Torus as phase space: Weyl quantization, dequantization, and Wigner formalism

2016/08/01 by Marilena Ligabò · 2 citations
Physics and Astronomy · Computer Science · #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #Nonlinear Dynamics and Pattern Formation

paper · doi:10.1063/1.4961325

Abstract

The Weyl quantization of classical observables on the torus (as phase space) without regularity assumptions is explicitly computed. The equivalence class of symbols yielding the same Weyl operator is characterized. The Heisenberg equation for the dynamics of general quantum observables is written through the Moyal brackets on the torus and the support of the Wigner transform is characterized. Finally, a dequantization procedure is introduced that applies, for instance, to the Pauli matrices. As a result we obtain the corresponding classical symbols.

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• Modeling Position and Momentum in Finite-Dimensional Hilbert Spaces via Generalized Pauli Operators
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