Probing phase-space noncommutativity through quantum beating, missing information, and the thermodynamic limit (original) (raw)

Environment-Induced Decoherence in Noncommutative Quantum Mechanics

International Journal of Quantum Information, 2007

We address the question of the appearance of ordinary quantum mechanics in the context of noncommutative quantum mechanics. We review our derivation of the noncommutative extension of the Hu–Paz–Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators. As a new contribution, we consider the particular case of an Ohmic regime.

Entanglement due to noncommutativity in phase space

The entanglement criterion for continuous variable systems and the conditions under which the uncertainty relations are fulfilled are generalized to the case of a noncommutative (NC) phasespace. The quantum nature and the separability of NC two-mode Gaussian states are examined.

J an 2 00 3 Quantum Dissipation Induced Noncommutative Geometry

The quantum statistical dynamics of a position coordinate x coupled to a reservoir requires theoretically two copies of the position coordinate within the reduced density matrix description. One coordinate moves forward in time while the other coordinate moves backward in time. It is shown that quantum dissipation induces, in the plane of the forward and backward motions, a noncommutative geometry. The noncommutative geometric plane is a consequence of a quantum dissipation induced phase interference which is closely analogous to the Aharanov-Bohm effect.

Towards an Observable Test of Noncommutative Quantum Mechanics

Ukrainian Journal of Physics

The conceptual incompatibility of spacetime in gravity and quantum physics implies the existence of noncommutative spacetime and geometry on the Planck scale. We present the formulation of a noncommutative quantum mechanics based on the Seiberg–Witten map, and we study the Aharonov–Bohm effect induced by the noncommutative phase space. We investigate the existence of the persistent current in a nanoscale ring with an external magnetic field along the ring axis, and we introduce two observables to probe the signal coming from the noncommutative phase space. Based on this formulation, we give a value-independent criterion to demonstrate the existence of the noncommutative phase space.

Quantum dissipation induced noncommutative geometry

Physics Letters A, 2003

The quantum statistical dynamics of a position coordinate x coupled to a reservoir requires theoretically two copies of the position coordinate within the reduced density matrix description. One coordinate moves forward in time while the other coordinate moves backward in time. It is shown that quantum dissipation induces, in the plane of the forward and backward motions, a noncommutative geometry. The noncommutative geometric plane is a consequence of a quantum dissipation induced phase interference which is closely analogous to the Aharanov-Bohm effect.

Entanglement induced by noncommutativity: anisotropic harmonic oscillator in noncommutative space

The European Physical Journal Plus, 2021

Quantum entanglement, induced by spatial noncommutativity, is investigated for an anisotropic harmonic oscillator. Exact solutions for the system are obtained after the model is re-expressed in terms of canonical variables, by performing a particular Bopp's shift to the noncommuting degrees of freedom. Employing Simon's separability criterion, we find that the states of the system are entangled provided a unique function of the (mass and frequency) parameters obeys an inequality. Entanglement of Formation for this system is also computed and its relation to the degree of anisotropy is discussed. It is worth mentioning that, even in a noncommutative space, entanglement is generated only if the harmonic oscillator is anisotropic. Interestingly, the Entanglement of Formation saturates for higher values of the deformation parameter θ, that quantifies spatial noncommutativity.

Noncommutative Quantum Mechanics

International Journal of Modern Physics A, 2002

Quantum mechanics in a noncommutative plane is considered. For a general two dimensional central field, we find that the theory can be perturbatively solved for large values of the noncommutative parameter ($\theta$) and explicit expressions for the eigenstates and eigenvalues are given. The Green function is explicitly obtained and we show that it can be expressed as an infinite series. For polynomial type potentials, we found a smooth limit for small values of theta\thetatheta and for non-polynomial ones this limit is necessarily abrupt. The Landau problem, as a limit case of a noncommutative system, is also considered.

Coherent quantum squeezing due to the phase space noncommutativity

Physica Scripta, 2015

The effect of phase space general noncommutativity on producing deformed coherent squeezed states is examined. A two-dimensional noncommutative quantum system supported by a deformed mathematical structure similar to that of Hadamard billiards is obtained and their components behavior are monitored in time. It is assumed that the independent degrees of freedom are two free 1D harmonic oscillators (HO's), so the system Hamiltonian does not contain interaction terms.

On noncommutative quantum mechanics

2012

This paper is dedicated to present model independent results for noncommutative quantum mechanics. We determine sufficient conditions for the convergence of the Born series and, in the sequel, unitarity is proved. We focus, afterwards, on the functional quantization of noncommutative systems. The compatibility between the operator and the functional approaches is established. We also study in detail the Feynman kernel for the noncommutative two dimensional harmonic oscillator. Electronic address: fbemfica,