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It is demonstrated numerically that smooth three degrees of freedom Hamiltonian systems which are arbitrarily close to three dimensional strictly dispersing billiards (Sinai billiards) have islands of effective stability, and hence are…

We present a comprehensive review of the nodal domains and lines of quantum billiards, emphasizing a quantitative comparison of theoretical findings to experiments. The nodal statistics are shown to distinguish not only between regular and…

We derive an analytical trace formula for the level density of the two-dimensional elliptic billiard using an improved stationary phase method. The result is a continuous function of the deformation parameter (eccentricity) through all…

We analyze the dynamics of a valence electron of the buckminsterfullerene molecule (C60) subjected to a circularly polarized laser field by modeling it with the motion of a classical particle in an annular billiard. We show that the phase…

We consider two nested billiards in $\mathbb R^d$, $d\geq3$, with $C^2$-smooth strictly convex boundaries. We prove that if the corresponding actions by reflections on the space of oriented lines commute, then the billiards are confocal…

This is the first survey of highly excited eigenstates of a chaotic 3D billiard. We introduce a strongly chaotic 3D billiard with a smooth boundary and we manage to calculate accurate eigenstates with sequential number (of a 48-fold…

Uniform hyperbolicity is a strong chaotic property which holds, in particular, for Sinai billiards. In this paper, we consider the case of a nonflat billiard, that is, a Riemannian manifold with boundary. Each trajectory follows the…

The spectral properties of a two-dimensional microwave billiard showing threefold symmetry have been studied with a new experimental technique. This method is based on the behavior of the eigenmodes under variation of a phase shift between…

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…

Establishing global well-posedness and convergence toward equilibrium of the Boltzmann equation with specular reflection boundary condition has been one of the central questions in the subject of kinetic theory. Despite recent significant…

In this paper we study convex caustics in Minkowski billiards. We show that for the Euclidean billiard dynamics in a planar smooth centrally symmetric and strictly convex body $K$, for every convex caustic which $K$ possesses, the "dual"…

In this paper, we show that two-dimensional billiards with point interactions inside exhibit a chaotic nature in the microscopic world, although their classical counterpart is non-chaotic. After deriving the transition matrix of the system…

We consider a model in which positive and negative particles with equal densities diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and oppositely-charged adjacent…

We apply a recently proposed novel thermostating mechanism to an interacting many-particle system where the bulk particles are moving according to Hamiltonian dynamics. At the boundaries the system is thermalized by deterministic and…

Generic one-parameter billiards are studied both classically and quantally. The classical dynamics for the billiards makes a transition from regular to fully chaotic motion through intermediary soft chaotic system. The energy spectra of the…

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…

The connected configuration space of a so called cylindric billiard system is a flat torus minus finitely many spherical cylinders. The dynamical system describes the uniform motion of a point particle in this configuration space with…

It is known that the non-equilibrium version of the Lorentz gas (a billiard with dispersing obstacles, electric field and Gaussian thermostat) is hyperbolic if the field is small. Differently the hyperbolicity of the non-equilibrium…

Under many circumstances many soft and hard materials are present in a puzzling wealth of non-equilibrium amorphous states, whose properties are not stationary and depend on preparation. They are often summarized in unconventional "phase…

In specific types of partially rectangular billiards we estimate the mass of an eigenfunction of energy $E$ in the region outside the rectangular set in the high-energy limit. We use the adiabatic ansatz to compare the Dirichlet energy form…