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

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Cited by in corpus (15)

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• 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