相关论文: Slow relaxation in weakly open vertex-splitting ra…
In this article, we study polygonal symplectic billiards. We provide new results, some of which are inspired by numerical investigations. In particular, we present several polygons for which all orbits are periodic. We demonstrate their…
We report a Monte Carlo investigation of the effect of a lattice of antidots on spin relaxation in twodimensional electron systems. The spin relaxation time is calculated as a function of geometrical parameters describing the antidot…
We study a class of elliptic billiards with a Keplerian potential inside, considering two cases: a reflective one, where the particle reflects elastically on the boundary, and a refractive one, where the particle can cross the billiard's…
We study chaotic properties of eigenstates depending on the degree of complexity in boundaries of a 2D periodic billiard. Main attention is paid to the situation when the motion of a classical particle is strongly chaotic. Our approach…
We study quantum-mechanical tunneling between symmetry-related pairs of regular phase space regions that are separated by a chaotic layer. We consider the annular billiard, and use scattering theory to relate the splitting of…
We study the low energy quantum spectra of two-dimensional rectangular billiards with a small but finite-size scatterer inside. We start by examining the spectral properties of billiards with a single pointlike scatterer. The problem is…
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
We show that there exists a $C^2$ open dense set of convex bodies with smooth boundary whose billiard map exhibits a non-trivial hyperbolic basic set. As a consequence billiards in generic convex bodies have positive topological entropy and…
We study length-minimizing closed generalized Euclidean billiard trajectories in convex bodies in $\mathbb{R}^n$ and investigate their relation to the inclusion minimal affine sections that contain these trajectories. We show that when…
A phenomenological model is proposed for melting of a vortex lattice, based on screening of the elastic shear modulus by mobile or partially pinned dislocations. A first-order softening line is found and ends at a critical point beyond…
Soft colloids allow to explore high density states well beyond random close packing. An important open question is whether softness controls the dynamics under these dense conditions. While experimental works reported conflicting results,…
We report calculations of spin relaxation dynamics of two-dimensional electron gas with spin-orbit interaction at the edge region. It is found that the relaxation of spin polarization near the edge is more slow than relaxation in the bulk.…
A mean-field kinetic model suggests that the relaxation dynamics of wormlike micellar networks is a long and complex process due to the problem of reducing the number of free end-caps (or dangling ends) while also reaching an equilibrium…
H${\acute{e}}$non [8] used an inclined billiard to investigate aspects of chaotic scattering which occur in satellite encounters and in other situations. His model consisted of a piecewise mapping which described the motion of a point…
In 1973, J. Moser proposed that his Twist Theorem could be used to show that orbits of the outer billiards map on a sufficiently smooth closed curve were always bounded. Five years later Moser asked the same question for a convex polygon.…
The spin relaxation of a two-dimensional electron system (2DES) formed in a symmetric quantum well is studied theoretically when the quantum well is parallel to the (110) plane of the zinc-blende structure, the spin polarization is…
We apply periodic orbit theory to a two-dimensional non-integrable billiard system whose boundary is varied smoothly from a circular to an equilateral triangular shape. Although the classical dynamics becomes chaotic with increasing…
This survey is based on a series of talks I gave at the conference "Dynamical systems and diophantine approximation" at l'Instut Henri Poincar\'e in June 2003. I will present asymptotic results (transitivity, ergodicity, weak-mixing) for…
Billiard systems offer a simple setting to study regular and chaotic dynamics. Gravitational billiards are generalizations of these classical billiards which are amenable to both analytical and experimental investigations. Most previous…
Understanding the timescales associated with relaxation to equilibrium in closed quantum many-body systems is one of the central focuses in the study of their non-equilibrium dynamics. At late times, these relaxation processes exhibit…