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Time irreversible billiards with piecewise-straight trajectories.
1Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, 22100 Como, Italy. giulio.casati@uninsubria.it
Physical Review Letters
|December 11, 2012
Summary
We developed novel billiards that break time reversal symmetry while maintaining ergodicity. These billiards exhibit unique correlation decay properties, potentially realizable with magnetic fields.
Area of Science:
- * Physics, specifically statistical mechanics and dynamical systems.
- * Quantum chaos and condensed matter physics.
Background:
- * Conventional billiards exhibit time-reversal symmetry and specific correlation decay properties.
- * Understanding systems that break time-reversal symmetry is crucial for exploring novel physical phenomena.
Purpose of the Study:
- * To introduce a new class of billiards that violate time-reversal symmetry.
- * To investigate the dynamical and statistical properties of these novel billiards.
- * To propose a physical implementation for these theoretical billiards.
Main Methods:
- * Theoretical modeling of billiards with piece-wise straight trajectories that break time-reversal symmetry.
- * Analysis of ergodic and mixing properties.
- * Mathematical derivation of correlation functions and their decay rates.
- * Exploration of physical implementation using magnetic fields.
Main Results:
- * A new family of billiards that break time-reversal symmetry has been introduced.
- * These billiards retain the ergodic and mixing properties of standard billiards.
- * Correlation decay can transition from power-law to exponential, characteristic of Sinai billiards.
- * A feasible physical implementation using squeezed magnetic fields is proposed.
Conclusions:
- * The introduced billiards offer a unique platform for studying systems with broken time-reversal symmetry.
- * These systems bridge properties of conventional and Sinai billiards.
- * The proposed magnetic field implementation provides a pathway for experimental verification.
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