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

TL;DR

This paper extends the Weyl-Wigner phase-space framework to non-linear Hamiltonians, analyzing quantum fluctuations and currents, with applications to prey-predator-like dynamics under statistical constraints.

Contribution

It introduces a generalized phase-space approach for non-linear Hamiltonians, including novel algorithms for quantum modifications and applications to ecological models.

Findings

Accurate quantum fluctuation patterns match classical phase-space results.

Framework successfully models prey-predator-like quantum dynamics.

Provides a new method to analyze quantum effects in non-linear systems.

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.