arXiv subjects

Francois Leyvraz

Publications and source records attributed to Francois Leyvraz.

25 records · Page 2Linked to original sources

arXiv2014

Temperature gradients in equilibrium: small microcanonical systems in an external field

We consider the statistical mechanics of a small gaseous system subject to a constant external field. As is well known, in the canonical ensemble the system i) obeys a barometric formula for the density profile and ii) the kinetic temperature is independent of height, even when the system is small. We show here that in the microcanonical ensemble the kinetic temperature of the particles affected by the field is not constant with height, but that rather, generally speaking, it decreases with a gradient of order 1/N. Even more, if we have a mixture of two species, one which is influenced by the field and the other which is not, we find that the two species' kinetic temperatures are generally different, even at the same height. These facts are shown in detail by studying a simple mechanical model: a Lorentz Gas where particles and spinning disks interact and the particles are subjected to a constant external force. In the microcanonical ensemble, the kinetic temperature of the particles is indeed found to vary with height; the disks' kinetic temperature, on the other hand, is height-independent, and thus, differs from that of the particles with which they interact.

cond-mat.stat-mech↗

arXiv2008

About Imperfect Mushroom Billiards

Imperfections of Bunimovich mushroom Billiards are analyzed. Any experiment will be affected by such imperfections, and it will be necessary to estimate their influence. In particular some of the corners will be rounded and small deviations of the angle of the underside of the mushroom head will be considered. The analysis displayed some unexpected non-generic features. The latter leads to a transition from a perfect mushroom behavior to either an ordinary KAM scenario or an abrupt transition to complete chaos, depending on the sign of the perturbation. The former produces a fractal area of islands and chaos, in fact a KAM scenario, not associated to the large island of stability of the mushroom billiard.

nlin.CD↗

arXiv2006

Metastability in Markov processes

We present a formalism to describe slowly decaying systems in the context of finite Markov chains obeying detailed balance. We show that phase space can be partitioned into approximately decoupled regions, in which one may introduce restricted Markov chains which are close to the original process but do not leave these regions. Within this context, we identify the conditions under which the decaying system can be considered to be in a metastable state. Furthermore, we show that such metastable states can be described in thermodynamic terms and define their free energy. This is accomplished showing that the probability distribution describing the metastable state is indeed proportional to the equilibrium distribution, as is commonly assumed. We test the formalism numerically in the case of the two-dimensional kinetic Ising model, using the Wang--Landau algorithm to show this proportionality explicitly, and confirm that the proportionality constant is as derived in the theory. Finally, we extend the formalism to situations in which a system can have several metastable states.

cond-mat.stat-mech↗

arXiv2005

A Definition of Metastability for Markov Processes with Detailed Balance

A definition of metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance is discussed. In particular, we identify a crucial condition that distinguishes genuine metastable states from other types of slowly decaying modes and which leads to properties similar to those postulated in the restricted ensemble approach \cite{pen71}. The intuitive physical meaning of this condition is simply that the total equilibrium probability of finding the system in the metastable state is negligible. As a concrete application of our formalism we present preliminary results on a 2D kinetic Ising model.

cond-mat.stat-mech↗

arXiv2001

Transport Properties of the Diluted Lorentz Slab

We study the behavior of a point particle incident from the left on a slab of a randomly diluted triangular array of circular scatterers. Various scattering properties, such as the reflection and transmission probabilities and the scattering time are studied as a function of thickness and dilution. We show that a diffusion model satisfactorily describes the mentioned scattering properties. We also show how some of these quantities can be evaluated exactly and their agreement with numerical experiments. Our results exhibit the dependence of these scattering data on the mean free path. This dependence again shows excellent agreement with the predictions of a Brownian motion model.

cond-mat.stat-mech↗

arXiv1998

Transmission and Scattering of a Lorentz Gas on a Slab

We perform numerical scattering experiments on a Lorentz array of disks centered on a triangular lattice with L columns and study its transmission and reflection properties. In the finite horizon case, the motion of the particles may be modeled as simple one dimensional random walks with absorbing walls for which the scaling of the transmission and reflection coefficients are known, and agree with those found numerically. In the infinite horizon case the analogy with a simple diffusive process is no longer valid. In this case we compare our results with those expected for a one dimensional Levy walk, again with absorbing walls, for which logarithmic corrections to the scaling relations appear. The scaling with L and the symmetry properties of the forward and the backward are also studied, and some of their salient features are discussed.

cond-mat.stat-mech↗

arXiv1994

Propagation and Extinction in Branching Annihilating Random Walks

We investigate the temporal evolution and spatial propagation of branching annihilating random walks in one dimension. Depending on the branching and annihilation rates, a few-particle initial state can evolve to a propagating finite density wave, or extinction may occur, in which the number of particles vanishes in the long-time limit. The number parity conserving case where 2-offspring are produced in each branching event can be solved exactly for unit reaction probability, from which qualitative features of the transition between propagation and extinction, as well as intriguing parity-specific effects are elucidated. An approximate analysis is developed to treat this transition for general BAW processes. A scaling description suggests that the critical exponents which describe the vanishing of the particle density at the transition are unrelated to those of conventional models, such as Reggeon Field Theory. P. A. C. S. Numbers: 02.50.+s, 05.40.+j, 82.20.-w

cond-mat↗