Related papers: On the limiting Markov process of energy exchanges…
This paper studies a billiards-like microscopic heat conduction model, which describes the dynamics of gas molecules in a long tube with thermalized boundary. We numerically investigate the law of energy exchange between adjacent cells. A…
We consider a class of mechanical particle systems interacting with thermostats. Particles move freely between collisions with disk-shaped thermostats arranged periodically on the torus. Upon collision, an energy exchange occurs, in which a…
We consider the motion of many confined billiard balls in interaction and discuss their transport and chaotic properties. In spite of the absence of mass transport, due to confinement, energy transport can take place through binary…
A fundamental problem of non-equilibrium statistical mechanics is the derivation of macroscopic transport equations in the hydrodynamic limit. The rigorous study of such limits requires detailed information about rates of convergence to…
We discuss the propagation of kinetic energy through billiard balls fixed in place along a one-dimensional segment. The number of billiard balls is assumed to be large but finite and we assume kinetic energy propagates following the usual…
A simple relation is developed between elastic collisions of freely-moving point particles in one dimension and a corresponding billiard system. For two particles with masses m_1 and m_2 on the half-line x>0 that approach an elastic barrier…
We discuss the thermoelectric (TE) transport in billiard systems of interacting particles, coupled to stochastic particle reservoirs. Recently in [1], analytical exact expressions for the TE transport of noninteracting gases of polyatomic…
We study the dynamics of three elastic particles in a finite interval where two light particles are separated by a heavy ``piston''. The piston undergoes surprisingly complex motion that is oscillatory at short time scales but seemingly…
Analytically tractable dynamical systems exhibiting a whole range of normal and anomalous deterministic diffusion are rare. Here we introduce a simple non-chaotic model in terms of an interval exchange transformation suitably lifted onto…
We study the transport properties of a large class of locally confined Hamiltonian systems, in which neighboring particles interact through hard core elastic collisions. When these collisions become rare and the systems large, we derive a…
Polygonal billiards exhibit a rich and complex dynamical behavior. In recent years polygonal billiards have attracted great attention due to their application in the understanding of anomalous transport, but also at the fundamental level,…
We consider the three-dimensional dynamics of systems of many interacting hard spheres, each individually confined to a dispersive environment, and show that the macroscopic limit of such systems is characterized by a coefficient of heat…
We revisit a time-dependent, oval-shaped billiard to investigate a phase transition from bounded to unbounded energy growth. In the static case, the phase space exhibits a mixed structure. The chaotic sea in the static scenario leads to…
We perform simulations to investigate how the energy carried by a molecule transfers to others in an equilibrium gas model. For this purpose we consider a microcanonical ensemble of equilibrium gas systems, each of them contains a tagged…
This paper explores two instances where dissipation plays a crucial role in curbing the unbounded energy growth of particles in time-dependent billiards. The first example involves an elliptical-like billiard with inelastic collisions…
This paper is concerned with the study of one-body dissipation effects in idealized models resembling a nucleus. In particular, we study the quantum mechanics of a free particle that collides elastically with the slowly moving walls of a…
One-dimensional billiard, i.e. a chain of colliding particles with equal masses, is well-known example of completely integrable system. Billiards with different particles are generically not integrable, but still exhibit divergence of a…
We explore some beginning steps in stochastic thermodynamics of billiard-like mechanical systems by introducing extremely simple and explicit random mechanical processes capable of exhibiting steady-state irreversible thermodynamical…
The probability distribution for multiple collisions observed in the chaotic low energy domain in the bouncing ball model is shown to be scaling invariant concerning the control parameters. The model considers the dynamics of a bouncing…
In this article we study the one-dimensional dynamics of elastic collisions of particles with positive and negative mass. We show that such systems are equivalent to billiards induced by an inner product of possibly indefinite signature, we…