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arXiv · 2409.04291

Extended Weyl-Wigner phase-space framework for non-linear systems: typical and modified prey-predator-like dynamics

Alex E. Bernardini·Orfeu Bertolami
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Abstract

The extension of the phase-space Weyl-Wigner quantum mechanics to the subset of Hamiltonians in the form of $H(q,\,p) = {K}(p) + {V}(q)$ (with $K(p)$ replacing single $p^2$ contributions) is revisited. Deviations from classical and stationary profiles are identified in terms of Wigner functions and Wigner currents for Gaussian and gamma/Laplacian distribution ensembles. The procedure is successful in accounting for the exact pattern of quantum fluctuations when compared with the classical phase-space pattern. General results are then specialized to some specific Hamiltonians revealing non-linear dynamics, and suggest a novel algorithm to treat quantum modifications mapped by Wigner currents. Our analysis shows that the framework encompasses, for instance, the quantized prey-predator-like scenarios subjected to statistical constraints.

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Alex E. Bernardini, Orfeu Bertolami. 2024-09-06. Extended Weyl-Wigner phase-space framework for non-linear systems: typical and modified prey-predator-like dynamics. https://arxiv.org/abs/2409.04291

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