Related papers: Diffractive orbits in isospectral billiards
We consider the SU_q (N) invariant spin chain with diagonal and non-diagonal integrable boundary terms. The algebraic study of spin chains with different types of boundary terms is used to motivate a set of spectral equivalences between…
This article is a part of a project investigating the relationship between the dynamics of completely integrable or close to completely integrable billiard tables, the integral geometry on them, and the spectrum of the corresponding…
We prove that any finitely smooth axially symmetric strictly convex domain, with everywhere positive curvature and sufficiently close to an ellipse is area spectrally rigid. This means that any area-isospectral family of domains in this…
It is proved the existence of nonclassical solutions of the Neumann problem for the harmonic functions in the Jordan rectifiable domains with arbitrary measurable boundary distributions of normal derivatives. The same is stated for the…
We consider a generalization of Dirac's comb model, describing a non-relativistic particle moving in a periodic array of generalized point interactions. The latter represent the most general point interactions rendering the kinetic-energy…
The spectral relations for the four-time fermionic Green's functions are derived in the most general case. The terms which correspond to the zero-frequency anomalies, known before only for the bosonic Green's functions, are separated and…
The transition between ballistic and diffusive motion poses difficult problems in several fields of physics. In this work we show how to calculate the spectra of the correlation functions between fields of arbitrary spatial dependence as…
It is known that at lemon and moon billiards that have a sufficiently small curvature on one of their circular arcs are hyperbolic. In this paper we show that replacing this circular arc by a more general boundary component of small…
We suggest a new scheme of derivation of a non-linear ballistic $\sigma$-model for a long range disorder and quantum billiards. The derivation is based on writing equations for quasiclassical Green functions for a fixed long range potential…
We classify the periodic digit strings which arise from periodic billiard orbits on the four convex $n$-gons $\Delta$ which tile $\mathbb{R}^2$ under reflection, answering problem a posed by Baxter and Umble. $\Delta$ is either an…
This paper concerns the spectral properties of the Neumann-Poincar\'e operator on $m$-fold rotationally symmetric planar domains. An $m$-fold rotationally symmetric simply connected domain $D$ is realized as the $m$th-root transform of a…
We show that if the eccentricity of an ellipse is sufficiently small then up to isometries it is spectrally unique among all smooth domains. We do not assume any symmetry, convexity, or closeness to the ellipse, on the class of domains. In…
Upper bounds for the eigenvalues of the Laplace-Beltrami operator on a hypersurface bounding a domain in some ambient Riemannian manifold are given in terms of the isoperimetric ratio of the domain. These results are applied to the…
For classical billiards we suggest that a matrix of action or length of trajectories in conjunction with statistical measures, level spacing distribution and spectral rigidity, can be used to distinguish chaotic from integrable systems. As…
Let M be an even dimensional compact Riemannian manifold with boundary and let D be a Dirac operator acting on the sections of the Clifford module E over M. We impose certain local elliptic boundary conditions for D obtaining a selfadjoint…
We study some natural generalizations of the spectral spaces in the contexts of commutative rings and distributive lattices. We obtain a topological characterization for the spectra of commutative (not necessarily unitary) rings and we find…
We construct semi-infinite billiard domains which reverse the direction of most incoming particles. We prove that almost all particles will leave the open billiard domain after a finite number of reflections. Moreover, with high probability…
We study the spectral rigidity problem for Sinai billiards with finite horizon, specifically asking whether the geometry of the billiard table can be recovered from the lengths of its (marked) periodic trajectories. To address this, we…
We derive Cayley's type conditions for periodical trajectories for the billiard within an ellipsoid in the Lobachevsky space. It appears that these new conditions are of the same form as those obtained before for the Euclidean case. We…
We investigate a rotated, orthogonal gravitational wedge billiard - a special case of the asymmetric wedge billiard - in which the dynamics are integrable. We derive equations and conditions under which periodic orbits may be constructed…