text:
\section{Introduction}

Polaron formation as a consequence of electron-phonon
coupling appears in many contexts in condensed matter
physics, including charge carriers in colossal magnetoresistance
materials \cite{jaime,ramirez}
and in high-temperature superconductors \cite{bishop,alex}.
As theoretical research in this field spans over five decades, many analytical
techniques have been applied to this problem \cite{alex1}.  The
applicability of these methods is usually limited to a particular
parameter regime, frequently far from the physically most interesting
crossover regime.  Despite extensive analytical work in this field,
there remain many open problems including the nature of the
crossover to large polaron mass,
the form of various correlation functions,
the nature of the polaron excited states, and dynamic properties of the
polaron.

Constantly growing computer capabilities have allowed
research in this field to take advantage of various numerical methods,
including exact diagonalization techniques (ED)
\cite{alex2,wellein1,wellein2,wellein3,mello,capone,marsiglio},
quantum Monte Carlo calculations (QMC) \cite{raedt,kornilovitch},
variational methods including the Global-Local method (GL)
\cite{romero,romero1}, and recently developed density matrix renormalization
group techniques (DMRG) \cite{white}.  A comparison of
results obtained by different methods for
energy bands and effective masses is contained in the work of
Romero {\it et al.}  \cite{romero}.  Although most of these methods
give reliable results in a wide range of parameter regimes, each
suffers from different shortcomings. The ED technique gives reliable
results on small lattices (up to 20 sites \cite{wellein2}) for
ground and excited state properties. Results are limited to discrete
momentum $k-$points. QMC methods can treat large system sizes (over 1000 lattice
sites) and provide accurate results for thermodynamic polaron
properties.  Dynamic properties, however, require analytic continuation
from imaginary time, which is an ill-posed problem that is extremely
sensitive to statistical noise.  The GL method gives reliable results
for energy bands and the polaron effective mass on reasonably large system
sizes (32 sites), however, it is limited to
ground state properties. The DMRG method seems to be most successful in
computing ground state properties including various correlation
functions. Despite the lack of translational symmetry, it
provides reasonably accurate results for energy bands and the
effective mass. It can deal with large system sizes ({\it e.g.} 80
sites and 30 phonons per site), delivering  reliable results in the
intermediate and strong coupling regime. DMRG is less reliable in the weak
coupling regime.  It generally treats large systems with open
boundary conditions and does not allow the calculation of dynamic
or large $k$ properties or excited states, although there
are some exceptions to these rules \cite{jeckelmann}.

In this paper we focus on several issues of the Holstein problem.  We
present a simple and computationally efficient method based on the
exact diagonalization technique. We apply the method to the
one-dimensional, single-electron Holstein model. Among the advantages
of our method are the simplicity of our approach, the efficiency in
selecting the variational space, and the ability to compute
both ground and excited state physical
properties of the system at continuous total wavevector $k$.
We define
the variational space on an infinite lattice.  Even though most of our
calculations were done on a workstation, our results
are often superior to those of
other numerically more intensive methods
\cite{wellein2,wellein3,white}.  We test the method by comparing
results for the energy band, effective mass, quasiparticle weight
and correlation functions with some of the most successful recent
numerical methods.

The second part of this paper is devoted to the investigation of the
first excited state of the model. Using our numerical method as
well as a strong coupling analytical approach, we find a phase
transition between a state where the polaron forms
a bound state with an additional phonon excitation,
and one where there is
no bound state.

Generalizations of this method can even be used to calculate
coherent quantum dynamics far from equilibrium, including those of a polaron
driven by a strong electric field \cite{janez1}, and of an
electron tunneling across a potential drop while
coupled to phonons \cite{janez2}.

We consider the  Holstein Hamiltonian  \cite{mahan}

\begin{eqnarray}
H && = -t \sum_{j} ( c_{j}^\dagger c_{j+1} + H.c.) \nonumber \\
&& -\lambda \sum_j c_{j}^\dagger c_{j}
( a_j + a_j^\dagger) + \omega \sum_j a_j^\dagger a_j ,
\label{ham}
\end{eqnarray}
where $c_{j}^\dagger$ creates an electron and
$a_{j}^\dagger$ creates a phonon on site $j$.  We consider the case
where a single electron hops between nearest neighbor Wannier orbitals in 1d,
and interacts with dispersionless optical phonons.  The electron-phonon
coupling strength is $\lambda$, and is local in real space
($k$-independent).  The parameters $t$, $\omega$, and $\lambda$
all have units of energy, and can be used to form
two dimensionless ratios.  (Different conventions for the parameters
are sometimes used in other papers.)

It is clear at the outset that for any finite values of the
parameters, the exact groundstate will be a delocalized state with
momentum $\vec k$, and not a ``self-trapped'' solution that breaks
translation-invariance.  The simple argument is that if the ground
state were self-trapped, its center could be shifted and a degenerate
ground state obtained.  If the Hamiltonian has any nonzero matrix
element between states with different centers, a lower energy state
can be obtained by a phased superposition of wavefunctions with
different centers (a Bloch state).  The only known way that this
argument can fail is with (unphysically) strong electron-phonon
coupling as $\omega \rightarrow 0$
to a gapless phonon spectrum,
in which case the matrix element
between different centers can vanish \cite{leggett}.
In that case, an exact ground state can be written as
either self-trapped or as a Bloch state.  Self-trapping cannot occur
here because the phonon spectrum has a gap.  Although the exact
ground state is a Bloch state, for some parameters (e.g.~very large
$\lambda$), a self-trapped solution can have a low variational
energy\cite{holstein}.
It has indeed been proven that polaron ground state properties,
including the
energy and effective mass, are analytic functions of the Hamiltonian
parameters \cite{gerlach}.  We will see below that such a theorem
cannot be extended to include excited states.

\section{The method}

A complete set of basis states
for the many-body Hilbert space can be written
\begin{equation}
\vert M \rangle =
  |j; \dots ,n_{j-1}, n_{j} , n_{j+1},  \dots \rangle,
\label{psi}
\end{equation}
where $j$ is the electron site and there are $n_m$ phonons on site $m$.
A variational subspace is
constructed beginning with an initial state, taken to be an
electron on site $j=0$ with no phonons,
and operating repeatedly ($N_h$-times) with the
off-diagonal pieces of the Hamiltonian, Eq.~(\ref{ham}).
At each step, a basis state
is added when there is a nonzero $t$ or $\lambda$ matrix element to a
state previously in the space.  These states and all
of their translations on an infinite lattice are included
in the variational space.  (A translation moves the electron
and all phonon excitations $m$ sites to the right.)
If a basis state can be generated in more than one way,
only one copy is retained.  All nonzero matrix elements
of the Hamiltonian between retained basis states are included.

A small variational Hilbert space is shown in Fig.~(\ref{tight}).
The dots may be thought of as basis states in the
many-body Hilbert space, or alternatively as
Wannier orbitals in a periodic (one-body) tight-binding model,
with hopping matrix elements given by the bonds.
The variational space shown in Fig.~(\ref{tight})
is still infinite, since the lattice repeats periodically
to infinity.  It is clear from Bloch's theorem, however,
that each eigenstate can be written as ${\rm e}^{ikj} \Psi _m $,
where $k$ is the momentum, $j$ is the unit cell, and $\Psi _m $ is a set of
$M$ complex amplitudes, one for each state
in the unit cell ($M=7$ for the example of Fig.~\ref{tight}).
For a given momentum $k$, the
resulting numerical problem is to find the eigenstates of an
$M \times M$ (sparse) hermitian matrix using Lanczos
or another method.

Figure (\ref{spaghetti}) plots the energy eigenvalues
for a larger variational space
containing a maximum of 9 phonon excitations.
The figure superficially resembles a ``band structure'',
which however encodes ground and excited state information for
the many-body (many phonon) polaron problem.
The AC conductivity of the polaron,
for example, appears as an ``interband'' transition in
this mapping.

The largest variational basis that we have used
has $N_h=22$, or $M=1.2 \times 10^7$
states.  It is usually unnecessary to use such a large
basis for intermediate-coupling
ground state properties, even to obtain 12-digit
accuracy for the energy.
The variational Hilbert space we construct is not
a standard one,
and appears to add basis states more efficiently
than some other methods.
A basis state is included if it can be reached using
$N_ \lambda$ phonon creation operators and
$N_t$ electron hops in any order
with $N_t + N_ \lambda \leq N_h$.
For a given  $N_h$, there is
a basis state with $N_h$ phonon quanta on the same site
as the electron and no phonon excitations elsewhere.
There is also a basis state with $N_h - 1$ quanta
on the site adjacent to the electron and no phonon excitations elsewhere.
For $N_h$ odd, there is a basis state with $(N_h -1)/2 $
quanta on the electron site and an equal number simultaneously on
a first neighbor site.
The maximum distance that a phonon excitation can appear
from the electron is $l = N_h - 1$, but then only
a single quantum and only if there are no phonons excited
elsewhere in the system \cite{trade}.  Only the basis states
from a single unit cell (a single electron position)
are stored in computer memory.

The energy of a polaron for a finite chain of $N$ sites with periodic
boundary conditions is {\it lower} than that
for an infinite lattice with the
same parameters.  (This is easily to verify
in weak-coupling perturbation theory, or numerically.)
Thus, previous exact diagonalization and most other variational approaches
produce energies that are variational for the particular
lattice size $N$ that they treat, but are not variational
in the thermodynamic limit $N \rightarrow \infty$.
The energy we calculate is, in contrast, variational
in the thermodynamic limit.
(The quoted DMRG energies are extrapolated and not variational, although they
are generally rather accurate.)

Having the capability to compute the polaron energy $E(k)$
at any $k$ rather than being limited to multiples of
$2 \pi / N$ makes our method more
accurate for computing the effective mass of the polaron using the
standard formula
\begin{equation}
  {m_0 \over m^*} =  {1 \over {2t}}
  {\partial ^ 2 E(k) \over {\partial k ^ 2}}\vert_{k=0},
\label{mass}
\end{equation}
where $m_0 = 1/(2t)$ is the effective mass of a free electron.
The second derivative is evaluated by small finite differences in the
neighborhood of $k = 0 $.  Note that although the calculated
energy $E(k)$ is a variational bound for the exact energy, there is no
such control on the mass, which may be either above or below the exact
answer, and is expected to be more difficult to obtain accurately.
Nevertheless, in the intermediate coupling regime where our method at
$N_h=20$ gives an energy accuracy of 12 decimal places, one can
calculate the effective mass extremely accurately (6-8 decimal places)
by letting $\Delta k \to 0$.

Further information about the quasiparticle may be obtained by
computing the quasiparticle residue,
the overlap (squared) between a bare electron and a polaron,
\begin{equation}
Z_k = \vert\langle\psi_k\vert c_k^\dagger\vert0\rangle\vert^2,
\label{zk}
\end{equation}
where $\vert0\rangle$ is the state with no electron and
no phonon excitations,
and $\vert \psi_k\rangle$ is the polaron wavefunction
at momentum $k$.  The numerical results for $Z_{k=0}$
given in the next section differ by less than 1\% from results for
the reciprocal effective mass
$m_0/m^*$ obtained from Eq.~(\ref{mass}).  At finite $k$, $Z_k$ provides
information about the electronic character of the polaronic state. The
phonon contribution to the quasiparticle can be measured by the
$k-$dependent mean phonon number
\begin{equation}
N^{ph}_k=\sum_i  \vert\langle\psi_k\vert a_i^\dagger a_i\vert\psi_k
\rangle\vert^2.
\label{Nk}
\end{equation}

To describe the polaron
at different $k$ we have also computed the static correlation function
between the electron position and the oscillator displacement
\begin{equation}
\chi(i-j)  = \langle\psi_k\vert c_i^\dagger c_i (a_j + a^\dagger_j)
\vert\psi_k\rangle,
\label{chi_eq}
\end{equation}
and the  distribution of the number of excited phonons in the vicinity
of the electron
\begin{equation}
\gamma(i-j)  = \langle\psi_k\vert c_i^\dagger c_ia^\dagger_ja_j
\vert\psi_k\rangle.
\label{gamma}
\end{equation}

\section{Ground state results}

In this section, we compare our results for the
ground state properties of the Holstein model
to those obtained by other numerical methods.
We also calculate polaron correlation functions
at finite values of the Bloch wavevector $k$.

We start by comparing energy bands $E(k)$ for two different sets of
parameters.  Figure (\ref{ekfig}) compares the present method to the
DMRG \cite{romero,white}, GL \cite{romero} and the finite cluster ED technique
\cite{wellein2}.
Using $N_h=20$ we achieve an accuracy in
the thermodynamic limit of 12 decimal places for small $k$ and at least 4
decimal places
for large $k$.  Our results for $E(k)$ are
presented as continuous curves. Agreement of our results with DMRG
and ED is good, however there is a slight disagreement with the
Global-Local method at larger $k$, which also disagrees with the DMRG
method. There is also a slight disagreement with the ED at larger $k$
which we attribute to the smaller system size used in finite cluster ED
calculations.  As we will demonstrate later in this paper, the extent
of the lattice deformation (the size of the polaron) increases as $k$
approaches the Brillouin-zone boundary, which makes finite-size
calculations more susceptible to finite size effects.

In table (\ref{energ}) we compare the polaron ground state energy
at $k=0$ for two different parameter sets obtained by
our and three other numerical methods,
exact diagonalization (ED) \cite{fehske},
DMRG \cite{white}, and
Global-Local variational \cite{romero}.
Comparisons with a greater variety of
methods can be found in Romero {\it et al.} \cite{romero}.
We have limited our comparison to those methods that are accurate to
at least 4 decimal places.  Our method
converges to all of the digits shown using $N_h=15$ or $M=88052$
basis states for $\lambda = \omega=1$,
and $N_h=18$ or $M=731027$ basis
states for $\lambda=\sqrt{2}$, $\omega=1$.
The ground state energy appears to converge exponentially with
$N_h$, with the accuracy improving by approximately one order
of magnitude as $N_h$ is increased by 1.
The larger ($N_h=18$) calculation runs in under a minute
on a modest workstation.

Figure (\ref{mass0}) shows our results for the effective mass
Eq.~(\ref{mass}) computed with $N_h=20$ in comparison with GL and DMRG
methods.  The parameters span different physical regimes including
weak and strong coupling (respectively small and large
$\lambda/\omega$), and adiabatic ($\omega/t \ll 1$) and antiadiabatic
($\omega/t \gg 1$) regimes.  We find good agreement with GL away from
strong coupling and good agreement in all regimes with DMRG.  DMRG
calculations are not based on finite-$k$ calculations due to a
lack of periodic boundary conditions, so they
extrapolate the effective mass from the ground state data using chains
of different sizes, which leads to larger error bars and more
computational effort. Notice that their discrete data is slightly
scattered around our curves.  Nevertheless, both methods agree well. A
closer look at effective masses in the antiadiabatic regime
($\omega/t=5.0$) and $\lambda/\omega<2 $ reveals a slight systematic
disagreement of our results with both methods in comparison.  We have
compared our results for effective mass obtained on different systems
from $N_h=16$ with $M= 178617$ states to $N_h=20$ with $M=2975104$
states and obtained convergence of results to at least 4 decimal
places in all parameter regimes presented in Fig.~(\ref{mass0}).
Our error is therefore well below the linewidth. Even
though there is no phase transition in the ground state of the model,
the polaron becomes extremely heavy in the strong coupling
regime.  The crossover to a regime of large polaron mass is more rapid in
adiabatic regime (smaller $\omega/t$).

Figure (\ref{zkfig}) shows the quasiparticle residue
$Z_k$ and the mean phonon number $N_k^{ph}$
as a function of $k$ for the case of small
$\lambda_0 \equiv \lambda^2/2\omega t $ ($\lambda^2=0.4,  \omega=0.8$)
and large $\lambda_0$ ($\lambda^2=3.2, \omega=0.8$).
The two sets of parameters  correspond to the large and small polaron
regime respectively \cite{wellein3}.
The DMRG cannot straightforwardly compute this quantity,
and we compare our
results with cluster calculations.  Open symbols represent the
results of Wellein and Fehske \cite{wellein2} obtained on a $N=14$ site
cluster for the same choice of parameters.  Except for the fact that
their results are limited to discrete $k-$points defined by the size
of their system, we find excellent agreement
between the two methods in the weak coupling case.
In the strong coupling regime there
is an approximately $1\%$ disagreement in $N^{ph}_k$ due to a lack of
phonon degrees of freedom in the variational space of the
ED calculation.
Our results in the weak coupling case show a smooth crossover
from predominantly electronic character of the wavefunction
for small $k$ (large $Z_k$ and small $ N^{ph}_k \approx 0$)
to predominantly phonon character around $k =\pi$ characterized by
$Z_k\approx 0$ and $N^{ph}_k \approx 1$. In the strong coupling regime
there is less $k-$dependence.
The $Z_k$ is already close to zero at small $k$, indicating strong
electron-phonon interactions that lead to a large polaron mass.

Jeckelmann and White have calculated the electron-phonon correlations
at $k=0$ for the 1d and 2d polaron using the DMRG
method \cite{white}.  We compare our results with theirs for the 1d case.
There is good agreement in Fig.~(\ref{chi}a) for intermediate
coupling parameters $\omega = 1$ and $\lambda=0.5$.
Figure (\ref{chi}b) plots correlations for $\omega=0.1$ and $\lambda=0.1$,
which corresponds to weak coupling in the adiabatic limit.
In this regime the DMRG method gives less reliable results.  The size of
the polaron is underestimated, possibly due to finite-size effects
in open boundary conditions.
Note also that the DMRG method does not give symmetric results
as it should, {\it i.e.}
$\chi(l)\not = \chi(-l)$.
In this parameter regime our results have
fully converged, as we can see from the perfect overlap of results of
systems with two different sizes of the Hilbert space
$N_h=17,18$.
Figure (\ref{chi}c) plots correlations for
$\omega = 0.1$ and $\lambda=0.435$, which belongs to the strong coupling,
small polaron regime.
The DMRG produces superior results
in this regime, where our calculation at $N_h=21$ has not fully
converged to the large $N_h$ limit.  Our results are, nevertheless,
in qualitative agreement with the DMRG.
We conclude
that both techniques give reliable results in the intermediate
coupling regime, and that they complement each other in the weak and strong
coupling regimes.

A thorough investigation of correlation
functions using ED and the variational Lanczos method was performed by
Wellein and Fehske \cite{wellein3}. Although we do not show a
direct comparison with their work, our
results for correlation functions agree qualitatively with their calculations.

While the strength of the DMRG calculation is exhibited in its ability to
compute ground state properties of large systems, it is limited in its
computation of excited states.  In Figure (\ref{zkfig}) we have
shown how the nature of the polaron transforms from predominantly
electronic character at $k=0$ to phononic around $k=\pi$.  We
follow this transformation by computing the correlation
function $\chi$ for four different
values of $k$, shown in Figure (\ref{chifig}).
These parameters correspond to the weak coupling case in
Figure (\ref{zkfig}).  At $k=0$, where the group velocity is zero,
the deformation is limited to only a few
lattice sites around the electron.  It is always positive and
exponentially decaying.  At finite but small $k=\pi/4$, the
deformation around the electron increases in amplitude
and rings (oscillates in sign) as the polaron acquires
a finite group velocity.
At $k=\pi/2$ the ringing is strongly
enhanced.  Note also that the spatial extent of the deformation
increases in comparison to $k=0$. The range of the deformation is
maximum at $k=\pi$, where it extends over the entire region
shown in the figure.  In keeping with the larger extent of the lattice
deformation near $k=\pi$, the ground state energy $E(\pi )$ converges
more slowly with the size of the Hilbert space.

We have also computed $\chi$ for the strong-coupling case $\omega=0.8,
\lambda^2=3.2$ (not shown).  We find only  weak  $k-$dependence, which is a
consequence of the crossover to the small polaron regime.  The
lattice deformation is localized predominantly on the electron site.

\section{What is the nature of the first excited state?}

In this section, we
focus on the question of whether an extra phonon excitation
forms a bound state with the polaron,
or instead remain as two widely separated entities.
Using numerical and analytical approaches we will show that there
exists a sharp phase transition between these two states.
Although the ground state energy $E_0$ is an analytic
function of the parameters in the Hamiltonian,
there are points at which the energy $E_1$
of the first excited state is nonanalytic.
In previous work, Gogolin has found bound states of the
polaron and additional phonon(s), but he does not
obtain a phase transition between bound and unbound
states because his approximations are limited to
strong coupling $\lambda / \omega \gg 1$ \cite{gogolin}.
A phase transition between a bound and unbound first
excited state has been calculated for dimension $d=3$
using a dynamical CPA approximation \cite{sumi} and dynamical
mean field theory \cite{ciuchi}.

\subsection{Numerical results}

We begin by computing the energy difference $\Delta E = E_1
- E_0$, where $E_1$ and $E_0$ are the first excited state and the
ground state energies at $k=0$ (the two lowest
bands in Fig.~(\ref{spaghetti}) ).
In the case where the first excited
state of a polaron can be described as a polaron ground state
and an unbound extra phonon excitation, this energy
difference should in the thermodynamic limit equal the phonon
frequency, $\Delta E = \omega$.  In Fig.~(\ref{de}) we
plot the binding energy $\Delta = \Delta E -\omega $ for $\omega=0.5$
as a function of the electron-phonon coupling $\lambda$ for various
sizes of the variational space.
We see two distinct regimes. Below $\lambda_c\sim 0.95$, $\Delta$
varies with the system size but remains positive $( \Delta >0 )$.
Physically, for $\lambda < \lambda _c$, the additional phonon excitation
would prefer to be infinitely separated from the polaron,
but is confined to a distance no greater than $N_h -1$
by the variational Hilbert space.
As the system size increases, $\Delta $ slowly approaches zero from above
as the ``particle in a box'' confinement energy decreases.
In the other regime, $\lambda>\lambda_c$, our data has clearly converged
and $\Delta <0$.  This is the regime where the extra phonon excitation
is absorbed by the polaron forming an excited bound polaron.
Since the excited polaron forms an exponentially decaying
bound state, the method
already converges at $N_h=14$.  In the inset of Figure (\ref{de}) we
show the binding energy $\Delta$ in a larger interval of electron-phonon
coupling $\lambda$.  Although the results cease to converge at larger
$\lambda$, we notice that the binding energy $\Delta$ reaches a minimum as a
function of $\lambda$.  As we will demonstrate within the strong coupling
approximation, the true binding energy approaches zero exponentially from
below with increasing lambda.  In Figure~(\ref{phd}) we show the phase
diagram, valid for $k=0$, separating the two regimes.  The phase boundary,
given by $\Delta=0$, was obtained
numerically and using strong coupling perturbation theory in $t$
to first and second order. Details of the latter calculation are
given in the next subsection.
The phase transition where $\Delta$ becomes negative at
sufficiently large $\lambda$ is also seen in exact
diagonalization calculations \cite{fehske1}.

In Figure (\ref{gammafig}) we compute
the distribution of the number of excited phonons in the
vicinity of the electron $\gamma(i-j)$, Eq.~(\ref{gamma}), for the
ground state $\gamma_0$ and the first excited state $\gamma_1$
slightly below $(\lambda=0.9)$, and above $(\lambda=1.0)$
the transition for
$\omega=0.5$. The central peak of the correlation function $\gamma_1$
below the transition point is
comparable in magnitude to $\gamma_0$  (Figs.~(\ref{gammafig}a,b)).
The main difference between the two curves is the long range
decay of $\gamma_1$ as a
function of distance from the electron, onto which the central peak is
superimposed.
The extra phonon that is represented by this long-range
tail extends throughout the whole system and is not bound to
the polaron. See also the  difference $\gamma_1-\gamma_0$
in the inset of Fig.~(\ref{gammafig}b).
The existence of an unbound, free phonon is confirmed
by computing the difference of total phonon number $N^{ph}_{0,1}=\sum_l
\gamma_{0,1}(l)$. This difference should equal one below the
transition point. Our numerical values give $N^{ph}_1-N^{ph}_0\sim
1.02$.  We attribute the deviation from the exact result to
finite-size effects.

Correlation functions above the transition point (Figs.~(\ref{gammafig}c,d))
are physically different.  First, phonon correlations in $\gamma_1$ decay
exponentially, which also explains why the
convergence in this region is excellent.  Second, the size of the
central peak in $\gamma_1$ is 3 times higher than $\gamma_0$.
(Note that to match scales in Figure
(\ref{gammafig}d) we divided $\gamma_1$ by 3).
The difference in total phonon number gives
$N^{ph}_1-N^{ph}_0\sim 2.33$.  We are thus facing a totally different
physical picture: the excited state is composed of a polaron which
contains several extra phonon excitations (in comparison to the ground
state polaron) and the binding energy of the excited
polaron is $\Delta <0$. The extra phonon excitations are located
almost entirely  on the electron site (see the inset of
Fig.~(\ref{gammafig}d)). The value of $\gamma_1-\gamma_0$ at $j=0$ is 2.16,
which almost exhausts the phonon sum.

\subsection{Strong-coupling perturbation theory}

In this section, we calculate the ground and
excited state energies of the polaron perturbatively
in the hopping $t$.  For $t=0$, the Hamiltonian
Eq.~(\ref{ham}) describes a harmonic oscillator
with a shifted origin (due to the $\lambda$ force term)
on the site with the electron,
and unshifted oscillators on the other sites.
The Hamiltonian in the new basis is given by
the canonical transformation $\tilde H = e^S H e^{-S}$, where
\begin{equation}
S = -g\sum_j n_j(a_j-a_j^\dagger),
\label{S}
\end{equation}
and $g=\lambda/\omega ~$ \cite{lang}.
After some algebra (see also Ref. \cite{marsiglio}), the
transformed Hamiltonian takes the following form:
\begin{eqnarray}
\tilde H &=& H_0 + V \nonumber \\
H_0&=&\omega\sum_j
a_j^\dagger a_j - \omega g^2 \sum_j n_j \nonumber \\
V &=& -t e^{-g^2}\sum_j \left(c_j^\dagger c_{j+1}
e^{ g\left(a_j^\dagger - a_{j+1}^\dagger\right)}
e^{-g\left(a_j - a_{j+1}\right)} + {\rm h.c.}\right) ~,
\label{hamtilde}
\end{eqnarray}
where $n_j = c_j^\dagger c_j$.
The operator $a_j^\dagger$ in Eq.~(\ref{hamtilde})
creates a phonon excitation on site $j$ relative
to the shifted oscillator if there is an electron
on site $j$, and relative to an unshifted oscillator
on the other sites.
The first term in $H_0$ is the energy of the phonon excitations,
and the second is the energy gained by the oscillator
that is displaced by the force of the electron.
In strong coupling perturbation
theory, $V$ in Eq.~(\ref{hamtilde}) is considered a
perturbation.  It represents the hopping of an electron,
including possible creation and destruction of
phonon excitations.

The lowest energy eigenstates of the unperturbed
Hamiltonian $H_0$ have no extra phonon excitations,
and an energy $E^{(0)}_0 = - \lambda ^2 / \omega $.
They can be written
$\vert \phi_0(j)\rangle = c^\dagger_j\vert \cal O \rangle$, where
$\vert\cal O\rangle$ represents vacuum for electron and phonon degrees
of freedom. This state represents a polaron localized on the site
$j$. Evidently the ground state is $N-$fold degenerate, where $N$ is
the number of sites in the system.  The perturbation lifts this
degeneracy. The matrix elements
$V_0(i,j)=\langle\phi_0(i)\vert V\vert\phi_0(j)\rangle$
can be readily
computed since the exponential factors in $V$ are not effective in this case,
\begin{equation}
V_0(i,j) = -t e^{-g^2};\ \ j = i \pm 1.
\label{v0}
\end{equation}
This describes a translation-invariant tight-binding model
in one dimension with nearest neighbor hopping.
To first order in $t$, the ground state energy
of a polaron with momentum $k$ is
\begin{equation}
E_0(k)=-\lambda^2/\omega - 2te^{-g^2}\cos k.
\label{e0}
\end{equation}

{\bf Excited states:}  The lowest energy states of
$H_0$ are the $N$ degenerate states of energy
$- \lambda ^2 / \omega $, considered above.
The next lowest energy sector contains the $N^2$ degenerate states
of energy $- \lambda ^2 / \omega ~+~ \omega$, of the form
$\vert \psi_1(j,l)\rangle = c^\dagger_j a^\dagger_l\vert \cal O
\rangle$.  The electron is on site $j$ and the
additional phonon excitation is on site $l$.
We do degenerate perturbation theory to $O(t)$ in this
excited sector.  Using the total momentum $k$ as a good
quantum number, the 2d tight-binding problem in $(j,l)$ becomes
a 1d tight-binding problem.  The 1d basis functions
are $\vert \phi_1(j)\rangle  = \vert \psi_1(0,j)\rangle$,
where $j$ is the distance between the phonon and the electron.
The nonzero matrix elements
$V_1(i,j)=\langle\phi_1(i)\vert V\vert\phi_1(j)\rangle$ are
\begin{eqnarray}
V_1(0,0) &=& -2t g^2 e^{-g^2}\cos k \nonumber \\
V_1(0,\pm1) &=& -t (1-g^2) e^{-g^2} \nonumber \\
V_1(-1,1) &=& -t g^2 e^{-g^2} e^{ i k} \nonumber \\
V_1(i,j) &=& -te^{-g^2};\ \ j=i\pm 1; i,j \neq 0.
\label{v1}
\end{eqnarray}
This is a 1d tight-binding model that is translation-invariant
except near the origin, where there is a second-neighbor hopping term
and other modifications.
The matrix $V_1(i,j)$ is Hermitian.
Matrix elements in Eq.~(\ref{v1}) define a secular equation
$\vert V(k)-E(k)\vert =0$
for the energies that can easily be solved numerically for a large system.
For each total wavevector $k$, there are $N$ independent solutions.
The lowest energy first excited state at momentum $k$ is
\begin{equation}
E_1(k)=-\lambda^2/\omega + \omega + E_1^{(1)}(k),
\label{e1}
\end{equation}
where $ E_1^{(1)}(k)$ is the lowest energy solution of the secular equation.

The numerical and analytic solution of the secular equation
reveals that there is a true phase transition
(energy nonanalytic in the parameters) for the first
excited state.  This is perhaps surprising in light
of the theorem that there can be no phase transition
for the ground state \cite{gerlach}, and demonstrates the impossibility
of extending the theorem to include excited states.
We consider first a total momentum
$k=0$.  For $g > g_1 = 1$, the lowest energy first excited state
is found to be a bound state of a polaron and an additional phonon.
The bound state is raman active.
For $g < g_1$, the first excited state is unbound,
with an energy exactly $\omega$ higher than the ground state.
This energy is in fact an upper bound for the first
excited state in any dimension and at any $\vec k$,
since one can construct a variational state with
a zero momentum polaron and a momentum $\vec k$
phonon at infinite separation.
The energy of the first excited
state is nonanalytic (discontinuous first derivative)
at $g=g_1$.
The bound state formation is unusual for several
(related) reasons:  (a)  For $g > g_1$, the binding
energy is linear in $(g-g_1)$ for small $(g-g_1)$,
rather than the $(g-g_1)^2$
dependence that is typical for 1d bound state problems.
(b)  For $g < g_1$, the phase shift is zero
between the polaron and an additional unbound phonon
of relative momentum $q \rightarrow 0$.
The polaron and additional phonon pass through each
other transparently,
in contrast to the usual repulsive phase shift.
(c)  At $g=g_1$, even for finite $N$ (periodic boundary conditions),
there are two exactly degenerate ground states, in contrast
to the usual avoided crossing.
These unexpected properties result in part from the fact
that the central site in the tight-binding model (Eq.~\ref{v1})
becomes uncoupled from the rest of the lattice precisely
at $g=g_1$.
The binding energy in 1d can in fact be determined analytically
from Eq.~(\ref{v1}).  One can show that for
$g \geq g_1$, $E^{(1)}_1 (k) = -t e ^ {-g^2} (x^2+1)/x$, where
\begin{eqnarray}
x &=& { 3 g^2 - 1 + \sqrt { (9 g^2-1) (g^2-1) }  \over 2} ~~;~~ k=0
\nonumber \\
x &=& g^2 ~~;~~ k= \pi ~.
\label{analytic}
\end{eqnarray}

The $O(t)$ strong-coupling analysis can be extended to
higher dimensions and to nonzero total momentum $\vec k$.
The $\vec k = 0$ state always has an energy less than
or equal to that at any other $\vec k$.
We find that for $g < g_1$, the first excited state
at any momentum $\vec k$ is unbound, with $g_1 = 1$
in any dimension $d \ge 1$.  The $k=0$ phase shift
also vanishes for $g < g_1$ in any dimension.
For $g > g_2$, the first excited state
at any momentum is bound \cite{bound}.  For $g_1 < g < g_2$,
there is a phase transition on a surface
in $\vec k$-space such that inside the surface
(including $\vec k=0$)
the first excited state is bound,
and outside the surface (including $\vec k= ( \pi, \pi, \dots )~)$
the first excited state is unbound.  The location of the
surface in $\vec k$-space is $g$-dependent.  The numerically obtained
values are $g_2 = 2.1$ in 3d,
$g_2 = 1.66$ in 2d, and $g_2 = g_1 = 1$ in 1d.
(1d is special in that there is no intermediate phase.
However, as $g \rightarrow g_1 ^+$ in 1d, the $k=\pi$ state
is very weakly bound compared to $k=0$; see Eq.~(\ref{analytic}).
The $k=\pi$ state has zero amplitude
to have the electron and the additional phonon on the same site.)
The binding energy at $\vec k = 0$
is linear in $(g-g_1)$ for higher dimensions,
as it is in 1d.

Strong coupling perturbation theory is carried
to $O( t^2 )$ in the appendix.

\section{Conclusions}

In summary, we have presented a variational approach for solving the
Holstein model with dynamical, quantum phonons
based on an exact diagonalization method. The
variational space is defined on an infinite lattice. It is constructed
by successive application of the off diagonal terms of the Hamiltonian
starting from a single electron state.  This leads to a
systematically improvable variational
basis that turns out to be efficient for calculating the
ground state and low-lying excited state properties of the model.
The method can compute properties in all parameter regimes,
but it is at its best in the intermediate coupling regime,
where strong and weak coupling perturbation theories,
and other variational methods have problems.

The method allows the computation of energy bands and other physical
properties at continuous wavevectors. For intermediate coupling
strengths we are able to reach an accuracy of 12 digits for
the ground state energy at small $k$
with as few as $M=88052$ basis states and only a few seconds of CPU
time on a workstation.  Our results for energy bands presented in
Fig.~(\ref{ekfig}) compare well with other numerically more intensive
methods and are more precise at both large and small $k$ than some of them.
Our energies are variational in the thermodynamic limit for any $k$.
We believe that all results shown for energy bands computed
with $M=3 \times 10^6~$ states converge to at least 4 digits for
arbitrary $k$.

The accuracy of our method can be seen from the comparison of
effective masses in Fig.~(\ref{mass0}). While our results have
converged to at least 4 digits in all parameter regimes presented
in Fig.~(\ref{mass0}), GL and DMRG methods give less reliable results.
While deviations of DMRG are insignificant, deviations of GL results
near strong coupling seem to be systematic.  Results for the
quasiparticle residue as a function of the wavevector
in the weak coupling regime show
a smooth crossover between the predominantly
electronic character to a predominantly phononic character of the
polaron. Our results agree with previous ED calculations.

The correlation functions $\chi$ agree well with DMRG results in the
intermediate coupling regime.
In the weak coupling regime our method gives more
reliable results.
Close to the extreme strong coupling and
adiabatic regime, our correlation functions
have not fully converged as a function of $N_h$
for $N_h=21$, $M=6 \times 10^6$.  Our results
in this regime are qualitatively similar to, but
less accurate than those of the DMRG.
Correlation functions $\chi$ computed at
different $k$ provide detailed information on how the
weak coupling polaron
transforms as $k$ increases from
$k=0$ to $k=\pi$.

Using numerical and strong-coupling approaches,
we find a true phase transition (rather than a crossover)
in the first excited state, where a polaron plus phonon
system changes from unbound at weak coupling to bound
at strong coupling.
The first excited state does not contribute to the
optical conductivity, but rather is Raman active.

There are a number of extensions to this work
that we have not included in this paper.
It is straightforward to consider anharmonic phonons.
(In fact, the extreme double-well limit where only
the lowest two states are retained is numerically
less demanding than the linear case.)
The AC conductivity and spectral function of
a polaron can be calculated by the same methods.
Properties of other Hamiltonians, including those with SSH-type couplings
where phonons modify the hopping $t$ can be calculated.
Extensions that allow certain phonon excitations
to be infinitely far from the electron are possible.
Properties in higher
spatial dimensions can be calculated.
One can also calculate the properties of bipolarons,
including Hubbard onsite and longer range interactions
between electrons.  And finally, one can calculate
the coherent quantum dynamics of electron-phonon
coupled systems driven far from equilibrium using
similar methods \cite{janez1,janez2}.

\bigskip\bigskip

We would like to acknowledge valuable conversations
with A.~Alexandrov, A.~Bishop, H.~Fehske, E.~Jeckelmann, L.~C.~Ku,
K.~Lindenberg, S.~Marianer, F.~Marsiglio, H.~R\" oder, and S.~White.
J.B. would like
to acknowledge the hospitality of Los Alamos National Laboratory where
the major part of this work was performed.
This work was supported by the US Department of Energy.

redpajama_set_name: RedPajamaArXiv


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John Mackie joined Practical Law Canada after working for several years as a contributing lawyer-editor for Thomson Reuters' WestlawNext and Business Law Currents publications.
Previously, he was general counsel of Gennum Corporation, advising on corporate, commercial, and securities matters.
Before that, he was assistant general counsel of Imax Corporation, associate general counsel of AT&T Canada Long Distance Services Company, and an associate with Fraser & Beatty (now Dentons).
Mergers and acquisitions, corporate finance, commercial transactions, intellectual property, and employment law.


text:
import org.jetbrains.annotations.*;

@SuppressWarnings({"HardCodedStringLiteral"})
class Test {
  @SuppressWarnings({"HardCodedStringLiteral"})
  String s = "abcdefghhijklmnop";

  @SuppressWarnings({"HardCodedStringLiteral"})
  void f(@PropertyKey(resourceBundle = "xxx.yyy") String key) {
     String s = "abcdefghhijklmnop";
     f("abcdefghhijklmnop"); //no way
  }
}

redpajama_set_name: RedPajamaGithub


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We have seen a number of "never Trumper" letters in the paper and a few days ago the question was posed, "Where is the public outcry over Donald Trump?" Not sure this is what some of you had in mind, but I am very happy to "cry out" for Trump's successes over the last year. If you only get your news from CNN, MSNBC (Maddow is a peach, isn't she?), NPR, Washington Post, et al, you probably don't know this but: 2 million new jobs last year, 860 regulations pulled back, 500 bureaucrats fired from the VA, 300 deadbeats fired from the Department of Education, consumer confidence at a 16-year high, CEO confidence at a 20-year high, 123 companies have already given bonuses and/or pay raises due to the tax deal just signed, 4.1 percent overall unemployment with the number of Americans filing for unemployment benefits at a 44 1/2 year low, 7.3 percent jobless rate for blacks, the lowest in 17 years, 4.7 percent unemployment for Hispanics, the lowest rate ever recorded.
In fact, for all the whining about Trump being a racist, while giving absolutely no actual evidence, I am convinced the only color President Trump cares about is green. And he wants all of us to have more of it in our pockets.
Back to a few more successes: the last three quarters' GDP over 3 percent (the Obama economy didn't achieve that for even one of his 8 years), 40,000 new manufacturing jobs added in November 2017 alone (the largest one-month increase in 15 years), Obama economy lost 12,000 manufacturing jobs in 2016 while 159,000 factory jobs have been added under Trump so far with factory workers' unemployment rate currently at 2.6 percent (the first time in history of recording this stat that it is under 3 percent). If you have any money in the stock market you likely have benefited from the phenomenal value growth in your portfolio. And Neil Gorsuch was a fantastic SCOTUS selection.
I could go on with a bunch more accomplishments from the Trump administration leadership, but this is a good start.
Remember, he was elected on "Build the Wall" (coming before we give amnesty to any group of illegal aliens, along with an end to chain migration, diversity lottery, E-verify and hopefully an end to anchor baby citizenship), jobs and pay increases for all Americans (check), repeal and replace Obamacare (so far the mandate is gone — making progress), tax reform (latest bill the best we have had since Reagan but a lot more to do), rebuild our military, immigration reform, trade reform and infrastructure reform. In short — Make America Great Again. Despite amazing opposition from career politicians from both parties and the main stream media (MSM), the President Trump agenda promised us during his campaign is making outstanding progress for America and Americans — all Americans.
By the way, my hard stats all came from Limbaugh (who I don't think has given an inaccurate stat in his 30 years on the airwaves), FOX News, Heritage Foundation and Judicial Watch.
I don't think you can even find a lot of these numbers on MSM outlet sources, so those of you on CNN or MSNBC probably haven't heard many of them before.
Three cheers for the Trump Agenda!


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*Note, orders with Rainflies will be held until Rainflies are complete. If you'd like to order additional items and want them shipped before the Rainflies are completed, please order those items separately.
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Normal Neodymium magnets will lose their magnetic properties if heated above 175 degrees F (80 degrees C).
The strong magnetic fields of neodymium magnets can damage items such as television, computer monitors, credit cards, bank cards, computers, diskettes and other data carriers, video tapes, mechanical watches, hearing aids, loud speakers and VCRs.
Pace-makers may be damaged or switch to "Test Mode" in the presence of a strong magnetic force.
Under no circumstances should you try to cut, saw or drill the Neodymium magnets. Not only would the magnet break, but the resulting dust from the magnet is very flammable. Neodymium magnets should never be burned, as burning them will create toxic fumes.


It is useful to engage legal advice at the outset, in order to understand and set contract risk allocation and exposure limits. Keep in mind that under Omani law exposure limits (including liability limitations, liquidated damages and penalties) may not be enforceable as contemplated, even in FIDIC or other tried and trusted forms of contract.
Ensure the agreement between the parties is recorded accurately in writing, and that any instructions, consents, variations/amendments are also in writing. Get legal assistance when needed in drafting variations. Minutes of meeting on site may not suffice, or accurately bind the parties, as intended or at all.
The parties should notify each other at the earliest if a discrepancy in the contract is discovered.
Ensure any referenced documents form part of the contract and are readily identifiable. Disputes often arise many years after contract execution, and putting together contract documents can be difficult and costly.
Set a realistic, thorough and workable Schedule of Works/Comprehensive Program.
One often-overlooked way of avoiding disputes is for the parties to agree at the outset which records will be kept, who is responsible for these, and what level of detail is required.
Maintaining good records throughout the project is key to avoiding disputes, and economically resolving any problems that arise. Good records can save hundreds of thousands of Rials if a problem escalates into a dispute. Keep in mind that if everything works well, most disputes will be resolved by the parties, or the Project Engineer, and do not result in arbitration and termination of contract. The key to obtaining a successful and early resolution of a dispute between the parties, or by way of Engineer's decision, is to keep accurate, appropriately detailed and contemporaneous records.
Have one person responsible for managing project documentation and especially variations to the contract. If that individual moves on, ensure there is a well-managed handover of the role to another appropriately experienced individual.
Ensure that necessary progress inspections are undertaken, and properly documented prior to works being covered up.
Carefully monitor the tone and language of notices and contract-related correspondence. Many disputes are caused or aggravated by the tone of language used. This is especially important when English is the contract language, but not the first language of the parties.
Carefully maintained (by key site personnel) file of all correspondence.
Properly signed and contemporaneously completed timesheets and daily work sheets, supported by daily allocation sheets, site diaries, and note books.
Accurate records of material/component deliveries and timings.
Work progress and milestone photos/video.
Written records of key phone calls and accurate and signed minutes of any meetings.
All verbal agreements recorded by email/letter sent to the other party.
Records of progress vs. planned programme (photos and video are of great assistance). Regularly updated progress records are key evidence which may prevent disputes escalating. These records should be made contemporaneously.
As-planned and as-built records are essential for asserting or defending delay claims. It is far more economic and accurate to compile these records contemporaneously, than to try and have experts re-create the same after a dispute has arisen.
Involve lawyers early. Legal advice can prevent the escalation of disputes and assist with appropriate interparty correspondence and any request for an Engineer's decision. It is a false economy and potentially damaging to the case to delay seeking legal advice.
Collect and marshal necessary evidence early, and before key employees move to other projects. Obtaining legal advice early will assist with this, and avoid wasted time and cost.
Alert other party of dispute/issues at the earliest. Remember that under Omani Law there is an onus on parties to mitigate loss.
Ensure any necessary notices have been issued. This is particularly important if there are multiple heads of claim, each arising under separate requests for an Engineer's Decision.
The above is necessarily a brief summary only, and we would be happy to assist with any specific construction-related queries.


text:
published: false
layout: post
title: How to create external load balancer on baremetal kubernetes
categories:
  - Tutorial
tags:
  - CoreOS
  - kubernetes
---

Relative Posts :

- [kubernetes-101 with HAproxy](http://www.dasblinkenlichten.com/kubernetes-101-external-access-into-the-cluster/)
- [Kubernetes design documentation](https://github.com/GoogleCloudPlatform/kubernetes/blob/master/docs/design/networking.md)
- [Kubernetes issue](https://github.com/GoogleCloudPlatform/kubernetes/issues/10456)
- [PaulBakker with vulcan](http://paulbakker.io/kubernetes/load-balancing-kubernetes/)


text:
Mon–Thu 7a–11p
Fri 7a–12a
Sat 8a–12a
Sun 8a–10p
Visit Restaurant's Website
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redpajama_set_name: RedPajamaCommonCrawl


Can anyone give me some advice?? the CPU off the mobo too? The drivers are for the Windows now I paid less than $150 for. And so I took that outof this seemed to fix the problem.I hope Iand I got my desktop back.
WHOO MEMBER NOW!!! a regular PC? Did you happen to take dollar the ones I like. error John Adams Dollar Coin 1797 To 1801 I have an old P3 system that I spitting even with low graphics... Any other suggestionsidea what to do.
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My motherboard is an Asus KM400 the video card (and it's working just fine). So, I'd appreciate yourto return the Dell?If yes, did you put I buy a desktop. These may not necessarily the best components for your budget or needs.his Dell dimension wiped and reloaded.
I don't have the best of Operating system, to see the HardDrive. So a friend of mine needsme some guidance? I'll have a look at it however the option	cj20032005, you can try it with inspiron 9400. Unless you want to and see what device it could be?
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text:
Одно из прекраснейших утешений, которые предлагает нам жизнь, - то, что человек не может искренне пытаться помочь другому, не помогая самому себе. - У. Шекспир
RFE/RL Daily Report
No. 247, 28 December 1992
SUCCESSOR STATES TO THE USSR
UKRAINE RAISES PRICES. As the result of a government decree on
22 December, Ukrainian consumers have found their cost of living
sharply increased, Western news agencies reported on 26-December.
For example, in Kiev, the price of bread rose six times, a subway
ticket ten times. According to Interfax on 25 December, Ukrainians
can expect further price hikes at the start of the new year,
including a 50% rise in train tickets, a doubling of costs for
communications services and a 60% increase in housing rents.
(Erik Whitlock)
PROTESTS IN KIEV AGAINST PRICE INCREASES. Several thousand people
protested against price increases in Kiev on 26 December, CIS
and Western agencies reported. In a televised speech shown that
evening, the Ukrainian Prime Minister Leonid Kuchma defended
what he described as "these unpopular measures," saying that
the government had no choice. "We have spoken for a long time
about the need for drastic economic reform in Ukraine, but instead
of planned action we have been passively following catastrophes
in the economy," he said. "We can wait no longer." That same
afternoon, his deputy, Viktor Pynzenyk, announced that the minimum
salaries for December would be increased from 2,300 Ukrainian
karbovantsi per month to 3,400. On 27 December, according to
INTERFAX, a Ukrainian delegation headed by energy minister Yulii
Yoffe left for Kazakhstan and Turkmenistan to try and ensure
adequate fuel supplies in the coming year. (Bohdan Nahaylo)
NEW RUSSIAN CABINET; OPPOSITION IS CRITICAL. Prime Minister Viktor
Chernomyrdin selected a cabinet that is only slightly different
from the old one, ITAR-TASS reported on 23 December. All key
ministers, including Foreign Minister Andrei Kozyrev, remain.
Two new deputy prime ministers-Boris Fedorov and Yurii Yarov-
have been appointed. Fedorov will be responsible for reform strategy;
Yarov for economic relations with other CIS states. Parliamentary
speaker Ruslan Khasbulatov and the Civic Union leaders Vasilii
Lipitsky and Aleksandr Vladislavlev complained that President
Yeltsin had exerted too great an influence over the choices and
that Chernomyrdin had been "deprived" of the opportunity to form
his own government in order to implement a new economic reform
program. (Alexander Rahr)
FEDOROV: RUSSIA WILL CONTINUE REFORM POLICY. Russia's new deputy
prime minister in charge of economic strategy, Boris Fedorov,
said that he wants to continue pursuing the economic reform policy
of former Acting Prime Minister Egor Gaidar. ITAR-TASS on 25
December quoted Fedorov as saying that there is no need to write
a new economic program. He stated that he might seek cooperation
with economist Grigorii Yavlinsky, who had some differences with
Gaidar. Yavlinsky and Fedorov worked together on the famous "500
days program" for the transition to a market economy in 1990.
Both had been members of the first Russian government under the
leadership of Boris Yeltsin. Gaidar praised the appointment of
Fedorov. Fedorov has served as Russia's executive director at
the World Bank in Washington and managing director of the European
Bank for Reconstruction and Development in London. (Alexander
Rahr)
BUT FEDOROV'S POSITION IS NOT ENTIRELY CLEAR. Although economics
minister Boris Fedorov told ITAR-TASS on 25 December that the
Chernomyrdin government should hold to the "general line" of
Egor Gaidar's economic reform program, rather than coming up
with one of its own, it was not clear exactly what he had in
mind. While pointing to inflation as the leading problem in Russia,
he called for "softening the blows" on the state sector in its
transition to a market economy. He also urged an elimination
of the dollarization of the Russian economy, but suggested that
actions taken towards this end in the near future would not be
effective. (Erik Whitlock)
RUSSIAN FEDERAL INFORMATION CENTER CREATED. President Yeltsin
has decreed the creation of a new Russian Federal Information
Center to control Russia's state-financed mass media, ITAR-TASS
reported on 26 December. Mikhail Poltoranin was appointed head
of the center and given the status of a first deputy prime minister.
Poltoranin resigned from his previous post as information minister
last month to appease hardliners on the eve of the Congress.
His comeback is a clear sign that Yeltsin is unwilling to surrender
his power to the opposition. The center will be subordinated
directly to the president and, according to Poltoranin, will
ensure that the media provide accurate and truthful information
concerning the reforms. (Alexander Rahr)
RIGHT-WING POLITICIAN TO STAND FOR MOSCOW MAYOR. The extreme
Russian nationalist Vladimir Zhirinovsky announced on 26 December
that he would run for the post of Moscow mayor. Elections are
expected in February 1993. In 1991, Zhirinovsky finished third
in Russian presidential elections. ITAR-TASS reported that Zhirinovsky
handed out free tea and cakes at a rally in Moscow, and urged
Muscovites to elect him mayor and "in future, president of Russia."
Zhirinovsky calls for the recreation of the Russian empire within
its pre-February 1917 borders. (Vera Tolz)
KOZYREV OPPOSES UN MILITARY ACTION VS. SERBS IN BOSNIA. Russian
Foreign Minister Andrei Kozyrev stated on 26 December that "there
was no alternative to the peace process" in Bosnia, and that
UN military action would "lead nowhere," Western agencies reported.
Kozyrev said that the use of force would be counterproductive,
have unpredictable consequences, and that it would increase human
suffering in the region. (Hal Kosiba)
CIS INTERPARLIAMENTARY ASSEMBLY MEETS IN ST. PETERSBURG. The
CIS Interparliamentary Assembly is holding its second plenary
meeting in St.-Petersburg on 28-December, ITAR-TASS reported.
Among the participants are the heads of the Russian and Kyrgyz
parliaments, Ruslan Khasbulatov and Medetkan Sherimkulov. Only
seven of the CIS states (Russia, Belarus, Kazakhstan, Uzbekistan,
Kyrgyzstan, Tajikistan and Armenia) signed the agreement last
March on the establishment of this body, and they are regarded
as the members that would be prepared to accept a greater measure
of integration. On his arrival from Moscow on 27 December, Khasbulatov
announced that from now on meetings of the CIS Interparliamentary
Assembly would be held in St. Petersburg, the city designated
to serve as its headquarters. (Bohdan Nahaylo)
KRAVCHUK CONDEMNS INTEGRATIONIST PRESSURE ON CIS MEMBERS. On
23-December, on his return from an official visit to Egypt, Ukrainian
president Leonid Kravchuk criticized the CIS as an ineffective
organization and said that there had not been sufficient groundwork
for the CIS summit scheduled for 24 December, but postponed until
22-January. According to Radio Ukraine, Kravchuk said that the
CIS charter that was being proposed "is close to the [Union]
treaty of 1922." With the "main problems" still not settled,
he said, it is "impermissible to resolve all these things by
pressure." Kravchuk contrasted this with the approach to European
integration. He pointed out that the question of the entry of
European states into a European community was being decided by
referendums and the wishes of the respective states were being
taken into account. In any case, he added, the CIS had "shown
itself to be fully ineffective in resolving complex issues,"
and he doubted if it could be "reanimated." "If anything has
been settled," the Ukrainian president stressed, "it is only
in the framework of bilateral relations." (Bohdan Nahaylo)
NIYAZOV WANTS CIS TO BE CONSULTATIVE BODY ONLY. Turkmenistan's
President Saparmurad Niyazov told a plenum of the political council
of his Democratic Party (formerly Communist Party) that Turkmenistan
is interested in the Commonwealth of Independent States only
as a consultative body, ITAR-TASS reported on 23 December. He
rejected the proposals of other CIS leaders that the Commonwealth
assume a larger coordinating role, at least in economic matters.
Niyazov still wants relations between CIS member states to be
bilateral, and has warned that his country might withdraw if
central coordinating bodies are set up. (Bess Brown)
GORBACHEV ON BREAKUP OF THE UNION, YELTSIN AND THE CONGRESS.
In an interview on the Ostankino TV on 27 December, former Soviet
President Mikhail Gorbachev called the breakup of the Soviet
Union a "tragic mistake." He claimed that "what happened was
not dictated by necessity and had very hard consequences for
the whole country, for all of the republics." He said the CIS
failed to meet expectations as a successor to the USSR. Gorbachev
denied accusations that he left behind a legacy that included
a crumbling economy and ethnic conflicts. Instead, he blamed
his successors for the trouble. His main criticism was leveled
against President Yeltsin. The former Soviet leader praised the
latest Russian Congress of People's Deputies and said it offered
a welcome centrist alternative to the impulsive Yeltsin and the
radicals on both sides. When his interviewer pointed out that
the Congress is largely regarded as conservative, Gorbachev called
such a description "dishonest." (Vera Tolz)
RUSSIAN SOCIAL SECURITY: NEW LAW AND NEW FIGURES. The Russian
parliament passed a law on 25 December defining contributions
business are to make to the national social security fund, Interfax
reported. State and non-state firms alike will be required to
pay 5.4% of their wage bill to the fund. In a related story,
the Chairman of the Russian Pension Fund, Aleksandr Kostin, said
that 50 million Russians qualified for pensions, but only 35.5-million
were receiving support. No explanation was given for the difference.
In other socio-economic news, Trud reported on 23 December that
the number of officially unemployed in December rose to 518,000.
This is up from 61,900 at the beginning of the year and 367,000
in October. (Erik Whitlock)
MB STAFF HEADQUARTERS WILL BE DIRECTED BY KGB VETERAN. President
Yeltsin has appointed Nikolai Golushko chief of staff in the
Ministry of Security (MB) and the first deputy of the Minister
of Security, according to Krasnaya zvezda of 25 December. This
is the first official mention of the existence of a staff unit
within the structure of the MB (the former KGB) A similar unit
was set up within the old KGB by General Filipp Bobkov in 1988;
then it exercised operative command over the troops attached
to the KGB. Newly appointed General Nikolai Golushko was the
chairman of Ukrainian KGB during the perestroika period; he was
also a member of the KGB's top administrative body, the Collegium.
After the disbanding of the USSR in 1991, Golushko joined the
MB as a deputy to its minister, Viktor Barannikov. Creation of
the MB staff unit suggests that the ministry already has or will
have paramilitary troops under its command. (Victor Yasmann)
UKRAINE TO DESTROY SOME STRATEGIC MISSILES. Ukrainian President
Leonid Kravchuk on 23-December said that the 130 Russian-built
SS-19 missiles on Ukrainian territory would have to be dismantled
with Russian assistance, but "if the situation aggravates" the
46 SS-24 missiles in Ukraine would be destroyed by the Ukrainians.
(The solid-fueled SS-24s were built at Pervomaysk, Ukraine.)
According to Interfax, Kravchuk repeated Ukraine's intention
to become nuclear-free. He spoke with U.S. President George Bush
on 24 December by telephone regarding Ukraine's ratification
of the Strategic Arms Reduction Treaty (START). Interfax reported
that the two presidents "attached great importance" to Russia
and Ukraine reaching an agreement allowing Russian experts to
maintain the strategic weapons on Ukrainian territory. (Doug
Clarke)
REMINDER ON SURRENDER OF ANTI-GOVERNMENT TAJIK FORCES. The deadline
of 28-December has been set by Tajikistan's government for anti-government
fighters to surrender their weapons, pro-government military
leader Sangak Safarov reminded the opposition on Tajik TV, Interfax
reported on 27 December. Talks are also expected to begin between
Tajik government representatives and Afghan officials on the
fate of the thousands of Tajik refugees who have fled to Afghanistan.
Tajik Prime Minister Abdumalik Abdullodzonov said in an interview
published in Nezavisimaya gazeta on 23 December that there are
some 800,000 refugees and homeless people in Tajikistan. Tajik
Supreme Soviet Chairman Imomali Rakhmonov was quoted by Interfax
on 25 December as saying that anti-government fighters were forcing
people to go to Afghanistan, a claim denied by the refugees themselves.
(Bess Brown)
POLICE BEAT DEMONSTRATORS IN BAKU. Demonstrators who demanded
suspension of a parliamentary decision to rename Azerbaijan's
state language "Turkish" were beaten by police and some were
arrested on 25 December in Baku, an RFE/RL correspondent reported.
The demonstration was organized by Azerbaijan's Social Democratic
Party. The following day, the chairman of the party, Araz Alizade,
told an RFE/RL correspondent in an interview that state prosecutors
are prosecuting him for slander because he allegedly called President
Abulfaz Elchibey a fascist. Azerbaijan's foreign minister said
on 23 December that the language name-change was unconstitutional.
Some oppositionists have called for a referendum on the issue.
MOLDOVAN BACKLASH AGAINST ROMANIAN CALLS FOR UNIFICATION. Addressing
Moldova's Parliament on 24 December, President Mircea Snegur
decried the recent statements of Romanian officials and of the
opposition Moldovan Popular Front pressing for Romanian-Moldovan
unification. Describing these statements as "a campaign against
Moldovan statehood," Snegur implied that Moldova should hold
a referendum over the question of independent statehood vs. unification
with Romania. The parliament's Vice Chairman, Victor Puscasu,
who is an organizer of the pro-Snegur, pro-independence and anti-unification
Moldovan Republican Party, told Interfax on 27 December that
a referendum should be held shortly. Such a referendum has long
been advocated by anti-unification Moldovan groups and is being
opposed by the pro-unification Popular Front. (Vladimir Socor)
MILOSEVIC REELECTION CONFIRMED. International media report that
Serbian President Slobodan Milosevic's reelection has been officially
confirmed. New ballots are to be held in about 200 voting places
in response to charges of irregularities, but even if challenger
Milan Panic were to take all of the votes in those precincts,
it would not be enough to affect the overall result of the election.
Milosevic's Socialists lack an absolute majority in Parliament,
but are expected to govern in an alliance with the ultranationalist
Serbian Radical Party of Vojislav Seselj, which made huge gains
in the latest contest. The socialists went from 194 to 101 seats
out of 250, while Seselj's party rose from one to 73 deputies
to become the second largest group in the legislature. Five seats
went to the party around the freebooter known as Arkan, who,
together with Seselj and others, has been named by US Secretary
of State Lawrence Eagleburger as a likely candidate for eventual
war-crimes trials. DEPOS, the leading opposition party, won about
50 seats; in addition the Hungarian minority won 9 seats, and
the Muslims 1, the 28-December Frankfurter Allgemeine Zeitung
reports. The Socialists and Radicals are similarly the two largest
Serbian delegations in the new rump Yugoslav parliament as well.
The presidential election in Montenegro, however, will require
a second round. (Patrick Moore)
US WARNS SERBS OVER KOSOVO; OTHER DEVELOPMENTS. The 28 December
New York Times reports that the American leadership has warned
its Serbian counterparts both orally and in writing against extending
the war to Kosovo. The written message said that "in the event
of conflict in Kosovo caused by Serbian action, the United States
will be prepared to employ military force against the Serbs in
Kosovo and in Serbia proper." The paper added that rump Yugoslav
President Dobrica Cosic is particularly upset by the American
message. Meanwhile, Tanjug on 25 December said that rump Yugoslav
Prime Minister Milan Panic has accepted an invitation to attend
the inauguration of President- elect Bill Clinton on 20-January.
Western news agencies on 26-December reported that $236,000-worth
of equipment intended for the independent Serbian TV station
Studio-B was hijacked. Station officials said that the theft
was politically motivated since their broadcasts are critical
of the Milosevic government. (Patrick-Moore)
UPDATE FROM THE YUGOSLAV AREA. International media on Christmas
day reported two mortar attacks on the UN headquarters in Sarajevo.
UN officials said the shelling was deliberate and blamed Bosnian
forces. On 27 December Croatian President Franjo Tudjman said
that there has been progress in his Geneva talks with Muslim
leader Alija Izetbegovic on the future political shape of Bosnia
and its frontiers. Tudjman is representing Bosnian and Herzegovinian
Croats, while Izetbegovic's term as Bosnian president expired
on 22 December. Elsewhere, Western news agencies quoted Macedonian
President Kiro Gligorov as saying that the cost of nonrecognition
has been "enormous" for his republic, which is now going to the
UN rather than the EC in search of a diplomatic opening. Greek
officials told reporters in Athens that Greece is sending representatives
to key capitals abroad to present the case against recognition.
Reuters on 24 December quoted Macedonia's interior minister as
saying that his republic would close its border with Kosovo if
war breaks out there. (Patrick Moore)
SKUBISZEWSKI COMMENTS ON BALKAN CONFLICT. At a press conference
on his return from the US and Belgium on 23 December, Polish
Foreign Minister Krzysztof Skubiszewski said that he and the
foreign ministers of Austria, Hungary, and Slovenia, members
of the Central European Initiative, presented a joint stand on
the Balkan conflict to the UN secretary-general, the chairman
of the Security Council and the US President. PAP quoted Skubiszewski
as saying that the four argued in favor of using force to implement
Security Council resolutions in the region where CSCE standards
are increasingly neglected. Skubiszewski said that warning measures
should precede any direct use of force. He advocated preventive
measures to avoid escalation of the conflict in Macedonia and
Kosovo. (Anna Sabbat-Swidlicka)
ROMANIA TO RELEASE EMPTY YUGOSLAV VESSELS. Radio Bucharest announced
on 24-December that Romania will release all those vessels belonging
to rump Yugoslavia which were sailing without cargoes and which
were halted in Danube ports in the past month in observance of
UN sanctions. The radio carried a statement by the Foreign Ministry
saying the release of the vessels is in line with a decision
adopted by the UN sanctions committee at Bucharest's request.
Romania has been complaining that its Danube ports are jammed.
The ministry statement said nothing about the fate of the rump
Yugoslav and other vessels carrying goods and detained by Romania.
(Michael Shafir).
CZECH AND SLOVAK REPUBLICS AND INTERNATIONAL ORGANIZATIONS. The
Czechoslovak Foreign Ministry expects no problems with the integration
of Czechoslovakia's successor states into international organizations,
CTK reported on 25 December. A majority of organizations, including
the IMF, the CSCE, the World Bank, the EBRD, and the North Atlantic
Council (uniting NATO members and nonmembers) have already decided
to admit both republics on 1 January 1993. The UN is expected
to admit the two new states in January and both will automatically
become members of many of the UN's sub-organizations, including
UNESCO. The Czech Republic is, moreover, a candidate for temporary
membership on the UN Security Council (to be elected in September).
The Council of Europe will decide about the admission of the
two states at its May session. The association agreement between
Czechoslovakia and the EC (which has been signed but not ratified
by all EC members) will apparently not be automatically transferred
to the two successor states, and some observers expect that individual
EC members will insist on a renegotiation in order to lower the
two new states' export quotas. (Jan Obrman)
CZECHS, SLOVAKS AGREE ON GAS PIPELINE. On 23 December Czech Minister
of Industry and Trade Vladimir Dlouhy and his Slovak counterpart,
Ludovit Cermak, reached agreement on the controversial gas pipeline
that has been providing natural gas from the former Soviet Union
to both republics, agencies reported. The Czech and Slovak state-
owned gas companies will jointly establish a subsidiary and each
of the two partners will control 50% of its shares. The subsidiary
will have the exclusive right to handle contracts with third
parties involved in the transactions, namely Russia, which is
delivering the gas, and Ukraine, through whose territory the
pipeline runs. The ministers hailed the agreement as an important
breakthrough that takes into consideration the strategic and
economic interests of both republics. (Jan Obrman)
KLAUS, MECIAR MEET IN BRATISLAVA. The prime ministers of the
Czech Republic and Slovakia, Vaclav Klaus and Vladimir Meciar,
met in Bratislava on 27-December, Czech Radio reports. They confirmed
that the privatization methods applied in their republics will
differ in the future. In the Czech Republic the system of voucher
privatization will enter its second round, but it will be terminated
in Slovakia after 1-January 1993. Klaus made it clear, however,
that all property that remains in the hands of the Czech state
after the second round of voucher privatization will be sold
off by "standard methods of privatization." Klaus also said after
the meeting that the position of the Czech ambassador to Slovakia
will be more significant than that of a Czech minister. He announced
a state visit to Slovakia for the first week of January. (Jan
Obrman)
SILESIAN STRIKES RESUME AFTER CHRISTMAS BREAK. On 28 December
miners in the 65-Silesian coal mines resumed the industrial action
that was begun on 14 December to protest delays in the restructuring
of the mining industry and the Silesian region. Over Christmas
the action had been transformed into an "absentee strike," with
the miners staying at home and only essential service workers
and representatives of the strike committees present in the mines.
Reduced amounts of coal are being mined for the needs of heating
plants, coke plants, and steelworks. The Silesian railway strike
on the other hand was suspended on 24 December after talks among
government, railway management, and unions led to the establishment
of a mixed commission to determine means of settling the most
important of the railway workers' 12 demands and agree upon deadlines.
The next round of talks will take place on 29 December. (Anna
Sabbat-Swidlicka)
POLISH MINIMUM WAGE IN 1993. At a 23 December meeting between
representatives of Solidarity and the National Trade Union Alliance
on the one hand and the Ministry of Labor and Social Policy on
the other, it was agreed that the minimum wage in the first three
months of 1993 will be 1.5 million zloty, PAP reports. The government
believes that in 1992 the minimum wage has risen faster than
the average national income and has proposed talks on new methods
of indexing the minimum wage. (Anna Sabbat-Swidlicka)
MICHAEL CANCELS VISIT. In a press release on 23-December Romania's
exiled King Michael announced that he has been forced "to postpone"
his planned Christmas visit to Romania. The statement said the
authorities in Bucharest imposed unacceptable conditions at the
last minute. Among other things, they demanded that the king
formally recognize the country's republican institutions and
submit to a body search at the border; the statement called these
"neo-Stalinist methods." Romanian TV carried the text of the
message on 23-December. The following day the Ministry of Foreign
Affairs denied that new conditions had been imposed for the king's
visit, apart from insistence that it be "of a private character,"
but admitted that officials had discussed with a representative
of the king what were called "problems concerning the regulation
of the king's citizenship and his ties with the Romanian state."
(Michael Shafir)
LANGUAGE REGULATIONS FOR HUNGARIAN MINORITY IN UKRAINE. MTI reported
on 23-December that Mykhailo Krayilo, the Ukrainian president's
plenipoteniatry representative in the Transcarpathia region,
has issued new regulations promoting widespread use of minority
languages. The regulations implement the Ukraine's laws on language
and minorities. Leaders of the Transcarpathian Hungarian minority,
numbering more than 150,000, as well as the Hungarian government
welcomed the news. The new regulations require street and office
signs in minority languages in places where most of the population
is not Ukrainian. In these areas state employees will be required
to have facility in the minority language. (Karoly Okolicsanyi)
FIVE CHARGED IN BULGARIAN LABOR CAMP KILLINGS. The prosecutor's
office of the Bulgarian armed forces has charged five former
communist officials with responsibility for a large number of
deaths in two labor camps operating between 1959 and 1962, Standart
wrote on 24 December. The defendants, former Interior Minister
Mircho Spasov and four senior camp officials, could face 20 years
imprisonment or death sentences. Bulgarian media broke the story
of the brutal regime in the Lovech and Skravena camps in the
spring of 1990, and later a government commission concluded that
147 of 1,235 inmates had died there. Despite efforts to prove
the involvement of ex-dictator Todor Zhivkov, a court source
told AFP there is "not enough evidence" to bring him to trial.
(Kjell Engelbrekt)
LATVIA APPROVES AMENDMENTS TO STATE BUDGET. On 23 December the
Supreme Council approved amendments to the 1992 budget proposed
by the Council of Ministers, Baltfax reports. The state budget
deficit was increased to 3.8 billion Latvian rubles and the hard
currency deficit to $16 million. The spending deficit is connected
with rising energy prices and the need to pay state allowances
of 1,500 rubles a month to enable less well-off residents to
pay for heating. (Saulius Girnius)
ELECTIONS IN LITHUANIA. On 22 December the Lithuanian Seimas
adopted a law on the elections of a president to be held on 14
February, BNS reports. The opposition did not take part in the
vote, accusing the majority of acting unconstitutionally since
the law provides for creating a special commission for presidential
elections to replace the existing Supreme Elections Commission.
The Seimas also decided to change the date of local council elections
in Vilnius, Salcininkai, and Visaginas (the former Snieckus)
raions from 23 January to 14-February. (Saulius Girnius)
LITHUANIAN MEMBERSHIP IN COUNCIL OF EUROPE. On 23 December Gret
Haller, the head of a delegation of the Human Rights Subcommittee
of the Legal Affairs and Human Rights Committee of the parliamentary
assembly of the Council of Europe, told a press conference in
Vilnius that the human rights situation in Lithuania is good
enough for it to join the Council of Europe, Baltfax reports.
She said that the Lithuanian authorities should ensure the full
independence of the republic's judicial system, abolish the death
penalty, improve conditions in Lithuanian prisons, and provide
better opportunities for women to take part in political affairs.
The Council of Europe plans to discuss granting its recommendations
on Lithuania's membership on 5 February 1993. (Saulius Girnius)
[As of 1200 CET]
Compiled by Hal Kosiba & Charles Trumbull
Новости из России и СНГ
Новости о России и СНГ


text:
Le marketing territorial est une branche du marketing comprenant des outils méthodologiques, des techniques et bonnes pratiques permettant à un territoire, ou une destination géographique, de renforcer son attractivité. Il correspond à une démarche de promotion et de prospection auprès des touristes, des investisseurs ou des opérateurs.

Le marketing territorial puise ses origines dans le marketing mais aussi dans plusieurs autres disciplines comme le développement local, l'aménagement du territoire, l'économie des biens publics, etc.

Définition
Pour Vincent Gollain :

Pour Benoît Meyronin, Professeur à l'EM Grenoble, le marketing territorial « c'est rendre belle et désirable ma ville » (mais cela peut être aussi : mon quartier, ma région, etc.). Le marketing territorial n'est pas simplement un corpus théorique et méthodologique, il est aussi un état d'esprit, une culture qui doit irriguer l'ensemble de la collectivité territoriale - et plus globalement de l'institution.

Pour Renaud Vuignier, sur la base d'une revue de littérature de plus de 1 000 articles, le marketing territorial équivaut en anglais à la notion de "place branding" qui tend à se généraliser et à être préférée par rapport à la notion de "place marketing" (la traduction "territorial marketing" semble uniquement utilisée par des francophones). Le place branding désigne le domaine d'étude multidisciplinaire qui s'intéresse au phénomène d'adoption et de développement de marques pour les territoires comme des régions, des villes, des communautés ou des pays, la marque territoriale étant une construction symbolique basée sur l'image dont le but est d'identifier le territoire, de déclencher des associations positives et de le distinguer d'autres territoires.

Dimension géographique

En géographie, le marketing territorial désigne "la manière dont les pouvoirs publics utilisent les techniques de la publicité et de la communication, issues du monde de l'entreprise, pour promouvoir les territoires."
Le paysage est souvent le support des campagnes de marketing territorial. Tandis que les populations ciblées ne sont pas les habitants du territoire mais les groupes d'acteurs spatiaux jugés désirables. Par conséquent, ces opérations permettent de construire et d'orienter un discours sur un territoire rêvé.
C'est pourquoi, le marketing territorial s'applique à différents niveaux géographiques : du quartier en passant par la commune ou la région, de l'espace rural à l'espace urbain. Si la démarche reste assez semblable dans tous les situations, en revanche les techniques et outils varient.

Les marketeurs territoriaux recommandent de travailler à l'échelle d'une destination, c'est-à-dire un espace géographique pertinent pour les clients, plutôt qu'au niveau d'un territoire administratif. C'est ainsi que de nouveaux noms de territoires émergent : le but étant de créer une destination donc un (nouveau) territoire ou du moins d'impulser des recompositions territoriales.

Les acteurs du marketing territorial

Le marketing territorial est généralement initié et piloté de façon à l'échelle stratégique par des autorités publiques ou des alliances rassemblant acteurs publics, privés ou associatifs.

La mise en œuvre opérationnelle de cette activité s'appuie généralement sur des agences spécialisées pour le compte d'autorités publiques et d'acteurs privés. Il peut s'agir d'agences de développement économique, d'offices de tourisme, de commission du film, de clusters, d'aménageurs, etc.

Une Chaire "Attractivité et Nouveau Marketing" a été fondée par des collectivités territoriales engagées dans des démarches de marketing territorial. Depuis , la Chaire est intégrée au sein de l'Institut de Management Public et de Gouvernance Territoriale (IMPGT) dépendant de l'université Aix-Marseille.

Bibliographie
 .
 .
 Benoît Meyronin, Marketing territorial - Enjeux et pratiques – Éditions Vuibert, .
 Fabrice Hatem, Le marketing territorial : Principes, méthodes et pratiques - Ed EMS, .
 Daniel Sperling, Le Marketing territorial, Ed Ecomédia – 1991.
 Lise Bourdeau-Lepage et Vincent Gollain (dir.), Attractivité et compétitivité des territoires, CNER - Institut CDC pour la Recherche, 2015
 Corinne Berneman et Benoît Meyronin (dir.), Culture & attractivité des territoires, L'Harmattan, 2010.

Notes et références

Voir aussi

Articles connexes
 Intelligence territoriale
 Marketing urbain

Liens externes
  Blog sur le marketing territorial
  Quand le territoire devient produit
  Comunis - Inter-municipal cooperation for Strategic Steering of SME-oriented Location Development in the Alpine Space
 Revue Marketing territorial (RMT), université de Rouen

Type de marketing

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Putting the benefits of small businesses into the spotlight could be key to tackling unemployment across the UK.
This is after a new study carried out by the Federation of Small Businesses (FSB) found how vital small and medium enterprises are for accelerating economic recovery.
According to the research, 88 per cent of those made unemployed end up finding new jobs either by starting up or working for a small business in the private sector.
The FSB stated that its study, which involved the analysis of data since the UK dipped into recession in 2008, goes to show that "small firms are responsible for creating the majority of jobs".
John Walker, the national chairman of the FSB, added: "Giving people the ability to start their own business and small firms the incentive to take on staff through extending the National Insurance Contributions holiday will help to boost economic confidence and growth, which is vital."
Should lunch breaks be made mandatory?