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

• URL: http://arxiv.org/abs/2409.04291v1
• Date: Fri, 6 Sep 2024 14:00:09 GMT
• Title: Extended Weyl-Wigner phase-space framework for non-linear systems: typical and modified prey-predator-like dynamics
• Authors: Alex E. Bernardini, Orfeu Bertolami,
• Abstract summary: Weyl-Wigner quantum mechanics extended to subset of Hamiltonians in form of $H(q,,p) = K(p) + V(q)$ (with $K(p)$ replacing single $p2$ contributions) We show that the framework encompasses, for instance, the quantized prey-predator-like scenarios subjected to statistical constraints.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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