Quantum Variance and Ergodicity for the baker's map

Abstract

We prove a Egorov theorem, or quantum-classical correspondence, for the quantised baker's map, valid up to the Ehrenfest time. This yields a logarithmic upper bound for the decay of the quantum variance, and, as a corollary, a quantum ergodic theorem for this map.

References in corpus (1)

• Quantum dynamical entropy and decoherence rate

Cited by in corpus (13)

• Out-of-time-ordered correlator in the quantum bakers map and truncated unitary matrices
• Resonances in open quantum maps
• Entropy of semiclassical measures of the Walsh-quantized baker's map
• Fractal Weyl Law for Open Chaotic Maps
• Resonances for open quantum maps and a fractal uncertainty principle
• On the resonance eigenstates of an open quantum baker map
• Resonance eigenfunction hypothesis for chaotic systems
• Quantum ergodicity for graphs related to interval maps
• Quantum ergodicity for quantum graphs without back-scattering
• Quantum-classical correspondence on compact phase space
• Chaotic Roots of the Modular Multiplication Dynamical System in Shor's Algorithm
• Spectral anomalies and broken symmetries in maximally chaotic quantum maps
• Eigenstates and spectral projection for quantized baker's map