Probing phase-space noncommutativity through quantum mechanics and thermodynamics of free particles and quantum rotors

Abstract

Novel quantization properties related to the state vectors and the energy spectrum of a two-dimensional system of free particles are obtained in the framework of noncommutative (NC) quantum mechanics (QM) supported by the Weyl-Wigner formalism. Besides reproducing the magnetic field aspect of a Zeeman-like effect, the momentum space NC parameter introduces mutual information properties quantified by the quantum purity related to the relevant coordinates of the corresponding Hilbert space. Supported by the QM in the phase-space, the thermodynamic limit is obtained, and the results are extended to three-dimensional systems. The noncommutativity imprints on the thermodynamic variables related to free particles are identified and, after introducing some suitable constraints to fix an axial symmetry, the analysis is extended to two- and- three dimensional quantum rotor systems, for which the quantization aspects and the deviation from standard QM results are verified.

28 pages, 09 figures. The section II of the manuscript corresponds to a short resumed review of preliminary results quoted through the references therein

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• Upper bound on the momentum scale in noncommutative phase space of canonical type
• Heat flow and noncommutative quantum mechanics in phase-space
• Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle
• Equilibrium Chiral Magnetic Effect: spatial inhomogeneity, finite temperature, interactions
• Generalized phase-space description of non-linear Hamiltonian systems and the Harper-like dynamics
• Noncommutative phase-space effects in thermal diffusion of Gaussian states
• Feynman Rules in terms of the Wigner transformed Green functions
• Quantum cloning and teleportation fidelity in the noncommutative phase-space
• Classical and statistical limits of the quantum singular oscillator
• System of interacting harmonic oscillators in rotationally invariant noncommutative phase space
• Phase-space elementary information content of confined Dirac spinors
• Negativity-Mutual Information conversion and coherence in two-coupled harmonic oscillators
• Relativistic dispersion relation and putative metric structure in noncommutative phase-space
• Quantum information aspects of noncommutative quantum mechanics
• Path-integral action of a particle in the noncommutative phase-space
• Harmonic oscillator chain in noncommutative phase space with rotational symmetry
• Thermostatistical analysis and negative heat capacities of Yukawa and Lee-Wick potentials in noncommutative phase spaces
• Lattice oscillator model on noncommutative space: eigenvalues problem for the perturbation theory