147 research outputs found
The Bose gas beyond mean field
We study a homogeneous Bose gas with purely repulsive forces. Using the Kac
scaling of the binary potential we derive analytically the form of the
thermodynamic functions of the gas for small but finite values of the scaling
parameter in the low density regime. In this way we determine dominant
corrections to the mean-field theory. It turns out that repulsive forces
increase the pressure at fixed density and decrease the density at given
chemical potential (the temperature is kept constant). They also flatten the
Bose momentum distribution. However, the present analysis cannot be extended to
the region where the mean-field theory predicts the appearence of condensate.Comment: 19 pages, 3 figure
Damped bounces of an isolated perfect quantum gas
The issue of the thermalization of an isolated quantum system is addressed by
considering a perfect gas confined by gravity and initially trapped above a
certain height. As we are interested in the behavior of truly isolated systems,
we assume the gas is in a pure state of macroscopically well-defined energy. We
show that, in general, for single-particle distributions, such a state is
strictly equivalent to the microcanonical mixed state at the same energy. We
derive an expression for the time-dependent gas density which depends on the
initial gas state only via a few thermodynamic parameters. Though we consider
non-interacting particles, the density relaxes into an asymptotic profile, but
which is not the thermal equilibrium one determined by the gas energy and
particle number
Reply to "Comment on `Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined' ''
In his Comment [see preceding Comment, Phys. Rev. A 82, 037601 (2010)] on the
paper by Roux [Phys. Rev. A 79, 021608(R) (2009)], Rigol argued that the energy
distribution after a quench is not related to standard statistical ensembles
and cannot explain thermalization. The latter is proposed to stem from what he
calls the eigenstate thermalization hypothesis and which boils down to the fact
that simple observables are expected to be smooth functions of the energy. In
this Reply, we show that there is no contradiction or confusion between the
observations and discussions of Roux and the expected thermalization scenario
discussed by Rigol. In addition, we emphasize a few other important aspects, in
particular the definition of temperature and the equivalence of ensemble, which
are much more difficult to show numerically even though we believe they are
essential to the discussion of thermalization. These remarks could be of
interest to people interested in the interpretation of the data obtained on
finite-size systems.Comment: 3 page
Thermal activation of rupture and slow crack growth in a model of homogenous brittle materials
Slow crack growth in a model of homogenous brittle elastic material is
described as a thermal activation process where stress fluctuations allow to
overcome a breaking threshold through a series of irreversible steps. We study
the case of a single crack in a flat sheet for which analytical predictions can
be made, and compare them with results from the equivalent problem of a 2D
spring network. Good statistical agreement is obtained for the crack growth
profile and final rupture time. The specific scaling of the energy barrier with
stress intensity factor appears as a consequence of irreversibility. In
addition, the model brings out a characteristic growth length whose physical
meaning could be tested experimentally.Comment: To be published in : Europhysics Letter
Long-range repulsive interaction between TTF molecules on a metal surface induced by charge transfer
The low-coverage adsorption of a molecular electron donor,
tetrathiafulvalene, on Au(111) is characterized by the spontaneous formation of
superlattice of monomers, whose spacing exceeds the equilibrium distance of
non-covalent interactions and depends on coverage. The origin of this peculiar
growth mode is due to a long-range repulsive interaction between molecules. The
analysis of molecular-pair distributions obtained by scanning tunneling
microscopy measurements permits us to determine that the nature of TTF
intermolecular interactions on Au (111) is electrostatic. A repulsion between
molecules is caused by the accumulation of charge due to electron donation into
the metal surface, as pictured through density functional theory calculations
Foundation of Statistical Mechanics under experimentally realistic conditions
We demonstrate the equilibration of isolated macroscopic quantum systems,
prepared in non-equilibrium mixed states with significant population of many
energy levels, and observed by instruments with a reasonably bound working
range compared to the resolution limit. Both properties are fulfilled under
many, if not all, experimentally realistic conditions. At equilibrium, the
predictions and limitations of Statistical Mechanics are recovered.Comment: Accepted in Phys. Rev. Let
Joule expansion of a pure many-body state
We derive the Joule expansion of an isolated perfect gas from the principles
of quantum mechanics. Contrary to most studies of irreversible processes which
consider composite systems, the gas many-body Hilbert space cannot be
factorised into Hilbert spaces corresponding to interesting and ignored degrees
of freedom. Moreover, the expansion of the gas into the entire accessible
volume is obtained for pure states. Still, the number particle density is
characterised by a chemical potential and a temperature. We discuss the special
case of a boson gas below the Bose condensation temperature
Equilibration of isolated macroscopic quantum systems
We investigate the equilibration of an isolated macroscopic quantum system in
the sense that deviations from a steady state become unmeasurably small for the
overwhelming majority of times within any sufficiently large time interval. The
main requirements are that the initial state, possibly far from equilibrium,
exhibits a macroscopic population of at most one energy level and that
degeneracies of energy eigenvalues and of energy gaps (differences of energy
eigenvalues) are not of exceedingly large multiplicities. Our approach closely
follows and extends recent works by Short and Farrelly [2012 New J. Phys. 14
013063], in particular going beyond the realm of finite-dimensional systems and
large effective dimensions.Comment: 19 page
Ratio of viscosity to entropy density in a strongly coupled one-component plasma
String theoretical arguments led to the hypothesis that the ratio of
viscosity to entropy of any physical system has a lower bound. Strongly coupled
systems usually have a small viscosity compared to weakly coupled plasmas in
which the viscosity is proportional to the mean free path. In the case of a
one-component plasma the viscosity as a function of the coupling strength shows
a minimum. Here we show that the ratio of viscosity to entropy of a strongly
coupled one-component plasma is always above the lower bound predicted by
string theory.Comment: 5 pages, revised version to be published in Europhysics Letter
Canonical thermalization
For quantum systems that are weakly coupled to a much 'bigger' environment,
thermalization of possibly far from equilibrium initial ensembles is
demonstrated: for sufficiently large times, the ensemble is for all practical
purposes indistinguishable from a canonical density operator under conditions
that are satisfied under many, if not all, experimentally realistic conditions
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