Classical limit in terms of symbolic dynamics for the quantum baker's map

Abstract

We derive a simple closed form for the matrix elements of the quantum baker's map that shows that the map is an approximate shift in a symbolic representation based on discrete phase space. We use this result to give a formal proof that the quantum baker's map approaches a classical Bernoulli shift in the limit of a small effective Plank's constant.

12 pages, LaTex, typos corrected

References in corpus (5)

• Using a quantum computer to investigate quantum chaos
• Realizing the quantum baker's map on an NMR quantum computer
• Overcoming the wall in the semiclassical baker's map
• Quantum baker map on the sphere
• A Canonical Quantization of the Baker's Map

Cited by in corpus (15)

• Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
• Quantum computers in phase space
• Entangling power of the quantum baker's map
• Decoherence for classically chaotic quantum maps
• Hypersensitivity and chaos signatures in the quantum baker's maps
• Irreversible Quantum Baker Map
• Entangling power of baker's map: Role of symmetries
• Decoherence and linear entropy increase in the quantum baker's map
• The classical limit for a class of quantum baker's maps
• Generalized Quantum Baker Maps as perturbations of a simple kernel
• On Quantum - Classical Correspondence for Baker's Map
• A simple necessary decoherence condition for a set of histories
• Reflections on the hyperbolic plane
• Initial states and decoherence of histories
• Classical predictability and coarse-grained evolution of the quantum baker's map