Phase space flow in the Husimi representation

Abstract

We derive a continuity equation for the Husimi function evolving under a general non-hermitian Hamiltonian and identify the phase space flow associated with it. For the case of unitary evolution we obtain explicit formulas for the quantum flow, which can be written as a classical part plus semiclassical corrections. These equations are the analogue of the Wigner flow, which displays several non-intuitive features like momentum inversion and motion of stagnation points. Many of these features also appear in the Husimi flow and, therefore, are not related to the negativity of the Wigner function as previously suggested. We test the exact and semiclassical formulas for a particle in a double well potential. We find that the zeros of the Husimi function are saddle points of the flow, and are always followed by a center. Merging or splitting of stagnation points, observed in the Wigner flow,does not occur because of the isolation of the Husimi zeros.

18 pages, 3 figures

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• Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model
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• Wave packet evolution in non-Hermitian quantum systems
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Cited by in corpus (8)

• Anharmonic quantum mechanical systems do not feature phase space trajectories
• Phase space representation of non-Hermitian system with $\mathcal{P}\mathcal{T}$-symmetry
• Husimi dynamics generated by non-Hermitian Hamiltonians
• Topological structures in the Husimi flow
• Joint quantum-classical Hamilton variation principle in the phase space
• Wigner's Phase Space Current for Variable Beam Splitters -Seeing Beam Splitters in a New Light-
• Quantum and semiclassical dynamics as fluid theories where gauge matters
• Quantum-to-semiclassical Husimi dynamics of non-Hermitian localization transitions