Localization in a rough billiard: A sigma model formulation

Abstract

We consider the quantum dynamics of a particle in a weakly rough billiard. The Floquet operator for reflection at the boundary is obtained as a unitary band matrix. The resulting dynamics in angular momentum space can be treated in the framework of the one-dimensional supersymmetric nonlinear sigma model. We find analytically localization and the corresponding localization length $\xi =D_{cl}$ where $D_{cl}$ is the classical diffusion constant due to boundary scattering.

4 pages, Revtex, no figures, to appear in Phys. Rev. B, Rapid Communications

Cited by in corpus (12)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Emergence of Quantum Ergodicity in Rough Billiards
• Level and Eigenfunction Statistics in Billiards with Surface Scattering
• Quantum relaxation in open chaotic systems
• Quantum mechanics of chaotic billiards
• Cantori and dynamical localization in the Bunimovich Stadium
• Diffusion and localization for the Chirikov typical map
• Classical limit of transport in quantum kicked maps
• Semi-classical spectrum of integrable systems in a magnetic field
• Weak localization in disordered systems at the ballistic limit
• A nearly closed ballistic billiard with random boundary transmission
• Leading and beyond leading-order spectral form factor in chaotic quantum many-body systems across all Dyson symmetry classes