Generalized phase-space description of nonlinear Hamiltonian systems and Harper-like dynamics

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

Authors

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

Journal

Title: Physical Review A

Vol. 105

ISSN: 2469-9926

Publisher: American Physical Society

Indexing

ISI Web of Knowledge - 5 Citations

Scopus - 5 Citations

Other information

Authenticus ID: P-00W-9CZ

DOI: 10.1103/physreva.105.032207

Abstract (EN): Phase-space features of the Wigner flow for generic one-dimensional systems with a Hamiltonian HW (q, p) constrained by the partial differential 2HW / partial differential q partial differential p = 0 condition are analytically obtained in terms of Wigner functions and Wigner currents. Liouvillian and stationary profiles are identified for thermodynamic (TD) and Gaussian quantum ensembles to account for exact corrections due to quantum modifications over a classical phase-space pattern. General results are then specialized to the Harper Hamiltonian system, which, besides working as a feasible test platform for the framework here introduced, admits a statistical description in terms of TD and Gaussian ensembles, where the Wigner flow properties are all obtained through analytical tools. Quantum fluctuations over the classical regime are therefore quantified through probability and information fluxes whenever the classical Hamiltonian background is provided. Besides allowing for a broad range of theoretical applications, our results suggest that such a generalized Wigner approach works as a probe for quantumness and classicality of Harper-like systems in a framework which can be extended to any quantum system described by Hamiltonians in the form of HW (q, p) = K(p) +V (q).

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 15