761 research outputs found
Langevin equation for the extended Rayleigh model with an asymmetric bath
In this paper a one-dimensional model of two infinite gases separated by a
movable heavy piston is considered. The non-linear Langevin equation for the
motion of the piston is derived from first principles for the case when the
thermodynamic parameters and/or the molecular masses of gas particles on left
and right sides of the piston are different. Microscopic expressions involving
time correlation functions of the force between bath particles and the piston
are obtained for all parameters appearing in the non-linear Langevin equation.
It is demonstrated that the equation has stationary solutions corresponding to
directional fluctuation-induced drift in the absence of systematic forces. In
the case of ideal gases interacting with the piston via a quadratic repulsive
potential, the model is exactly solvable and explicit expressions for the
kinetic coefficients in the non-linear Langevin equation are derived. The
transient solution of the non-linear Langevin equation is analyzed
perturbatively and it is demonstrated that previously obtained results for
systems with the hard-wall interaction are recovered.Comment: 10 pages. To appear in Phys. Rev.
On the adiabatic properties of a stochastic adiabatic wall: Evolution, stationary non-equilibrium, and equilibrium states
The time evolution of the adiabatic piston problem and the consequences of
its stochastic motion are investigated. The model is a one dimensional piston
of mass separating two ideal fluids made of point particles with mass . For infinite systems it is shown that the piston evolves very rapidly
toward a stationary nonequilibrium state with non zero average velocity even if
the pressures are equal but the temperatures different on both sides of the
piston. For finite system it is shown that the evolution takes place in two
stages: first the system evolves rather rapidly and adiabatically toward a
metastable state where the pressures are equal but the temperatures different;
then the evolution proceeds extremely slowly toward the equilibrium state where
both the pressures and the temperatures are equal. Numerical simulations of the
model are presented. The results of the microscopical approach, the
thermodynamical equations and the simulations are shown to be qualitatively in
good agreement.Comment: 28 pages, 10 figures include
Proof of phase separation in the binary-alloy problem: the one-dimensional spinless Falicov-Kimball model
The ground states of the one-dimensional Falicov-Kimball model are
investigated in the small-coupling limit, using nearly degenerate perturbation
theory. For rational electron and ion densities, respectively equal to
, , with relatively prime to and
close enough to , we find that in the ground state
the ion configuration has period . The situation is analogous to the Peierls
instability where the usual arguments predict a period- state that produces
a gap at the Fermi level and is insulating. However for far
enough from , this phase becomes unstable against phase
separation. The ground state is a mixture of a period- ionic configuration
and an empty (or full) configuration, where both configurations have the same
electron density to leading order. Combining these new results with those
previously obtained for strong coupling, it follows that a phase transition
occurs in the ground state, as a function of the coupling, for ion densities
far enough from .Comment: 22 pages, typeset in ReVTeX and one encapsulated postscript file
embedded in the text with eps
Ground States and Flux Configurations of the Two-dimensional Falicov-Kimball Model
The Falicov-Kimball model is a lattice model of itinerant spinless fermions
("electrons") interacting by an on-site potential with classical particles
("ions"). We continue the investigations of the crystalline ground states that
appear for various filling of electrons and ions, for large coupling. We
investigate the model for square as well as triangular lattices. New ground
states are found and the effects of a magnetic flux on the structure of the
phase diagram is studied. The flux phase problem where one has to find the
optimal flux configurations and the nuclei configurations is also solved in
some cases. Finaly we consider a model where the fermions are replaced by
hard-core bosons. This model also has crystalline ground states. Therefore
their existence does not require the Pauli principle, but only the on-site
hard-core constraint for the itinerant particles.Comment: 42 pages, uuencoded postscript file. Missing pages adde
Dynamical mean-field theory for light fermion--heavy boson mixtures on optical lattices
We theoretically analyze Fermi-Bose mixtures consisting of light fermions and
heavy bosons that are loaded into optical lattices (ignoring the trapping
potential). To describe such mixtures, we consider the Fermi-Bose version of
the Falicov-Kimball model on a periodic lattice. This model can be exactly
mapped onto the spinless Fermi-Fermi Falicov-Kimball model at zero temperature
for all parameter space as long as the mixture is thermodynamically stable. We
employ dynamical mean-field theory to investigate the evolution of the
Fermi-Bose Falicov-Kimball model at higher temperatures. We calculate spectral
moment sum rules for the retarded Green's function and self-energy, and use
them to benchmark the accuracy of our numerical calculations, as well as to
reduce the computational cost by exactly including the tails of infinite
summations or products. We show how the occupancy of the bosons,
single-particle many-body density of states for the fermions, momentum
distribution, and the average kinetic energy evolve with temperature. We end by
briefly discussing how to experimentally realize the Fermi-Bose Falicov-Kimball
model in ultracold atomic systems.Comment: 10 pages with 4 figure
From the adiabatic piston to macroscopic motion induced by fluctuations
The controversial problem of an isolated system with an internal adiabatic
wall is investigated with the use of a simple microscopic model and the
Boltzmann equation. In the case of two infinite volume one-dimensional ideal
fluids separated by a piston whose mass is equal to the mass of the fluid
particles we obtain a rigorous explicit stationary non-equilibrium solution of
the Boltzmann equation. It is shown that at equal pressures on both sides of
the piston, the temperature difference induces a non-zero average velocity,
oriented toward the region of higher temperature. It thus turns out that
despite the absence of macroscopic forces the asymmetry of fluctuations results
in a systematic macroscopic motion. This remarkable effect is analogous to the
dynamics of stochastic ratchets, where fluctuations conspire with spatial
anisotropy to generate direct motion. However, a different mechanism is
involved here. The relevance of the discovered motion to the adiabatic piston
problem is discussed.Comment: 14 pages,1 figur
Phase Separation and Charge-Ordered Phases of the d = 3 Falicov-Kimball Model at T>0: Temperature-Density-Chemical Potential Global Phase Diagram from Renormalization-Group Theory
The global phase diagram of the spinless Falicov-Kimball model in d = 3
spatial dimensions is obtained by renormalization-group theory. This global
phase diagram exhibits five distinct phases. Four of these phases are
charge-ordered (CO) phases, in which the system forms two sublattices with
different electron densities. The CO phases occur at and near half filling of
the conduction electrons for the entire range of localized electron densities.
The phase boundaries are second order, except for the intermediate and large
interaction regimes, where a first-order phase boundary occurs in the central
region of the phase diagram, resulting in phase coexistence at and near half
filling of both localized and conduction electrons. These two-phase or
three-phase coexistence regions are between different charge-ordered phases,
between charge-ordered and disordered phases, and between dense and dilute
disordered phases. The second-order phase boundaries terminate on the
first-order phase transitions via critical endpoints and double critical
endpoints. The first-order phase boundary is delimited by critical points. The
cross-sections of the global phase diagram with respect to the chemical
potentials and densities of the localized and conduction electrons, at all
representative interactions strengths, hopping strengths, and temperatures, are
calculated and exhibit ten distinct topologies.Comment: Calculated density phase diagrams. Added discussions and references.
14 pages, 9 figures, 4 table
Lower bound for the segregation energy in the Falicov-Kimball model
In this work, a lower bound for the ground state energy of the
Falicov-Kimball model for intermediate densities is derived. The explicit
derivation is important in the proof of the conjecture of segregation of the
two kinds of fermions in the Falicov-Kimball model, for sufficiently large
interactions. This bound is given by a bulk term, plus a term proportional to
the boundary of the region devoid of classical particles. A detailed proof is
presented for density n=1/2, where the coefficient 10^(-13) is obtained for the
boundary term, in two dimensions. With suitable modifications the method can
also be used to obtain a coefficient for all densities.Comment: 8 pages, 2 figure
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