Noncommutative phase-space Lotka-Volterra dynamics: The quantum analog

• Type: Article in International Scientific Journal
• Date: 2022

Authors

Bernardini, AE (Author) Other; Bertolami, O (Author) FCUP

Journal

The Journal is awaiting validation by the Administrative Services.

Title: PHYSICAL REVIEW E

Vol. 106

ISSN: 2470-0045

Indexing

ISI Web of Knowledge - 5 Citations

Scopus - 5 Citations

Other information

Authenticus ID: P-00W-ZPZ

DOI: 10.1103/physreve.106.024202

Abstract (EN): The Lotka-Volterra (LV) dynamics is investigated in the framework of the Weyl-Wigner (WW) quantum mechanics extended to one-dimensional Hamiltonian systems, H(x, k) constrained by the partial derivative H-2/partial derivative x partial derivative k = 0 condition. Supported by the Heisenberg-Weyl noncommutative algebra, where [x, k] = i, the canonical variables x and k are interpreted in terms of the LV variables, y = e(-x) and z = e(-k), eventually associated with the number of individuals in a closed competitive dynamics: the so-called prey-predator system. The WW framework provides the ground for identifying how classical and quantum evolution coexist at different scales and for quantifying quantum analog effects. Through the results from the associated Wigner currents, (non-)Liouvillian and stationary properties are described for thermodynamic and Gaussian quantum ensembles in order to account for the corrections due to quantum features over the classical phase-space pattern yielded by the Hamiltonian description of the LV dynamics. In particular, for Gaussian statistical ensembles, the Wigner flow framework provides the exact profile for the quantum modifications over the classical LV phase-space trajectories so that Gaussian quantum ensembles can be interpreted as an adequate Hilbert space state configuration for comparing quantum and classical regimes. The generality of the framework developed here extends the boundaries of the understanding of quantumlike effects on competitive microscopical biosystems.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 12