Ergodic billiards that are not quantum unique ergodic

Ergodic Billiards That Are Not Quantum Unique Ergodic

Partially rectangular domains are compact two-dimensional Riemannian manifolds X, either closed or with boundary, that contain a flat rectangle or cylinder. In this paper we are interested in partially rectangular domains with ergodic billiard flow; examples are the Bunimovich stadium, the Sinai billiard or Donnelly surfaces. We consider a one-parameter family Xt of such domains parametrized by...

Open Billiards and Ergodic Theory

More Ergodic Billiards with an Infinite Cusp

In [Le2] the following class of billiards was studied: For f : [0,+∞) −→ (0,+∞) convex, sufficiently smooth, and vanishing at infinity, let the billiard table be defined by Q, the planar domain delimited by the positive x-semiaxis, the positive y-semiaxis, and the graph of f . For a large class of f we proved that the billiard map was hyperbolic. Furthermore we gave an example of a family of f ...

Ergodic Quantum Computing

We propose a (theoretical ;-) model for quantum computation where the result can be read out from the time average of the Hamiltonian dynamics of a 2-dimensional crystal on a cylinder. The Hamiltonian is a spatially local interaction among WignerSeitz cells containing 6 qubits. The quantum circuit that is simulated is specified by the initialization of program qubits. As in Margolus’ Hamiltonia...

Deviation of Ergodic Averages for Rational Polygonal Billiards

We prove a polynomial upper bound on the deviation of ergodic averages for almost all directional flows on every translation surface, in particular, for the generic directional flow of billiards in any Euclidean polygon with rational angles.