Probing phase-space noncommutativity through quantum beating, missing information and the thermodynamic limit

Abstract

In this work we examine the effect of phase-space noncommutativity on some typically quantum properties such as quantum beating, quantum information, and decoherence. To exemplify these issues we consider the two-dimensional noncommutative quantum harmonic oscillator whose components behavior we monitor in time. This procedure allows us to determine how the noncommutative parameters are related to the missing information quantified by the linear quantum entropy and by the mutual information between the relevant Hilbert space coordinates. Particular questions concerning the thermodynamic limit of some relevant properties are also discussed in order to evidence the effects of noncommutativity. Finally, through an analogy with the Zeeman effect, we identify how some aspects of the axial symmetry of the problem suggest the possibility of decoupling the noncommutative quantum perturbations from unperturbed commutative well-known solutions.

34 pages, 8 figures

References in corpus (9)

• Violation of Heisenberg's Measurement-Disturbance Relationship by Weak Measurements
• Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
• Berry Phase in the Gravitational Quantum Well and the Seiberg-Witten map
• Non-Canonical Phase-Space Noncommutativity and the Kantowski-Sachs singularity for Black Holes
• Violation of the Robertson-Schrödinger uncertainty principle and non-commutative quantum mechanics
• Exact master equation for a noncommutative Brownian particle
• Noncommutative Field Theory from Quantum Mechanical Space-Space Noncommutativity
• What kind of noncommutative geometry for quantum gravity ?
• Deformation quantization of noncommutative quantum mechanics and dissipation

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• Entanglement due to noncommutativity in the phase-space
• Exact solution of two dimensional Dunkl harmonic oscillator in Non-Commutative phase-space
• Probing phase-space noncommutativity through quantum mechanics and thermodynamics of free particles and quantum rotors
• Phase-space noncommutative extension of the Robertson-Schroedinger formulation of Ozawa's uncertainty principle
• Bell operator and Gaussian squeezed states in noncommutative quantum mechanics
• Seiberg-Witten map and quantum phase effects for neutral Dirac particle on noncommutatiave plane
• Quantum engines and the range of the second law of thermodynamics in the noncommutative phase-space
• Non-Hermitian noncommutative quantum mechanics
• Heat flow and noncommutative quantum mechanics in phase-space
• Quantum speed limit for a relativistic electron in the noncommutative phase space
• Generalized phase-space description of non-linear Hamiltonian systems and the Harper-like dynamics
• Gaussian fidelity distorted by external fields
• Coherent quantum squeezing due to the phase space noncommutativity
• Noncommutative phase-space effects in thermal diffusion of Gaussian states
• Pauli equation on noncommutative plane and the Seiberg-Witten map
• Classical and statistical limits of the quantum singular oscillator
• Quantum cloning and teleportation fidelity in the noncommutative phase-space
• Noncommutative Brownian motion
• 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
• Collapsing Shells and Black Holes: a quantum analysis
• Quantum information aspects of noncommutative quantum mechanics
• Entanglement and separability in the noncommutative phase-space scenario
• Path-integral action of a particle in the noncommutative phase-space
• A Phase-Space Noncommutative Picture of Nuclear Matter
• Test of Space-Time Non-Commutativity at the Future Circular Collider
• Lattice oscillator model on noncommutative space: eigenvalues problem for the perturbation theory
• Emergent time crystals from phase-space noncommutative quantum mechanics