. We argue that in order to address the question of the time spent in the barrier region by a particle that is \textit{eventually transmitted} (\textit{reflected}) one \textit{must} perform a \emph{post-selection} of the final state. Then, making use of an \textit{asymptotic condition} ensuring that for asymptotic times the incident and the transmitted/reflected wave packets are well localized far from the potential, it is possible to trace out the particle's degrees of freedom in order to ``read" the clock's final state. The average times obtained through this procedure are shown to have sensible physical properties in the context of quantum tunneling of gaussian wave packets through static symmetric potentials.

This work is organized as follows. In section \ref{clock} we briefly review the formalism introduced by Peres \cite{Per80} and its generalization to the time dependent situation (also see \cite{Lea93, Par09}), introducing the necessary steps to take into account only particles that are eventually transmitted (reflected) by the potential. We discuss some properties of the average times obtained and compare them with other time scales suggested in the literature. In Section \ref{tun} we study the behavior of these average times for the scattering of a gaussian wave packet, centered around a tunneling wave number, by a single rectangular barrier and a double delta barrier, with emphasis on the opaque regime and the possible emergence of the Hartman effect and, in particular, its generalized version. In section \ref{concl} we present our conclusions.

\section{The Salecker-Wigner-Peres Clock}
\label{clock}

The Salecker-Wigner clock \cite{SWi58}, as considered by Peres \cite{Per80}, is just a quantum rotor with Hamiltonian given by
\begin{equation}
H_c = -i \hbar \omega\frac{\partial}{\partial\theta}\; ,
\end{equation}
with $\omega \equiv 2\pi/(N\tau)$, where $\tau$ is the time resolution of the clock and $N= 2j+1$ is the dimension of the Hilbert space (with $j$ being a non-negative integer or half-integer).

The eigenfunctions $u_m(\theta)= \frac{1}{\sqrt{2\pi}}e^{i m\theta}$ ($0\leq \theta < 2\pi$) of $H_c$ have eigenvalues $\mathcal{V}_m = m\hbar\omega$
with $m= -j, \ldots , +j$. A more convenient orthogonal basis for the clock is given by $v_r(\theta)$ ($r=0, \ldots , N-1$) \cite{Per80}
\begin{equation}
v_r(\theta) =  \frac{1}{\sqrt{N}}\sum_{m=-j}^j \exp \left(- 2\pi i\frac{r m}{N} \right) u_m(\theta)\; ,
\end{equation}
which has the advantage of having a sharp peak at $\theta = 2\pi r/N$ for large $N$, so that the clock's pointer indicates the $r$th ``hour" (with uncertainty $\pm \frac{\pi}{N}$). Under time evolution such states change as $v_r(\theta)\to v_r(\theta-\omega t)$, thus making possible to associate a time duration $t$ to an arbitrary interval just by observing the translation of the peak of a free clock's wave function $v_r$ in that interval.

We are interested in measuring the time associated with the one-dimensional scattering of a particle of mass $\mu$ by a (real) static potential $V(z)$ confined to the region $0\leq z\leq a$. Following \cite{Per80}, the particle and the clock are coupled
through the interaction Hamiltonian
\begin{equation}
H_I = \mathcal{P}(z)H_c\, ,
\end{equation}
where the projection operator  $\mathcal{P}(z)$ satisfies  $\mathcal{P}(z)\!=\!1$ if $z\!\in \![0,a]$ and equals zero otherwise. The clock is assumed to
be initially at the state $v_0(\theta)$. Thus, the general form of the initial wave function of the whole system is
\begin{equation}
 \Psi_{inc}(\theta,z,t) = \Phi (z,t)v_0(\theta)\, ,
\end{equation}
where $\Phi (z,t)$ is a wave packet corresponding to a particle incident from the
left of the potential which, from the symmetries of the problem \cite{Mer}, can be written as
\begin{equation}
\Phi (z, t) = \int \frac{dk}{2\pi} \;A(k) e^{i\left(kz - \frac{E(k)t}{\hbar}\right)}\, ,
\label{wavepack}
\end{equation}
with all integrals in $k$ going from $-\infty$ to $+\infty$. The Fourier coefficient $A(k)$ is assumed to be centered around a positive $k_0$ corresponding to a tunneling energy.

After the scattering the particle and the clock become entangled due to the interaction $H_I$ and the general form of the wave function is \cite{Lea93}
\begin{equation}\label{coupled}
\Psi(\theta,z,t) = \frac{1}{\sqrt{N}}\sum_{m=-j}^j \Phi^{(m)}(z,t)u_m(\theta)\, ,
\end{equation}
where
\begin{equation}
\Phi^{(m)} (z, t) = \int \frac{dk}{2\pi} \; A(k) \psi^{(m)}
 (k,z) e^{-i\frac{E(k)t}{\hbar}}\, .
\label{wavepackm}
\end{equation}

The wave function $\Psi (\theta,z,t)$ satisfies the Schr\"{o}dinger equation with the Hamiltonian $H=\frac{p^2}{2\mu}+V(z)+H_I$. The orthogonality of the $u_m(\theta)$'s, together with the fact that they are eigenfunctions of $H_c$, imply that
$\psi^{(m)}(k,z)$ satisfy the time-independent Schr\"{o}dinger equation for energy $E(k)$ and potential
\begin{equation}
V^{(m)}(z) = V(z) + \mathcal{V}_m \mathcal{P}(z)\, ,
\end{equation}
where $\mathcal{V}_m = m\hbar\omega $. In order to ensure a weak coupling between the clock and the system it is assumed that $\mathcal{V}_m$ is a small perturbation, i.e.,
$|E|\gg\mathcal{V}_m$ and $|V(z)-E|\gg\mathcal{V}_m$.

Since we are interested in measuring the transmission time asymptotically after the interaction, let us focus on the transmitted wave packet.
The solution of the above stationary problem in the region to the right of the potential $V^{(m)}(z)$ is
$$
\psi_{trans}^{(m)}(k,z) = T^{(m)}(k)e^{ikz}
= \left| T^{(m)}(k) \right| e^{i\varphi_T^{(m)}(k)+ikz}\, .
$$
By using the weak coupling condition we can assume that
$\left| T^{(m)}(k) \right| \simeq \left| T(k) \right|$ and expand the phase $\varphi_T^m(k)$ up to first order in $\mathcal{V}_m$ \cite{Per80}:
\begin{equation}\label{1order}
\varphi_T^{(m)}(k) \simeq \varphi_T (k) + \mathcal{V}_m  \left( \frac{\partial }{\partial\mathcal{V}_m}\varphi_T^{(m)}(k)\right)_{\mathcal{V}_m=0}\, ,
\end{equation}
where $\varphi_T (k)$ denotes the phase of the transmission coefficient corresponding to the unperturbed potential $V(z)$. Finally, substituting the above expressions in (\ref{coupled})-(\ref{wavepackm}), and using the explicit form of the functions $u_m(\theta)$, the asymptotic transmitted wave function is given by
\begin{eqnarray}
\Psi_{trans}(\theta, z,t) &\!=\!& \int \frac{dk}{2\pi} \; A(k) T(k) e^{i(kz-\frac{E(k)t}{\hbar})} \nonumber \\
&&\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\times\, v_0\left(\theta - \omega t_c^T(k) \right)\, ,
\label{psi_tr}
\end{eqnarray}
where
\begin{equation}\label{tc}
t_c^T (k)= - \hbar \left( \frac{\partial }{\partial\mathcal{V}_m}\varphi_T^{(m)}(k)\right)_{\mathcal{V}_m=0}
\end{equation}
is the transmission time used by Peres in \cite{Per80}. A similar expression can be obtained for the reflection time $t_c^R(k)$ in terms of the reflection phase $\varphi_R^{(m)}(k)$. It can be \emph{proved} that these \emph{clock times} satisfy \cite{CLM09} (also see \cite{SBa})
\begin{equation} \label{rel}
\tau_D(k) = |T(k)|^2t_c^T(k) + |R(k)|^2t_c^R(k),
\end{equation}
where $\tau_D(k)$ stands for the stationary dwell time \cite{But83}, and $T(k)$ and $R(k)$ are the transmission and reflection amplitudes, respectively. It is important to stress that, for the clock times used here, the above relation can be proved to be a \emph{direct consequence} of Schr\"{o}dinger's equation. Thus the criticism to such a relation for supposedly not being compatible with quantum mechanics due to the absence of an interference term, which sometimes appear in the literature (see, e.g., \cite{LMa94}), does not apply to the present case (for details see \cite{CLM09}).

It should be noticed that, in order to strictly enforce the conditions $|E|\gg\mathcal{V}_m$ and $|V(z)-E|\gg\mathcal{V}_m$, the integral in (\ref{psi_tr}) should in principle be truncated by a small cutoff excluding the regions in which these conditions are not warranted. However, the continuity of the integrand allow us to extend the integration over the whole $k$-space up to first order for a very small $\mathcal{V}_m$, consistent with the approximations in (\ref{1order}). This requires a large time resolution $\tau$ for the clock, since it is related to the reciprocal of $\mathcal{V}_m$ \cite{Lea93}. However, as observed by Davies \cite{Dav05}, there is no difficulty since the clock can be treated within the weak measurement theory of Aharonov \textit{et al.} \cite{AAV88, AVa90} and a precise value can be obtained for a large enough ensemble.

Here we are interested in finding an average \emph{transmission} time. Therefore, we must consider only the sub-ensemble of all scattered particles that are eventually transmitted, i.e., we must perform a \emph{post-selection} of the final state (in addition to the \emph{pre-selection} of the initial one). The post-selected (transmitted) state can be described, with a slight change in notation, by the density matrix of the particle-clock asymptotic state $\varrho^{\textrm{trans}} \equiv \alpha \left|\Psi_{trans}\right\rangle\left\langle \Psi_{trans}\right| $, where
$\alpha$ is a normalization constant and $\left|\Psi_{trans}\right\rangle$ corresponds to the state (\ref{psi_tr}). In order to observe the final state of the clock we assume an \emph{asymptotic condition}, stating that long after the interaction the transmitted wave packet is completely localized to the right of the potential. Then, we can trace out the particle's degrees of freedom (by extending the $z$-integral
over the whole space) and obtaining the clock's reduced density matrix for the transmitted sub-ensemble, given by
\begin{eqnarray}\nonumber
\!\!\!\!\!\!\! \varrho_{c}^{\textrm{trans}} &\!\!=\!\!& \alpha \int \frac{dk}{2\pi} \left|A(k)T(k)\right|^2 \\
&&\times \left|v_0\left(\theta-\omega t_c^T(k)\right)\right\rangle \left\langle v_0\left(\theta-\omega t_c^T(k)\right)\right|\, ,\label{dc}
\end{eqnarray}
where the normalization requirement ${\rm Tr} (\varrho_{c}^{\textrm{trans}}) =1$ implies $\alpha \!=\! \left\{\int \frac{dk}{2\pi} |A(k)T(k)|^2 \right\}^{-1}$.

Now, since the clock's reading is associated with the peak of its wave function, we \emph{define} the \textit{average transmission time} as $\langle t_c^T\rangle ={\rm Tr}\left( \varrho_{c}^{\textrm{trans}} \frac{\hat{\theta}}{\omega}\right)$,
where $\hat{\theta}$ is an operator giving the peak of $v_k$ \cite{AMM03}. Then,
\begin{equation}\label{time-av}
\langle t_c^T \rangle = \int dk  \, \rho_T(k) \, t_c^T(k)\, ,
\end{equation}
where $\rho_T(k)\!=\!\frac{\left| A(k)T(k)\right|^2}{\int dk \left| A(k)T(k)\right|^2 }$ is the probability density to find mode $k$ in the final transmitted wave packet. An analogous procedure for the reflected sub-ensemble results in the \textit{average reflection time}:
\begin{equation}\label{time-avR}
\langle t_c^R \rangle = \int dk \, \rho_R(k) \, t_c^R(k)\, ,
\end{equation}
with $\rho_R(k)\!=\!\frac{\left| A(k)R(k)\right|^2}{\int dk \left| A(k)R(k)\right|^2 }$ the corresponding probability density to find mode $k$ in the reflected wave packet.

In the special case of a very sharply peaked wave packet, $|A(k)|^2/(2\pi) \simeq \delta (k - k_0)$, definitions (\ref{time-av})-(\ref{time-avR}) reduce to the corresponding stationary times, as expected. However, for more physical incident wave packets, which necessarily involve a finite dispersion in wave numbers, these definitions have the important property of weighting the contribution of each $t_c^T(k)$ ($t_c^R(k)$) by the \emph{probability density of having the mode $k$ in the final transmitted (reflected) wave packet}, thus minimizing the contributions of modes leading to the most improbable results. This is in contradistinction with the approach of considering the density matrix of the transmitted and reflected wave packets together, which is equivalent to averaging the dwell time with respect to the initial wave packet components -- a procedure that leads to many well known difficulties \cite{Par09, Nus00}.

The expressions (\ref{time-av})-(\ref{time-avR}) coincide with the real part of the \emph{complex time} obtained by Leavens and Aers \cite{LAe89} in their analysis of double barrier resonant times using the Larmor clock (see also \cite{LAe89-2} which deals with similar averages for the time obtained in \cite{HFF87}). These definitions could also be inferred from the analysis of the Larmor clock by Falck and Hauge \cite{FHa88}. The main advantage of the above treatment (in which only the position of the clock's pointer is observed \cite{AVa90, Joz07}) is that it introduces a unique \textit{real} time scale, thus avoiding the problem of interpreting complex times.

The above average reflection and transmission times can be used to generalize relation (\ref{rel}) for a wave packet. First, we observe that the
asymptotic probability to find the particle in the region at the right of the potential (i.e., the total probability for the particle to be transmitted) is given by $P_T\!=\lim_{t\to\infty}\!\int_a^\infty dz \int_0^{2\pi}d\theta |\Psi_{trans}(\theta ,z,t)|^2$. Under the asymptotic condition stated above the
$z$-integration can be extended to the whole space and this probability reduces to
\begin{equation}\label{pt}
P_T \!=\! \int\frac{dk}{2\pi}|A(k)T(k)|^2\, .
\end{equation}
Analogously, assuming a similar asymptotic condition stating that long after the interaction the reflected wave packet is completely localized to the left of the potential, the total probability for the particle to be reflected is
$P_R =\int\frac{dk}{2\pi}|A(k)R(k)|^2$. From the normalization of the initial wave packet these probabilities satisfy $P_T+P_R\!=\!1$ (as required, since long after the interaction transmission and reflection are complementary outcomes). Then, defining the mean dwell time as \cite{Nus00, Par09}
\begin{equation} \label{dwell-av1}
\overline{\tau_D} \equiv \int \frac{dk}{2\pi}|A(k)|^2 \tau_D(k)\, ,
\end{equation}
where the overbar indicates averages over the \emph{initial} wave packet, the above
definitions, combined with (\ref{rel}), imply that
\begin{eqnarray}\nonumber
\overline{\tau_D} &\!\!=\!\!& \int \frac{dk}{2\pi}|A(k)T(k)|^2t_c^T(k) \\
&&+\, \int \frac{dk}{2\pi}|A(k)R(k)|^2t_c^R(k) \nonumber \\ \nonumber \\
&=& P_{T}\langle t_c^T \rangle +P_{R}\langle t_c^R \rangle\, . \label{dwell-av}
\end{eqnarray}
This relation says that the usually defined average of the dwell time over the initial wave packet (which does not take into account whether the particle is eventually reflected or transmitted) can be viewed as an average over the transmission and reflection average times, weighted by the total probabilities for transmission and reflection, respectively. It must be stressed that \emph{a necessary requirement} for this interpretation is that the \emph{asymptotic conditions be satisfied}. Relation (\ref{dwell-av}) appears as the real part of a similar \emph{complex} relation in \cite{LAe89} -- again, the advantage here is that the SWP clock provides only real times.

\section{Tunneling through symmetric barriers}
\label{tun}

In this section we study the average transmission time for a gaussian wave packet incident from the left on two kinds of symmetric localized potentials, namely a single rectangular barrier and the double delta barrier. In both cases, we shall be mainly concerned with the behavior of $\langle t_c^T \rangle$ in the regime of opaque barriers (characterized by very small transmission amplitudes for non resonant tunneling energies), in order to examine the emergence or not of the Hartman effect \cite{Har62} (single barrier) and its generalized version \cite{ORS02} (double delta barrier).

We assume that at $t=0$ the particle is in a state described by a right-moving gaussian wave packet centered around a tunneling wave number $k_0>0$, and
spatially centered around a position $z_0<0$, i.e.,
\begin{equation} \label{psi0}
\Phi (z, 0) = \frac{1}{(2\pi)^{1/4}\sqrt{\sigma}} \exp\left\{ ik_0 z - \frac{(z-z_0)^2}{4\sigma^2} \right\}\, ,
\end{equation}
where $\sigma$ is a scale measuring the spatial extent of the initial wave packet (its inverse is proportional to the wave packet's momentum dispersion).

In what follows we will always make use of the fact that, as a consequence of (\ref{rel}), for symmetric potentials $t_c^T(k)$ and $t_c^R(k)$ coincide with the dwell time $\tau_D(k)$ \cite{FHa88}. Therefore, the average times (\ref{time-av}) and (\ref{time-avR}) are just the dwell time averaged over the transmitted and reflected sub-ensembles, respectively.

\subsection{The single rectangular barrier}
\label{single}

Let us now consider a square potential barrier of height $V_0$ and width $a$, $V(z) = V_0\Theta (z) \Theta (a -z)$. For a tunneling incident energy, $E<V_0$, the
stationary dwell time is well known and given by \cite{But83}
\begin{eqnarray}\nonumber
   \!\!\!\! \tau_D(k)&\!=\!&\frac{2\mu}{\hbar}\frac{k}{q}\\
    &&\!\!\!\!\!\!\!\!\!\!\!\!\!\! \!\!\!\!\!\!\!\! \times\frac{\left[ (k^2+q^2)\tanh (qa) + qa(q^2-k^2){\rm sech}^2(qa) \right]}{\left[ 4q^2k^2 + (q^2-k^2)^2 \tanh^2(qa)\right]}\, ,\label{tc1B}
\end{eqnarray}
where $k=\frac{1}{\hbar}\sqrt{2\mu E}$ and $q=\frac{1}{\hbar}\sqrt{2\mu (V_0-E)}$. For energies above the barrier, $E>V_0$, the stationary dwell time can be obtained from the above expression through the substitution $q\to i k_1$, with $k_1=\frac{1}{\hbar}\sqrt{2 \mu (E-V_0)}$), while the transmission amplitude $T(k)$ can be found in any textbook on quantum mechanics (see, e.g., \cite{Mer}). In the opaque limit, characterized by $qa \gg 1$ for a given $E< V_0$, the stationary dwell time (\ref{tc1B}) becomes independent of the barrier width $a$, which is the Hartman effect \cite{Har62,ORS02}. This effect has been at the origin of an intense debate in the recent literature concerning, among other problems, the apparent superluminality of the tunneling process (see, for example, \cite{Win06-1,ORS02, Olk09,LMa07,CLM09} and references therein). It should be noticed that a time can be defined, based on an analogy with fluid mechanics \cite{HCP74}, such that in the \emph{stationary case} it reduces to the dwell time divided by the transmission coefficient and, therefore, does not saturate with the barrier width \cite{HCP74} (also see \cite{MAl90, SCP90, GIA04}); but a complete analysis of \emph{time dependent} tunneling using such time scale is yet to be achieved \cite{HCP74, Lea91}.

In Figure 1 we investigate the typical behavior of the average times (\ref{time-av}) and (\ref{time-avR}) with increasing barrier widths. For comparison we have also plotted the average reflection time (\ref{time-avR}), the mean dwell time (\ref{dwell-av1}), and the time spent by the incident packet (characterized by its peak wavelength $k_0$) in the region $[0,a]$ in the absence of the potential, i.e., $t_{free}= \frac{\mu a}{\hbar k_0}$.
The choice of parameters in these figures ensures that the initial wave packet (\ref{psi0}) is, to an excellent approximation, confined to the left of the barrier (at $t=0$ the probability to find the particle in the region $z>0$ is less than $10^{-15}$). Also, tunneling components are dominant in the Fourier decomposition of the initial wave packet.
We observe that in the extreme opaque regime (in this case characterized by very large barrier widths), while $\overline{\tau_D}$ saturates to a value independent of $a$,  $\left\langle t^T_c\right\rangle$  increases linearly with the barrier width. In the inset, showing in detail the region of small to moderate barrier widths, we observe that for thin barriers all the average times are very similar. The similarity between $\left\langle t^T_c\right\rangle$ and $\left\langle t^R_c\right\rangle$ [hence, from (\ref{dwell-av}), their similarity with $\overline{\tau}_D$] is expected, since for thin barriers the post-selected probability density distributions $\rho_R$ and $\rho_T$ are almost indistinguishable from the incident one, $\rho_{inc}$. As the barrier thickness increases $\langle t^R_c\rangle$
becomes smaller than the free time and soon saturates, as expected for a wave packet centered in a tunneling wave number, since one would anticipate that the wave function cannot penetrate beyond a certain barrier depth. The average transmission time, $\left\langle t^T_c\right\rangle$, also becomes smaller than the free time for intermediate values of the barrier width, indicating that the barrier speeds up the wave packet in the transmission channel; however, in the very opaque region its behavior suffers an abrupt change, growing suddenly until it attains a regime of linear growth -- as shown for large $a$'s in Fig. 1, in this regime $\left\langle t^T_c\right\rangle > t_{free}$ (The wave packet width exerts an important role in determining the values of $a$ for which this abrupt change occurs, with the barrier width for that change increasing with $\sigma$; for a similar conclusion using a different time average see \cite{BSM94}). Therefore, we observe that $\left\langle t^T_c\right\rangle$ \emph{never saturates}, as one would expect of a well defined average transmission time. Finally, as it is well known, the mean dwell time initially increases with $a$ and soon saturates (the Hartman effect); this is a consequence of the fact that in the opaque region $P_R\simeq 1$ and the reflection term dominates the r.h.s of Eq. (\ref{dwell-av}).
\begin{center}
\begin{figure}
\includegraphics[width=9.5cm,height=5.5cm]{fig1}
\caption{(Color online) Behavior of the average times with respect to the barrier width $a$. All quantities are expressed in \emph{atomic units} (a.u.): $\mu=1$, $\sigma=10$, $k_0=0.7$, $z_0=-8\sigma$, and $V_0=0.5$. \emph{Inset}: \emph{zoom} of the region of small and moderate barrier widths [the horizontal dotted line indicates the saturated value of the stationary dwell time $\tau_D(k_0)$]. The free time, $t_{free}$, is plotted for comparison. \label{fig1}}
\end{figure}
\end{center}

It is instructive to compare the \emph{qualitative} behavior of the average times shown in Fig. \ref{fig1} with the results presented in \cite{GIA04}, even though \cite{GIA04} considers the time \emph{independent} situation. In both cases the reflection times saturate and the transmission times always increase with the barrier width, not showing any sign of the Hartman effect. However, there are important differences: in \cite{GIA04} the reflection time starts from infinite for $a=0$ and it is very large for very small barrier widths before staurating; furthermore, in \cite{GIA04} the transmission time tends to increase exponentially with $a$ in the extreme opaque limit (also see \cite{HCP74, MAl90, SCP90, Hag93}). These are unexpected properties and there is some debate about the interpretation of these times \cite{HCP74, Hag93, Win06-1} (nevertheless, the transmission dwell time used in \cite{GIA04} has been shown to have practical use in the study of the half life of radioactive nuclei decaying by the emission of an $\alpha$-particle \cite{KCN09}). By contrast, $\langle t^R_c\rangle$ is small for small barrier widths, a plausible result since this time is interpreted as the average time spent into the potential region by the wave packet which is eventually reflected. In addition, $\langle t^T_c\rangle$ tends to increase \emph{linearly} with $a$ in the extreme opaque limit. Such good properties of $\langle t^T_c\rangle$ and $\langle t^R_c\rangle$ emerge as a consequence of averaging over pos-selected sub-ensembles.

The behavior of the average transmission time observed in Fig. 1 is a consequence of the fact that for the transmitted wave packet in the opaque regime $\left\langle t_c^T \right\rangle$ is dominated by above the barrier components. If one truncates wave packet to include only under the barrier components, the corresponding ``truncated" transmitted wave packet is dominated by the contribution of a single component, completely lacking localizability in the opaque limit and approaching a plane wave and, therefore, saturating [but in this case, strictly speaking, the definition (\ref{time-av}) does not apply]. The above the barrier dominance is, of course, well known (by the way, methods to avoid such dominance, by compensating for the reflection of lower $k$ components in the state preparation, have been developed and result in average times that saturate \cite{HSM04}).

\subsection{The double delta barrier}
\label{double}

The \textit{generalized} Hartman effect states that for two potential barriers the tunneling time becomes independent of the distance between the barriers in the opaque limit \cite{ORS02, LLB02, Esp03, Win05} (see, however, \cite{LRo05} for an alternative view of the \emph{stationary} case using a multiple peak decomposition). In order to investigate this effect we will consider the double delta barrier $V(z) = \gamma\delta (z) + \gamma\delta (z-d)$, where $\gamma>0$ gives the barrier strength and $d$ is the separation between the barriers and we will assume that the SWP clock runs only when the particle is in the region $0<z<d$. This potential has the advantages of being the easiest way to study the generalized Hartman effect \cite{AER03} and that all the wave packet components are tunneling (for a study of stationary traversal times for this potential, see \cite{SBC94}).

For a stationary wave incident from the left, the transmission coefficient is given by (in the limit $\mathcal{V}_m = 0$)
\begin{equation}
\left|T(k)\right|^2=\frac{1}{1+4\alpha^2\left[\alpha\sin(kd)+\cos(kd)\right]^2}
\label{amptransdelta}.
\end{equation}
where $\alpha \equiv \frac{\mu\gamma}{\hbar^2 k}$. In the opaque limit, characterized by $\alpha \gg 1$ (equivalently, $\gamma \gg k$), $|T(k)|^2$ goes to zero almost everywhere (as $\gamma^{-4}$), except at the (countable) infinite set of resonances $k_n$. The resonances are given, for \emph{any} $\gamma>0$ and $d>0$, by the solutions of the transcendental equation \cite{Ricco}
\begin{equation}
k=-\frac{1}{d} \tan^{-1}\left(\frac{\hbar^2 k}{\mu\gamma}\right)\label{rescond},
\end{equation}
with the location of the $n$th resonance strongly dependent on $d$, in such way that the spacing between successive resonances decreases with $d$ (see \cite{POl05} and references therein). For $\gamma\to\infty$ the resonance spectrum tends to the spectrum of an infinite rectangular well of width $d$,  i.e. $k_n=\frac{n\pi}{d}$ (with $n=\pm 1,\pm 2,\pm 3,\cdots$) \cite{Mer}.

The stationary dwell time in the region between the barriers, as follows from (\ref{tc}), is given by
\begin{eqnarray}
&&\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\tau_D(k)= t_c(k) = \frac{\mu}{\hbar k^2}\nonumber\\
 &&\!\!\!\!\!\!\!\!\!\!\times \,\frac{\left( 1+2\alpha^2\right)kd+2\alpha\sin^2(kd)-\alpha^2 \sin(2kd)}{1+4\alpha^2\left[\alpha\sin(kd)+\cos(kd)\right]^2},\label{stattimedelta}
\end{eqnarray}
and at the $n$th resonance, $k_n$, its value is
\begin{equation}
\tau_D(k_n)=\frac{\mu}{\hbar k_n^3} \left[2\frac{\mu\gamma}{\hbar^2} +\left(2 \frac{\mu^2\gamma^2}{\hbar^4}+k_n^2\right)\, d\right],\label{restime}
\end{equation}
as can be found by substituting (\ref{rescond}) into  (\ref{stattimedelta}). For a fixed $d$, the opaque limit of the resonant dwell time behaves asymptotically as $\tau_D(k_n)\sim \frac{2 \mu^3}{\hbar^5}\frac{\gamma^2}{k_n^3}\, d$, thus diverging in the extreme opaque limit  $\gamma\to\infty$. On the other hand, the off resonance dwell time behaves in the opaque limit as $ \tau_D(k) \propto \gamma^{-2}$, thus characterizing the generalized Hartman effect by the fact that $\tau_D(k)\to 0$ as $\gamma\to\infty$ (however, such a convergence to zero is \emph{non-uniform} in any neighborhood of a resonance).
\begin{center}
\begin{figure}
\includegraphics[width=9.0cm,height=5.5cm]{fig2}
\caption{(Color online) Wave number distribution for the transmitted (solid curve, \emph{non normalized}) and the incident wave packets (dashed curve), for opaque barriers. Atomic units are used, with $\gamma=16$, $\sigma=6$ and $k_0=1.2$. \label{fig4}}
\end{figure}
\end{center}

Let us now consider a gaussian wave packet sharply peaked around $k_0$, eq. (\ref{psi0}), and investigate the behavior of the average transmission time in the opaque limit (which is now characterized by $\gamma \gg k_0$). It is useful to first analyze the
wave-number distribution of the transmitted and incident wave packets, given by the probability densities $\rho_T(k)$ and $\rho_{\textrm{inc}}(k)\equiv |A(k)|^2/(2\pi )$, respectively. As shown in Figure \ref{fig4}, for small $d$ there are few, if any, resonances in the domain of $\rho_{\mathrm{inc}}(k)$. However, as $d$ increases the resonances become densely distributed within that domain and we expect the transmitted packet to be dominated by them. Such a dominance is especially pronounced in the opaque regime, where the off resonance components are strongly suppressed (a similar behavior was found for the double \textit{square} barriers in \cite{POl05}). It is important to emphasize that even when the transmitted spectrum is dominated by resonances, \textit{in the extreme opaque limit the wave packet total transmission probability tends to vanish}, since in the limit $\gamma\to\infty$ the integrand in (\ref{pt}) tends to zero almost everywhere, except in a zero-measure set (the countable set of resonances) -- this is illustrated in Figure \ref{fig5}.
\begin{figure}
\includegraphics[width=8.5cm,height=5.0cm]{fig3}
\caption{(Color online)  Behavior of the total probability for the particle transmission with increasing strength $\gamma$. We observe that this probability goes to zero as the barrier strength $\gamma$ increases, irrespective the eventually large number of resonant components in the initial packet wave number distribution. In this plot $k_0=1.2$ and $\sigma=6$ in atomic units. \label{fig5}}
\end{figure}

Figure \ref{fig6}a displays $\left\langle t_c^R \right\rangle$, $\left\langle t_c^T \right\rangle$ and $\overline{\tau_D}$, in a logarithmic scale, for small to moderate barrier separations, and for $\gamma$ in the opaque domain. One observes that the average reflection time only deviates significantly from the mean dwell time when resonances are present around $k_0$, since there the reflection coefficient $|R|^2$ is very small. Thus, when resonances are densely distributed around $k_0$ (e.g., when $d$ is large) one expects significative differences between $\left\langle t_c^R \right\rangle$ and $\overline{\tau_D}$, as it is shown in Fig \ref{fig6}b, for vary large $d$'s.

In Figure \ref{fig6}b we observe the typical behavior of the average times for a wide range of values of the barrier separation $d$. Contrary to the generalized Hartman effect statement, this figure reveals that $\left\langle t_c^T \right\rangle$ always varies with $d$ (the plot corresponds to an initial wave packet having a narrow width $\Delta k\thicksim \frac{1}{\sigma}$ around $k_0$) and, in fact, for large enough barrier spacing $\left\langle t_c^T \right\rangle$ tends to grow linearly with $d$ (although not shown here, we observed a similar behavior for several sets of values of $\gamma$ and $\sigma$). This is a consequence of the fact that for large $d$ any small neighborhood of a given $k$ will be densely populated by resonances (see Fig. \ref{fig4}) and, as $d$ varies, these resonances (of different orders) enter and exit that neighborhood, with the net effect of a linear dependence on $d$ according to eq. (\ref{restime}) (with $n$ \emph{not} fixed, in a way that $k_n$ is always within such a neighborhood). On the other hand, the behavior of $\left\langle t_c^T \right\rangle$ for small and moderate barrier separations $d$ tends to be oscillatory because there are few resonances in the transmitted spectrum (see Fig. \ref{fig5}) and, as $d$ increases and a new single resonance eventually enters the domain of the transmitted spectrum, the peak of $\tau_D(k)$ at that resonance causes a peak in $\left\langle t_c^T \right\rangle$.

Summarizing, Figures \ref{fig6}a and \ref{fig6}b show that the average transmission time depends on $d$, showing no evidence of the generalized Hartman effect. This is in opposition to the conclusions of \cite{POl05,POl06} (using a different definition of average time, but with similar parameters) who assert that in regions of small $d$ located between the peaks associated to successive resonances (such that $ k_n - k_{n-1}\gg \Delta k $) the generalized Hartman effect occurs, as characterized by plateaus in between the peaks in the plot \emph{time} versus $d$ (here such plateaus would be at zero) -- no such plateaus appear for $\left\langle t_c^T \right\rangle$ (in fact, not even for $\overline{\tau_D}$) in the corresponding regions in Fig. \ref{fig6}a. In addition, Figure \ref{fig6}b shows that in the opaque regime $\gamma>>1$ the mean dwell time is dominated by the average reflection time, as one would expect from relation (\ref{dwell-av}), and for very large $d$  the mean dwell time tends to behave as the free time. In that range of $d$, $\left\langle t_c^T \right\rangle$ shows that the particle slows down for large $\gamma$, as expected due to the multiple reflections occurring in the region between the barriers.

\begin{center}
\begin{figure}
\includegraphics[width=9.2cm,height=5.0cm]{fig4a}
\includegraphics[width=9.4cm,height=5.0cm]{fig4b}
\caption{(Color online) Behavior of the average transmission time $\left\langle t_c^T \right\rangle$ with respect to the barrier separation $d$ for a wave packet having a narrow wave number distribution around the central wave number $k_0$. All quantities are expressed in atomic units: $\gamma = 16$, $k_0=1.2$, $\sigma=20$, $z_0=-8\sigma$. The mean dwell time $\overline{\tau_D}$, the average reflection time $\left\langle t_c^R \right\rangle$, and the free time $t_{\mathrm{free}}$ are also shown for comparison. Fig (\emph{a}) corresponds to the range of small to moderate barrier widths (in which we used a log scale for the vertical axis). Fig. (\emph{b}) shows a wide range of barrier widths [we have multiplied all the times, except $\left\langle t_c^T \right\rangle$, by a convenient factor ($=130$), in order to display all the curves in the same plot]. \label{fig6}}
\end{figure}
\end{center}

\section{Concluding Remarks}
\label{concl}

We considered the extension of the SWP clock to treat the one-dimensional tunneling of a particle, represented by a wave packet, through a static potential and addressed the question of how much time a particle that is eventually transmitted (reflected) spends in the potential region. Taking into account that to properly analyze this question one must consider only the sub-ensemble of the scattered particles that are finally transmitted (reflected), which corresponds to a post-selection of the final state, the SWP clock attributes a well-defined average time for these process, namely eqs. (\ref{time-av}) and (\ref{time-avR}). These are to be compared with the mean dwell time obtained in \cite{Par09} for the SWP clock. That $\langle
t_c^T\rangle$ and $\langle t_c^R\rangle$ are good candidates to transmission and reflection
times also follows from the fact that they naturally satisfy the generalization of the ``weighted average rule" \cite{LAe89-2} for the time dependent case [eq. (\ref{dwell-av})], provided the asymptotic conditions are satisfied. Also, the above approach has the advantage of providing these average values as the only time scale, in contradistinction with previous treatments of the Larmor clock in which they appear as the real part of a complex time \cite{LAe89,LAe89-2,HFF87}.

We analyzed the properties of the average transmission and reflection times for the scattering of a gaussian wave packet, centered on a tunneling wave number, by a square barrier and a double delta barrier and found that they would deviate from the mean dwell time only when the transmission or the reflection coefficients were very small [for symmetric potentials $t_c^T(k)$ and $t_c^R(k)$ equal the stationary dwell time and the average times (\ref{time-av}) and (\ref{time-avR}) are an average dwell time weighted by the transmission and reflection probability density, respectively]. Then, by carefully considering the opaque limit we found that $ \langle t_c^T\rangle$ shows no evidence of either the Hartman effect \cite{Har62} (single barrier) or its generalized version \cite{ORS02} (double delta barrier), and it also shows that the tunneling particle is slowed down
by extremely opaque barriers. These properties indicate that $ \langle t_c^T\rangle$ is a good candidate for an average transmission time. It should also be noticed that our conclusions concerning the emergence of the generalized Hartman effect are in disagreement with those of \cite{POl05, POl06} (who used a different definition for the average transmission time) \emph{in the region of small barrier spacing}, for they claim the existence of such effect for a wave packet as long as the width $\Delta k$ of the wave packet is much smaller than the spacing between resonances, while our results for $ \left\langle t_c^T\right\rangle$ show that the generalized Hartman effect does not emerge in \emph{any} region of the parameters. We stress that \emph{average} tunneling times are the most one can expect due to the lack of a well defined time operator and the consequent impossibility to obtain an eigenvalue for time.

The above analysis shows that the saturation of the transmission time, a feature associated with the Hartman effect, is a consequence of not taking into account the fact that the definition of a meaningful traversal time associated to a tunneling particle requires localizability, a requirement impossible to be satisfied in the stationary case. In addition, it is also a consequence of not taking the probability of transmission into account properly.

It should be noticed that even though the average transmission time does not saturate, for intermediate barrier widths $ \left\langle t_c^T\right\rangle$ increases very slowly with $a$ (single barrier) or $d$ (double delta), so that the transmitted wave packet ``speeds up" in comparison to the free wave packet (see Figs. \ref{fig1} and \ref{fig6}). Although this phenomenon is well-known \cite{LMa94}, it could be interpreted as a ``remnant" of the Hartman effect and it deserves further investigation (in the realm of relativistic quantum mechanics) due to the fact that it could allow for (non-causal) superluminal average speeds in this range of barrier widths.

Finally, given the sensible properties exhibited by the average times $\langle t_c^R\rangle$ and $\langle t_c^T\rangle$, it would be interesting to consider its possible application to the analysis of quantum tunneling in graphene, a field of much current interest and in which many of the issues discussed in this paper are of practical relevance (see, e.g., \cite{GGu09} and references therein), including the controversy around the Hartman effect \cite{WCL09, DDr10}.

\section{Acknowledgments}

This work was partially supported by NASA Minnesota Space Grant Consortium (L.A.M.) and Concordia College (A.T.N.).

redpajama_set_name: RedPajamaArXiv


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Within the framework of International Alert's 'Increasing tolerance in selected municipalities to promote social cohesion in Kyrgyzstan' project, trainings on mediation, conflict sensitivity, social tolerance and legal aspects of relations between local governments, religious organisations and civil society were held for activists, representatives of local governments and religious leaders. The most active participants of the trainings formed an initiative group and produced the project 'Reducing conflicts among adolescents,' which is aimed at preventing and reducing potential for conflicts among adolescents and youth, as well as strengthening the social cohesion of the community of the Yuryevka aiyl aimak.
Participants taking part in an interactive game as part of the training .
A woman from the Yuryevka village tells us:
I didn't even know you could gather so many people at the same time in one place in our village. Even those, whom I rarely meet in the village, came, and there were not only religious people in the hall, but also almost all of our villagers with their children. I have never seen so many women at the meeting.
With the support of International Alert, the Development Centre for children and adolescents was opened at the House of Culture of the Yuryevka aiyl aimak. The Centre offers free courses on English, Korean and Arabic, as well as sports sessions on judo, wrestling, boxing, dance and chess. With the involvement of conflict psychologists, teachers, social pedagogues, local government representatives, religious leaders, and parents will also have the opportunity to improve their knowledge and skills in preventing and reducing conflicts among adolescents.
"It's great we finally have a place where we can participate in extracurricular activities, develop, and learn languages. In our school, many children are considering going to the Development Centre as there is a large selection of free courses. We didn't have the opportunity to do any hobbies before. We used to have a dance club, but after a couple of months the teacher stopped coming. Now, the Centre wants to offer more courses so that we can learn a profession," a student of the Yuryevka school.
The leadership of the local government fully supported this initiative and provided space for the Centre in the local House of Culture. At the parent-teacher meeting, parents also asked to open seamstress courses, programming courses, and furniture-making courses. The first step was to make furniture. All of the Centre's furniture is the work of the children themselves. Many of them have already begun to think about their future profession.
Religious leaders taking part in training.
"I've been working at a school for 17 years, so I know the problem from inside. Conflicts happen constantly: when children are left without supervision after school they start conflicts, including inter-ethnic ones. During the project, we had the opportunity to propose the idea of opening a youth centre. At trainings, Alert taught us what conflicts are and how to solve them. The imams of our village, representatives of aiyl okmotu, were with us in the group. We all offered our views and ideas, and as a result we were able to open the youth centre." Aziz Zarlykov, a social worker and head of the initiative group goes on to say:
We have various conflicts in life because of water, religion and the nation. Such problems are usually solved at the village gatherings but almost no one comes along to that, but a lot of people do gather for Friday prayer. After prayer, we can discuss the problems of our village, ways to solve them, and achieve reconciliation. We took the opportunity to invite imams and religious leaders to talk about the conflicts of our village and find peaceful solutions.
"This year is declared the year of digitalisation, and we want to conduct online courses on IT with the help of the IT Academy. The Chui regional library will also cooperate with us, and the sports federations of KR have promised to help us conduct tournaments and competitions. Soon we will also make our own greenhouse. Thanks to the Centre's project, children will be able to learn new professions, and perhaps someone will be able to start a business," member of the initiative group.
The project 'Increasing tolerance in selected municipalities to promote social cohesion in Kyrgyzstan' supported civic participation and peaceful dialogue between communities, religious groups and local authorities.
Focusing on six municipalities in Chui, Issyk-Kul, Naryn and Osh oblasts (regions), we ran focus groups, organised public debates and discussions on the role of religion in a secular state and provided training for religious leaders in mediation, conflict analysis and resolution, gender issues, and the social and legal role of religion and religious organisations in the country. We also piloted a scheme to give small grants to communities.
This project ran from March 2019 to March 2020, working with the following local partners: Development Policy Institute, Muftiyat, State Agency for Local Self-governance and Inter-ethnic Relations, Kyrgyzstan and State Agency for Religious Affairs, Kyrgyzstan.
International Alert is grateful for the kind support of our donors.
The path of a Youth Peer Mentor: the story of Malika Kartanbaeva
Imam Muhammad Durgalov and his service to the people
Preventing early marriages
Friendship wins in Zhazy
Against early marriage in Gulistan
Constructive dialogues on religion and democracy in Kyrgyzstan: Policy briefs – 2nd compilation
Published December 2019
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text:
Zambia Elections Tracker 2021: Pre-election developments
Posted by Dr Craig Moffat | Aug 11, 2021 | 0 |
Since Zambia's independence in 1964, the country has experienced several successful changes in leadership, and peaceful transfers of power. However, there have been instances of political violence and points of instability. Zambians are preparing to head to the polls, which are predicted to be a tight contest between the opposition candidate, Hakainde Hichilema (UPND), and the incumbent President Edgar Lungu (PF). Because of COVID-19 precautions, no official rallies or mass gatherings have been permitted, which may put the opposition parties on an unequal footing. The vote will mostly likely be fought around economic issues. Zambia's anticipated GDP growth this year is 0.6%, after a 3.5% contraction last year, among the worst on the continent. Zambia may be characterised as having relatively high levels of trust deficit, increasing repression, and growing questions around whether the election process will be free fair and credible.
Election contenders
The Electoral Commission of Zambia (ECZ) approved 16 presidential candidates to participate in the 2021 general election. The main opposition candidate is Hakainde Hichilema of the UPND. Other notable contenders include Anglican bishop Trevor Mwamba (United National Independence Party), award-winning journalist Fred M'membe (Socialist Party), former Information Minister Chishimba Kambwili (National Democratic Congress Party), and former vice-president Nevers Mumba (Movement for Multiparty Democracy).
Hakainde Hichilema, contesting for the sixth time, narrowly lost the last election, obtaining 47.6% of the vote. After the last elections in 2016, Hichilema was imprisoned for four months. Initially he was charged for a traffic violation, which later became a more serious charge of treason.
Political violence and campaign restrictions
In June 2021, the electoral board suspended election rallies due to the surge in COVID-19 cases, but previous elections indicate a pattern of unfair treatment of election campaigning by President Lungu's government and ECZ.
Political violence has increased dramatically over the past five years. More recently, the military was deployed after ruling PF party supporters were killed by attackers suspected to be aligned to the UPND in Kanyama. Since then, the UPND has been banned from holding election rallies, and has claimed that Danny Chingangu, a victim of the killings, was in fact one of their party members and not from the PF.
In the absence of physical gatherings, opposition parties have taken their campaigning to social media to rally their supporters.
Zambia's total publicly guaranteed debt constituted 104% of GDP, around $12 billion, almost 80% of the country's GDP being in external debt. The country recently defaulted on paying a Eurobond to the tune of $42.5 billion.
In 2020, inflation rose to 17.4% and remained above the targeted 6-8% range. In the same period, the country's real GDP contracted by almost 5%.
The government's shift towards Chinese financing has compounded its debt problem, and concerns over corruption and lack of transparency in these loan deals have been increasingly apparent.
The International Labour Organization (ILO) estimates that unemployment rose to 12.17% in 2020, the highest since the PF took office in 2011.
Youth unemployment is also high. One in five young people are without a job.
The cost of living has also increased rapidly.
Zambia owes more than $12bn (£8.6bn) to foreign lenders, resulting in the government spending at least 30% of its revenue on interest payments, according to credit ratings firm S&P Global.
Citizen sentiment
Recent citizen surveys indicate growing discontent with President Lungu and the progress of the country's democracy overall. The president's approval rating declined to 46% and just 37% of citizens were satisfied with the way democracy was working in the country.
Poverty has risen sharply, with 74% of Zambians indicating that they frequently go without basic life necessities.
Rumours of an internet shutdown during the elections spread over the past week, but have since been deemed false by the government. A statement from the Ministry of Information and Broadcasting Services said that the information was false and intended to cause alarm.
International election observer participation
The African Union (AU) accepted an invitation to deploy a short-term observer mission for election day. The mission leader is Dr Ernest Bai Koroma, former president of the Republic of Sierra Leone.
The European Union Election Observer Mission (EU-COM) was the first international body to respond to the invitation to observe Zambia's elections. The EU-COM sent 32 long-term observers to Zambia's 10 provinces, along with 11 analysts based in Lusaka. The mission will be led by chief observer Maria Arena, a member of the European Parliament from Belgium.
The Commonwealth Secretary-General has sent 14 observers since late July to observe both the pre-election, election preparation and the election day. The group will be led by former president of Tanzania, Dr Jakaya Kikwete.
The Common Market for Eastern and Southern Africa (COMESA) agreed to deploy a short-term observer mission, and will include observers from Burundi, Democratic Republic of Congo, Egypt, Kenya, Libya, Malawi, Rwanda, Sudan, Somalia and Zimbabwe, as well as the COMESA Secretariat staff. Ambassador Ashraf Gamal Rashed of Egypt, with the assistance of Madam Hope Kivengere of Uganda, will lead the mission. The Secretariat has observed the pre-election environment, as it is based in Lusaka.
On 6 August, the Southern African Development Community (SADC) stated that it would not deploy the SADC Electoral Observer Mission (SEOM) due to concerns over the COVID-19 pandemic. The organisation has had virtual consultations with the ECZ, political parties, academics, and non-governmental organisations. Consultations will continue during the pre-election, election and post-election phases, which conclude on 14 August 2021.
During these consultations, the SADC has learnt of and expressed regret over reports of sporadic acts of political violence in some areas of Zambia that resulted in the loss of lives. It has called upon political party leaders to guide their supporters towards mutual political tolerance, calm and a peaceful settlement of political disputes.
Dr Craig Moffat
Craig Moffat, PhD is the Head of Programme: Governance Delivery and Impact for Good Governance Africa. He has more than 17 years of practical experience working for government institutions and multilateral organisations. He was previously employed by the South African Foreign Service, where he worked extensively at identifying and analysing security threats towards South Africa as well as the southern Africa region. Previously, he was the political advisor for the Pretoria Regional Delegation of the International Committee of the Red Cross. He holds a PhD in Political Science from Stellenbosch University.
https://gga.org/author/dr-craig-moffat/
Hung councils, coalitions, minority governments and the precarious future of South Africa's municipalities
eSwatini national dialogue forum could strengthen foundation for success amid the kingdom's political crisis
Cry the beloved Kingdom – Lessons for King Mswati III
SA municipal elections - Unpacking the coalition puzzle
Monique Bennett
Monique Bennett holds a Master's degree in International Relations from the University of the Witwatersrand. Her interest in the field of data science and statistics was sparked by her quantitative methodology course during her studies. Her research focuses on development theory, governance, and the environment within the African context. She has written for news outlets such as the Daily Maverick and supports her research team by providing data-driven evidence for their research/op-eds. She has worked as a research assistant for In On Africa and as a public relations manager for the student organisation, Wits Inala Forum.
https://gga.org/author/monique-bennett/
East Africa's locust crisis reveals importance of disaster preparedness
Transnational climate governance or national climate policy – what matters more?
Zambia election day 2021: Summary
Stuart Mbanyele
Stuart is a Junior Researcher in the Governance Delivery and Impact programme at Good Governance Africa. He holds a Master of Arts degree in Security and Strategic Studies from the University of Pretoria. His dissertation explored the linkages between marginalisation and insecurity, looking at the securitisation of service delivery protests in South Africa. Before joining Good Governance Africa, He was a Junior Research Fellow with the Centre for Law and Society at the University of Cape Town. Before that, he worked as a research consultant at the Institute of Security Studies with the Justice and Violence Prevention Programme and as a Junior Lecturer for the Department of Political Sciences at the University of Pretoria.
https://gga.org/author/stuart-mbanyele/
Getting back the elusive youth vote
The Governance Performance Index – How do South Africa's metros rank?
GGA's Stuart Mbanyele on the importance of good governance within municipalities
PreviousRwanda and Mozambique army forces take control of key northern port of Mocimboa da Praia
NextZambia election day 2021: Summary
South African local government elections 2021 timeline
SADC technical deployment to Mozambique
Tanzania Election Tracker 2020
SADC extraordinary summit on Cabo Delgado


Corpse Bride Hidden Numbers is a online find the numbers game by Games2Dress. Asses your observing skill by finding the hidden numbers which are in Corpse Bride image. Avoid clicking unnecessarily, as otherwise your score will get reduced. You need to finish the level in 5 minutes, as otherwise game will comes to an end. Good luck and have fun.


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Thomas Rhett and Kelsea Ballerini Return to Host the 2019 CMA Fest Sunday, August 4 on ABC
By Jim Donnelly
The Country Music Association has announced country music superstars Thomas Rhett and Kelsea Ballerini will return to host CMA Fest, the music event of the summer, with multimedia personality Bobby Bones tapped as a special guest host. CMA Fest, the three-hour prime-time concert special, which brings country music's ultimate fan experience to a national television audience, airs SUNDAY, AUG. 4 (8:00 – 11:00 p.m. EDT), on ABC. Be sure to watch on the ABC app from your smartphone and tablet (iOS and Android), computer on ABC.com and connected devices (Roku, AppleTV and Amazon Fire TV).
"This year's CMA Fest offers something for every music fan," says Sarah Trahern, CMA chief executive officer. "From surprise collaborations to some of country music's most exciting, emerging and legendary talent, we're excited to bring the festival to millions of fans around the world later this summer."
"CMA Fest is always the summer's must-see music event with the biggest names in country music," says Rob Mills, senior vice president, Alternative Series, Specials & Late-Night Programming, ABC Entertainment. "With Thomas Rhett and Kelsea Ballerini returning for their third year, and Bobby Bones joining them as special guest host, we know this summer's festival will knock it out of the park."
Filmed during Nashville's annual four-day CMA Fest, Thursday through Sunday, June 6–9, the television special features more than 30 performances and surprise collaborations onstage at Nissan Stadium. 2019 marks the 16th consecutive year of the broadcast, a feat no other U.S. music festival has achieved. Last year's broadcast generated ABC's top summertime non-sports ratings, leading ABC to the most-watched network that night (source: Nielsen Media Research).
Thomas Rhett returns to host CMA Fest for a fourth year, first co-hosting the special in 2016, while Ballerini returns for a third year.
CMA Fest hosts Kelsea Ballerini and Thomas Rhett
CMA Fest is executive produced by Robert Deaton. More than 300 artists perform at CMA Fest, donating their time so a portion of ticket proceeds can directly benefit high-quality music education initiatives across the United States through the CMA Foundation. CMA Fest is unlike any other, with tens of thousands of country music fans descending upon downtown Nashville for four straight days of live music on 11 official stages, as well as meet-and-greets and up-close-and-personal experiences for fans at Xfinity Fan Fair X. CMA Fest's outdoor daytime stages are free and open to the public. All stage lineups are available in the Official CMA Fest App as well as CMAfest.com. Artist lineups are subject to change.


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How do I find the incoming and outgoing mail server?
I am facing problem related to my email. I just want to know How do I find the incoming and outgoing mail server. If anyone have good knowledge about this. Then please share with me.
Re: How do I find the incoming and outgoing mail server?
For Incoming Mail Server enter imap.one.com as Host Name, example.com being your domain hosted by One.com. Enter your full email address as User Name e.g. [email protected]. Enter your Password that you selected for the email account in the Control Panel. For Outgoing Mail Server enter send.one.com as Host Name.


A stated income commercial mortgage loan is a loan that usually involves commercial real estate bought either as a rental, or as part of a business expansion plan. In either case these loans are regulated different from stated income mortgages for owner-occupied properties.
Due to the specifics of stated income commercial loans, a lending corporation may have a whole subdivision dealing exclusively with stated income commercial mortgages. It has been proven that standard full doc commercial mortgages may not provide the best solution for the borrower even though the whole process is thoroughly documented. Even the opposite - investment properties demand much greater funding flexibility and involvement from the lender's side. Commercial lenders actively contributing with advice and commercial loan counseling play a major role in their borrowers' success.
How to get the best stated income commercial mortgage loan?
Most investors don't even need a fully documented commercial loan. It may cost you more to pay the Certified Public Accountant to document your business cash flow rather than simply go for a stated income investment property loan. The best you could do is approach a commercial lender, or a big lender's subdivision who specialize solely in funding commercial real estate loans. The more involved the lender is, the better business strategy you are going to come up with together. Also, every business has their individualized needs and the probability of success is greater when this is taken into account.


Still waiting for the weight to drop more....2 months now and reduced 17 lbs. Not too much so I hope I can reduce more. I will continue to use this botanical silmming soft gel and looking for a better result.


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The purpose of the present study is to analyze the content of the guidance school experimental sciences textbooks in Iran in terms of environmental problems consideration. For this purpose, three experimental sciences textbooks of guidance school were analyzed by using content analysis method. The statistical population is three experimental sciences textbooks of guidance school in the academic year of 2012-2013. Therefore, sampling method was not used in this study and the statistical population and sample population were the same. This study was done by using checklist content analysis tool including four major components such as environmental problems of air, water, soil and sound and 45 sub-components. The William Scott formula was used to determine the reliability of data collection tool and its reliability amount was .82. The research findings showed that environmental problems are ignored in the guidance school experimental sciences textbooks. The most attention was paid to the environmental problems in the third grade experimental science textbook and the lowest attention was paid in the second grade experimental science textbook of guidance school. In relation to the environmental problems, the most attention was paid to the soil problems and the lowest attention was paid to sound problems in experimental sciences textbooks of guidance school. These findings necessitate paying attention to more important issue of the educational content formulating and editing by scientific and literary experts in educational content formulating regarding environmental problems in these books. Therefore, due to the industrialization path of today's society and educational system evolution and review of the content of the textbooks, textbook authors should consider educational content.


Written by Mark Ransom on date 12 October 2011 .
I've been trying to learn Vim, which is a terminal based text editor used by uber geeks and longbeards. I know how to get around in Vim, I've been using it for years because it's one of the only text editors available when I ssh into a Linux server, but I'm not nearly as fast using it as I am when using good old GEdit with a bunch of helpful plugins. The thing about Vim is that it has a ton of shortcuts keys for doing stuff, which is both awesome and terrifying because of the steep learning curve that this creates. I have tried switching all of my text editing needs to Vim before, but I'd always hit a snag after a little while and in frustration I'd quit and just use GEdit.
This time I'm cutting myself some slack, I don't have to quit all other text editors cold turkey, it's okay to fall back on them if I'm in a hurry and just need to get something done. But when I have time to use Vim to do what I need to do, when I can pull up Google and learn how to unindent a whole block of text at once instead of saying "this is stupid, it's so easy to do this in GEdit!", I should take that time, because in truth it's not particularly hard to do the things I want to do in Vim, I just have to force myself to learn how, even if it's frustrating to hit those road blocks.
My daughter is 6 and for her birthday we baught her a brand new pink bike, with streamers on the handlebars and a little basket. She loves that bike, but there's just one problem; she won't ride it. Oh she'll sit on it, but she won't peddle it around unless one of us is hovering nearby, because she's scared she'll fall off. Now this fear isn't completely unfounded; shortly after she got the bike she was riding it down our street and she started to tip over and instead of putting her feet down to stabilize herself she tried to jump clear of the bike and ended up getting tangled in the peddles and scraping her knee. We keep trying to tell her that she just needs to get back on the bike and try again, and she does try from time to time, but until she decides that she's ready to face her fear, and possibly sustain additional injury, she's just going to sit on it and not go anywhere.
And that's fine. We all have to decide how and when we want to grow, to step outside of our comfort zone because we know (or at least hope) that the price at the end will be worth the pain. It's often difficult to make ourselves take risks if we haven't yet convinced ourselves that it's going to be worth it, we don't yet know what we will gain from the experience. I've decided that learning Vim will allow me to become even more keyboard-centric, it will free me from clunky GUI based text editors and possibly increase my text editing speeds. My daughter will eventually decide that she wants to be able to ride her bike with the other kids in the neighborhood, and hopefully that desire will help her overcome her fear, or at least face it. When your desire to achieve outweighs your fear of failing, or your frustration with having to slow down to learn, then the time is right to commit.
Because learning and growing can hurt, you have to be committed to following through, even when things aren't easy. A committment isn't just a decision, because you can change your mind about a decision, but a commitment is something that holds you to a course, even when you might want to change your mind. Breaking a commitment needs to have reprocussions, you need to have an incentive to follow through, and the most basic incentive is just knowing that you had committed to doing something and that you would be letting yourself down by quitting. I prefer to bind myself more strongly to a committment, like tweeting about it or blogging about it, hence this post. Whatever it takes to get you to your goal, that's what you need to do to force yourself to follow through.
Now go. Do. Accomplish something that now seems scary and out of reach. Get on that bike and ride.