pinecone/core-2020-05-10-deduplication huggingface dataset:
Mesoscopic Systems With Fixed Number of Electrons

In this paper, we study the physics of mesoscopic systems with
noninteracting, but fixed number of electrons. From a technical point of view,
this means a discussion of the differences between the canonical and the grand
canonical ensemble (fixed versus fluctuating number of particles). Such a
discussion is not trivial since the grand canonical ensemble is the most
convenient basis for the statistics of identical particles and one has to spend
labour in order to retrieve the canonical ensemble. Specifically, we are
considering ensembles of mesoscopic systems with disorder, either by atomic
defects or by fluctuations in their geometric definitions and we discuss
various forms of disorder averages.Comment: 34 pages, revtex, 1 (postscript) figur
Event-Enhanced Quantum Theory And Piecewise Deterministic Dynamics

The standard formalism of quantum theory is enhanced and definite meaning is
given to the concepts of experiment, measurement and event. Within this
approach one obtains a uniquely defined piecewise deterministic algorithm
generating quantum jumps, classical events and histories of single quantum
objects. The wave-function Monte Carlo method of Quantum Optics is generalized
and promoted to the level of a fundamental process generating all the real
events in Nature. The already worked out applications include SQUID-tank model
and generalized cloud chamber model with GRW spontaneous localization as a
particular case. Differences between the present approach and quantum
measurement theories based on environment induced master equations are
stressed. Questions: what is classical, what is time, and what are observers
are addressed. Possible applications of the new approach are suggested, among
them connection between the stochastic commutative geometry and
Connes'noncommutative formulation of the Standard Model, as well as potential
applications to the theory and practice of quantum computers.Comment: 10 pages, twocolumn, REVTE
Topological Investigation of the Fractionally Quantized Hall
  Conductivity

Using the fiber bundle concept developed in geometry and topology, the
fractionally quantized Hall conductivity is discussed in the relevant
many--particle configuration space. Electron-magnetic field and
electron-electron interactions under FQHE conditions are treated as functional
connections over the torus, the torus being the underlying two-dimensional
manifold. Relations to the $(2+1)$--dimensional Chern--Simons theory are
indicated. The conductivity being a topological invariant is given as
$\frac{e^2}{h}$ times a linking number which is the quotient of the winding
numbers of the self-consistent field and the magnetic field, respectively. Odd
denominators are explained by the two spin structures which have been
considered for the FQHE correlated electron system.Comment: LaTeX-file with psfig 1.
Zero and Finite Temperature Phase Diagram of the Spinless Fermion Model
  in Infinite Dimensions

The phase diagram of the model of spinless fermions with repulsive nearest
neighbour interaction is calculated analytically on a hypercubic lattice in
infinite dimensions $(d\to \infty)$. In spite of its simplicity the model
displays a rich phase diagram depending on the doping $\delta$, the interaction
$U$ and the temperature $T$. The system can be in the homogeneous phase (HOM),
the nonsegregated AB charge density wave (AB-CDW), the AB phase separation
region (PS-AB/HOM; coexistence of AB-CDW and HOM), the incommensurate phase
(IP) or the IP phase separation region (PS-AB/IP; coexistence of AB-CDW and
IP). We identify three important values of the interaction $U_{IPL}=0.572<
U_{IPH}=1.914<U_{IP/PS}=4.212$ which distinguish four intervals of $U$. These
imply four different types of phase diagrams. In all the three phase diagrams
with $U$ below $U_{IP/PS}$ the IP appears. We propose a {\em new} general
ansatz for the order parameter of this phase. A competition between the IP, the
PS-AB/IP and the PS-AB/HOM is found. The relevance of our findings for the
phase scenario of the Hubbard model is shown.Comment: 26 pages, latex, uuencoded compressed postscript files, 11 figures
  included; accepted by Annalen der Physik, Heidelberg; key words:
  incommensurate phases, CDW, infinite dimension
Driven Interface Depinning in a Disordered Medium

The dynamics of a driven interface in a medium with random pinning forces is
analyzed. The interface undergoes a depinning transition where the order
parameter is the interface velocity $v$, which increases as $v \sim
(F-F_c)^\theta$ for driving forces $F$ close to its threshold value $F_c$. We
consider a Langevin-type equation which is expected to be valid close to the
depinning transition of an interface in a statistically isotropic medium. By a
functional renormalization group scheme the critical exponents characterizing
the depinning transition are obtained to the first order in $\epsilon=4-D>0$,
where $D$ is the interface dimension. The main results were published earlier
[T. Nattermann et al., J. Phys. II France {\bf 2} (1992) 1483]. Here, we
present details of the perturbative calculation and of the derivation of the
functional flow equation for the random-force correlator. The fixed point
function of the correlator has a cusp singularity which is related to a finite
value of the threshold $F_c$, similar to the mean field theory. We also present
extensive numerical simulations and compare them with our analytical results
for the critical exponents. For $\epsilon =1$ the numerical and analytical
results deviate from each other by only a few percent. The deviations in lower
dimensions $\epsilon = 2,3$ are larger and suggest that the roughness exponent
is somewhat larger than the value $\zeta = \epsilon / 3$ of an interface in
thermal equilibrium.Comment: 32 pages, 14 figures, REVTeX, to be published in Annalen der Physi
Low temperature equilibrium correlation functions in dissipative quantum
  systems

We introduce a new theoretical approach to dissipative quantum systems. By
means of a continuous sequence of infinitesimal unitary transformations, we
decouple the small quantum system that one is interested in from its
thermodynamically large environment. This yields a trivial final transformed
Hamiltonian. Dissipation enters through the observation that generically
observables ``decay'' completely under these unitary transformations, i.e. are
completely transformed into other terms. As a nontrivial example the spin-boson
model is discussed in some detail. For the super-Ohmic bath we obtain a very
satisfactory description of short, intermediate and long time scales at small
temperatures. This can be tested from the generalized Shiba-relation that is
fulfilled within numerical errors.Comment: 38 pages, LaTeX2e, seven postscript figures included, figure 8 is
  available on request from one of the authors (A.M.). The revised version
  contains minor changes, it will appear in this form in Ann. Physik (Leipzig)
  199
Universal Elementary Constituents of Potential Transformations Shifting
  Waves (Qualitative Theory)

It is shown that the potential perturbation that shifts a chosen standing
wave in space is a block of potential barrier and well for every wave bump
between neighbouring knots. The algorithms shifting the range of the primary
localization of a chosen bound state in a potential well of finite width are as
well applicable to the scattering functions if states of the continuous
spectrum are considered as bound states normalized to unity but distributed on
an infinite interval with vanishing density. The potential perturbations of the
same type on the half-axis concentrate the scattering wave at the origin, thus
creating a bound state embedded into the continuous spectrum (zero width
resonance). It is an improved version of paper: Annalen der Physik, 6 (1997)
136.Comment: 11 pages, 5 figure
A unified treatment of Ising model magnetizations

We show how the spontaneous bulk, surface and corner magnetizations in the
square lattice Ising model can all be obtained within one approach. The method
is based on functional equations which follow from the properties of corner
transfer matrices and vertex operators and which can be derived graphically. In
all cases, exact analytical expressions for general anisotropy are obtained.
Known results, including several for which only numerical computation was
previously possible, are verified and new results related to general anisotropy
and corner angles are obtained.Comment: Plain Tex, 30 pages, 21 figures in eps format. Revised for
  publication in Annalen der Physi
Similarity renormalization of the electron--phonon coupling

We study the problem of the phonon-induced electron-electron interaction in a
solid. Starting with a Hamiltonian that contains an electron-phonon
interaction, we perform a similarity renormalization transformation to
calculate an effective Hamiltonian. Using this transformation singularities due
to degeneracies are avoided explicitely. The effective interactions are
calculated to second order in the electron-phonon coupling. It is shown that
the effective interaction between two electrons forming a Cooper pair is
attractive in the whole parameter space. For a simple Einstein model we
calculate the renormalization of the electronic energies and the critical
temperature of superconductivity.Comment: 17 pages, LaTeX2e, uses AMS-fonts, 5 ps-figures included. Replaced by
  a completely revised version that contains several new results on the
  renormalization of single particle energies, on the superconducting gap, and
  on the critical temperatur
Traffic flow models with 'slow-to-start' rules

We investigate two models for traffic flow with modified acceleration
('slow-to-start') rules. Even in the simplest case $v_{max}=1$ these rules
break the 'particle-hole` symmetry of the model. We determine the fundamental
diagram (flow-density relationship) using the so-called car-oriented mean-field
approach (COMF) which yields the exact solution of the basic model with
$v_{max}=1$. Here we find that this is no longer true for the models with
modified acceleration rules, but the results are still in good agreement with
simulations. We also compare the effects of the two different slow-to-start
rules and discuss their relevance for real traffic. In addition, in one of
these models we find a new phase transition to a completely jammed state.Comment: Latex, 15 pages, 6 ps-figure
Non-linear conductivity of charge-density-wave systems

We consider the problem of sliding motion of a charge-density-wave subject to
static disorder within an elastic medium model. Starting with a
field-theoretical formulation, which allows exact disorder averaging, we
propose a self-consistent approximation scheme to obtain results beyond the
standard large-velocity expansion. Explicit calculations are carried out in
three spatial dimensions. For the conductivity, we find a strong-coupling
regime at electrical fields just above the pinning threshold. Phase and
velocity correlation functions scale differently from the high-field regime,
and static phase correlations converge to the pinned-phase behaviour. The
sliding charge-density-wave is accompanied by narrow-band noise.Comment: 16 pages, 6 figure
Exact solutions to the time-dependent supersymmetric muliphoton
  Jaynes-Cummings model and the Chiao-Wu model

By using both the Lewis-Riesenfeld invariant theory and the invariant-related
unitary transformation formulation, the present paper obtains the exact
solutions to the time-dependent supersymmetric two-level multiphoton
Jaynes-Cummings model and the Chiao-Wu model that describes the propagation of
a photon inside the optical fiber. On the basis of the fact that the two-level
multiphoton Jaynes-Cummings model possesses the supersymmetric structure, an
invariant is constructed in terms of the supersymmetric generators by working
in the sub-Hilbert-space corresponding to a particular eigenvalue of the
conserved supersymmetric generators (i.e., the time-independent invariant). By
constructing the effective Hamiltonian that describes the interaction of the
photon with the medium of the optical fiber, it is further verified that the
particular solution to the Schr\"{o}dinger equation is the eigenfunction of the
second-quantized momentum operator of photons field. This, therefore, means
that the explicit expression (rather than the hidden form that involves the
chronological product) for the time-evolution operator of wave function is
obtained by means of the invariant theories.Comment: 14 pages, Latex. This is a revised version of the published paper:
  Shen J Q, Zhu H Y 2003 Ann. Phys.(Leipzig) Vol.12 p.131-14
Weakly nonlocal irreversible thermodynamics

Weakly nonlocal thermodynamic theories are critically revisited. A
relocalized, irreversible thermodynamic theory of nonlocal phenomena is given,
based on a modified form of the entropy current and new kind of internal
variables, the so called current multipliers. The treatment is restricted to
deal with nonlocality connected to dynamic thermodynamic variables. Several
classical equations are derived, including Guyer-Krumhansl, Ginzburg-Landau and
Cahn-Hilliard type equations.Comment: 30 pages, no figure
Hubbard Hamiltonian in the dimer representation. Large U limit

We formulate the Hubbard model for the simple cubic lattice in the
representation of interacting dimers applying the exact solution of the dimer
problem. By eliminating from the considerations unoccupied dimer energy levels
in the large U limit (it is the only assumption) we analytically derive the
Hubbard Hamiltonian for the dimer (analogous to the well-known t-J model), as
well as, the Hubbard Hamiltonian for the crystal as a whole by means of the
projection technique. Using this approach we can better visualize the
complexity of the model, so deeply hidden in its original form. The resulting
Hamiltonian is a mixture of many multiple ferromagnetic, antiferromagnetic and
more exotic interactions competing one with another. The interplay between
different competitive interactions has a decisive influence on the resulting
thermodynamic properties of the model, depending on temperature, model
parameters and assumed average number of electrons per lattice site. A
simplified form of the derived Hamiltonian can be obtained using additionally
Taylor expansion with respect to $x=\frac{t}{U}$ (t-hopping integral between
nearest neighbours, U-Coulomb repulsion). As an example, we present the
expansion including all terms proportional to t and to $\frac{t^2}U$ and we
reproduce the exact form of the Hubbard Hamiltonian in the limit $U\to \infty
$. The nonperturbative approach, presented in this paper, can, in principle, be
applied to clusters of any size, as well as, to another types of model
Hamiltonians.Comment: 26 pages, 1 figure, LaTeX; added reference
Radion-induced gravitational wave oscillations and their phenomenology

We discuss the theory and phenomenology of the interplay between the massless
graviton and its massive Kaluza-Klein modes in the Randall-Sundrum two-brane
model. The equations of motion of the transverse traceless degrees of freedom
are derived by means of a Green function approach as well as from an effective
nonlocal action. The second procedure clarifies the extraction of the particle
content from the nonlocal action and the issue of its diagonalization. The
situation discussed is generic for the treatment of two-brane models if the
on-brane fields are used as the dynamical degrees of freedom. The mixing of the
effective graviton modes of the localized action can be interpreted as
radion-induced gravitational-wave oscillations, a classical analogy to meson
and neutrino oscillations. We show that these oscillations arising in
M-theory-motivated braneworld setups could lead to effects detectable by
gravitational-wave interferometers. The implications of this effect for models
with ultra-light gravitons are discussed.Comment: 27 pages, to appear in Annalen Phy
Influence of surface roughness on subdominant pairing in d-wave
  superconductors

We study a d-wave superconductor with dominant $d_{x^2-y^2}$-wave order
parameter and subdominant pairing in either the $s$- or the $d_{xy}$-wave
channel near a surface. In particular we analyze the influence of surface
roughness on the mixed order parameter which may break the time-reversal
symmetry. We find that the subdominant component is suppressed by the roughness
independent of its pairing symmetry; for very rough surfaces the subdominant
component may even vanish completely. Additionally we discuss a possible
real-valued admixture which counteracts the suppression of the
$d_{x^2-y^2}$-wave order parameter at the surface.Comment: 8 pages, 6 figures, 1 table; minor changes to published versio
Mirages, anti-mirages, and further surprises in quantum corrals with
  non-magnetic impurities

We investigate the local density of states (LDOS) for non-interacting
electrons in a hard wall ellipse in the presence of a single non-magnetic
scattering center. Using a T-matrix analysis we calculate the local Green's
function and observe a variety of quantum mirage effects for different impurity
positions. Locating the impurity near positions with LDOS maxima for the
impurity free corral can either lead to a reduction or an enhancement of the
LDOS at the mirror image point, i.e. a mirage or anti-mirage effect, or even
suppress LDOS maxima in the entire area of the corral.Comment: 6 pages, 7 figure
Quasiclassical theory of charge transport in disordered interacting
  electron systems

We consider the corrections to the Boltzmann theory of electrical transport
arising from the Coulomb interaction in disordered conductors. In this article
the theory is formulated in terms of quasiclassical Green's functions. We
demonstrate that the formalism is equivalent to the conventional diagrammatic
technique by deriving the well-known Altshuler-Aronov corrections to the
conductivity. Compared to the conventional approach, the quasiclassical theory
has the advantage of being closer to the Boltzmann theory, and also allows
description of interaction effects in the transport across interfaces, as well
as non-equilibrium phenomena in the same theoretical framework. As an example,
by applying the Zaitsev boundary conditions which were originally developed for
superconductors, we obtain the $P(E)$-theory of the Coulomb blockade in tunnel
junctions. Furthermore we summarize recent results obtained for the
non-equilibrium transport in thin films, wires and fully coherent conductors.Comment: 46 pages; review articl
On explicit solutions to the stationary axisymmetric Einstein-Maxwell
  equations describing dust disks

We review explicit solutions to the stationary axisymmetric Einstein-Maxwell
equations which can be interpreted as disks of charged dust. The disks of
finite or infinite extension are infinitesimally thin and constitute a surface
layer at the boundary of an electro-vacuum. The Einstein-Maxwell equations in
the presence of one Killing vector are obtained by using a projection
formalism. The SU(2,1) invariance of the stationary Einstein-Maxwell equations
can be used to construct solutions for the electro-vacuum from solutions to the
pure vacuum case via a so-called Harrison transformation. It is shown that the
corresponding solutions will always have a non-vanishing total charge and a
gyromagnetic ratio of 2. Since the vacuum and the electro-vacuum equations in
the stationary axisymmetric case are completely integrable, large classes of
solutions can be constructed with techniques from the theory of solitons. The
richest class of physically interesting solutions to the pure vacuum case due
to Korotkin is given in terms of hyperelliptic theta functions. The Harrison
transformed hyperelliptic solutions are discussed.Comment: 44 pages, 11 figures, revie
The Quantum Supersymmetric Vector Multiplet and Some Problems in
  Non-Abelian Supergauge Theory

We consider the supersymmetric vector multiplet in a purely quantum
framework. We obtain some discrepancies with respect to the literature in the
expression of the super-propagator and we prove that the model is consistent
only for positive mass. The gauge structure is constructed purely deductive and
leads to the necessity of introducing scalar ghost superfields, in analogy to
the usual gauge theories. The construction of a consistent supersymmetric gauge
theory based on the vector model depends crucially one the definition of gauge
invariance. We find some significant difficulties to impose a supersymmetric
gauge invariance condition for the usual expressions from the literature.Comment: 41 pages, LATEX2
Weakly interacting electrons and the renormalization group

We present a general method to study weak-coupling instabilities of a large
class of interacting electron models in a controlled and unbiased way. Quite
generally, the electron gas is unstable towards a superconducting state even in
the absence of phonons, since high-energy spin fluctuations create an effective
attraction between the quasi-particles. As an example, we show the occurrence
of d-wave pairing in the repulsive Hubbard model in two dimensions. In one
dimension or if the Fermi surface is nested, there are several competing
instabilities. The required renormalization group formalism for this case is
presented to lowest (one-loop) order on a most elementary level, connecting the
idea of the ``parquet summation'' to the more modern concept of Wilson's
effective action. The validity and restrictions of the one-loop approximation
are discussed in detail. As a result, three different renormalization group
approaches known in the literature are shown to be equivalent within the regime
of applicability. We also briefly discuss the open problem of a two-dimensional
Fermi system at Van Hove filling without nesting.Comment: 33 pages, 15 figures, minor correction
The 2-matrix of the spin-polarized electron gas: contraction sum rules
  and spectral resolutions

The spin-polarized homogeneous electron gas with densities $\rho_\uparrow$
and $\rho_\downarrow$ for electrons with spin `up' ($\uparrow$) and spin `down'
($\downarrow$), respectively, is systematically analyzed with respect to its
lowest-order reduced densities and density matrices and their mutual relations.
The three 2-body reduced density matrices $\gamma_{\uparrow\uparrow}$,
$\gamma_{\downarrow\downarrow}$, $\gamma_a$ are 4-point functions for electron
pairs with spins $\uparrow\uparrow$, $\downarrow\downarrow$, and antiparallel,
respectively. From them, three functions $G_{\uparrow\uparrow}(x,y)$,
$G_{\downarrow\downarrow}(x,y)$, $G_a(x,y)$, depending on only two variables,
are derived. These functions contain not only the pair densities but also the
1-body reduced density matrices. The contraction properties of the 2-body
reduced density matrices lead to three sum rules to be obeyed by the three key
functions $G_{ss}$, $G_a$. These contraction sum rules contain corresponding
normalization sum rules as special cases. The momentum distributions
$n_\uparrow(k)$ and $n_\downarrow(k)$, following from $f_\uparrow(r)$ and
$f_\downarrow(r)$ by Fourier transform, are correctly normalized through
$f_s(0)=1$. In addition to the non-negativity conditions
$n_s(k),g_{ss}(r),g_a(r)\geq 0$ [these quantities are probabilities], it holds
$n_s(k)\leq 1$ and $g_{ss}(0)=0$ due to the Pauli principle and $g_a(0)\leq 1$
due to the Coulomb repulsion. Recent parametrizations of the pair densities of
the spin-unpolarized homogeneous electron gas in terms of 2-body wave functions
(geminals) and corresponding occupancies are generalized (i) to the
spin-polarized case and (ii) to the 2-body reduced density matrix giving thus
its spectral resolutions.Comment: 32 pages, 4 figure