39,767 research outputs found
Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
This review is devoted to the problem of thermalization in a small isolated
conglomerate of interacting constituents. A variety of physically important
systems of intensive current interest belong to this category: complex atoms,
molecules (including biological molecules), nuclei, small devices of condensed
matter and quantum optics on nano- and micro-scale, cold atoms in optical
lattices, ion traps. Physical implementations of quantum computers, where there
are many interacting qubits, also fall into this group. Statistical
regularities come into play through inter-particle interactions, which have two
fundamental components: mean field, that along with external conditions, forms
the regular component of the dynamics, and residual interactions responsible
for the complex structure of the actual stationary states. At sufficiently high
level density, the stationary states become exceedingly complicated
superpositions of simple quasiparticle excitations. At this stage, regularities
typical of quantum chaos emerge and bring in signatures of thermalization. We
describe all the stages and the results of the processes leading to
thermalization, using analytical and massive numerical examples for realistic
atomic, nuclear, and spin systems, as well as for models with random
parameters. The structure of stationary states, strength functions of simple
configurations, and concepts of entropy and temperature in application to
isolated mesoscopic systems are discussed in detail. We conclude with a
schematic discussion of the time evolution of such systems to equilibrium.Comment: 69 pages, 31 figure
An exact solution of the inelastic Boltzmann equation for the Couette flow with uniform heat flux
In the steady Couette flow of a granular gas the sign of the heat flux
gradient is governed by the competition between viscous heating and inelastic
cooling. We show from the Boltzmann equation for inelastic Maxwell particles
that a special class of states exists where the viscous heating and the
inelastic cooling exactly compensate each other at every point, resulting in a
uniform heat flux. In this state the (reduced) shear rate is enslaved to the
coefficient of restitution , so that the only free parameter is the
(reduced) thermal gradient . It turns out that the reduced moments of
order are polynomials of degree in , with coefficients that
are nonlinear functions of . In particular, the rheological properties
() are independent of and coincide exactly with those of the
simple shear flow. The heat flux () is linear in the thermal gradient
(generalized Fourier's law), but with an effective thermal conductivity
differing from the Navier--Stokes one. In addition, a heat flux component
parallel to the flow velocity and normal to the thermal gradient exists. The
theoretical predictions are validated by comparison with direct Monte Carlo
simulations for the same model.Comment: 16 pages, 4 figures,1 table; v2: minor change
A Cartan-Eilenberg approach to Homotopical Algebra
In this paper we propose an approach to homotopical algebra where the basic
ingredient is a category with two classes of distinguished morphisms: strong
and weak equivalences. These data determine the cofibrant objects by an
extension property analogous to the classical lifting property of projective
modules. We define a Cartan-Eilenberg category as a category with strong and
weak equivalences such that there is an equivalence between its localization
with respect to weak equivalences and the localised category of cofibrant
objets with respect to strong equivalences. This equivalence allows us to
extend the classical theory of derived additive functors to this non additive
setting. The main examples include Quillen model categories and functor
categories with a triple, in the last case we find examples in which the class
of strong equivalences is not determined by a homotopy relation. Among other
applications, we prove the existence of filtered minimal models for \emph{cdg}
algebras over a zero-characteristic field and we formulate an acyclic models
theorem for non additive functors
Stochastic Model in the Kardar-Parisi-Zhang Universality With Minimal Finite Size Effects
We introduce a solid on solid lattice model for growth with conditional
evaporation. A measure of finite size effects is obtained by observing the time
invariance of distribution of local height fluctuations. The model parameters
are chosen so that the change in the distribution in time is minimum.
On a one dimensional substrate the results obtained from the model for the
roughness exponent from three different methods are same as predicted
for the Kardar-Parisi-Zhang (KPZ) equation. One of the unique feature of the
model is that the as obtained from the structure factor for
the one dimensional substrate growth exactly matches with the predicted value
of 0.5 within statistical errors. The model can be defined in any dimensions.
We have obtained results for this model on a 2 and 3 dimensional substrates.Comment: 8 pages, 7 figures, accepted in Phys. Rev.
Impurity in a granular gas under nonlinear Couette flow
We study in this work the transport properties of an impurity immersed in a
granular gas under stationary nonlinear Couette flow. The starting point is a
kinetic model for low-density granular mixtures recently proposed by the
authors [Vega Reyes F et al. 2007 Phys. Rev. E 75 061306]. Two routes have been
considered. First, a hydrodynamic or normal solution is found by exploiting a
formal mapping between the kinetic equations for the gas particles and for the
impurity. We show that the transport properties of the impurity are
characterized by the ratio between the temperatures of the impurity and gas
particles and by five generalized transport coefficients: three related to the
momentum flux (a nonlinear shear viscosity and two normal stress differences)
and two related to the heat flux (a nonlinear thermal conductivity and a cross
coefficient measuring a component of the heat flux orthogonal to the thermal
gradient). Second, by means of a Monte Carlo simulation method we numerically
solve the kinetic equations and show that our hydrodynamic solution is valid in
the bulk of the fluid when realistic boundary conditions are used. Furthermore,
the hydrodynamic solution applies to arbitrarily (inside the continuum regime)
large values of the shear rate, of the inelasticity, and of the rest of
parameters of the system. Preliminary simulation results of the true Boltzmann
description show the reliability of the nonlinear hydrodynamic solution of the
kinetic model. This shows again the validity of a hydrodynamic description for
granular flows, even under extreme conditions, beyond the Navier-Stokes domain.Comment: 23 pages, 11 figures; v2: Preliminary DSMC results from the Boltzmann
equation included, Fig. 11 is ne
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