Heat flow and noncommutative quantum mechanics in phase-space

Four formulations of quantum mechanics on noncommutative Moyal phase spaces are reviewed. These are the canonical, path-integral, Weyl–Wigner and systematic formulations. Although all these formulations represent quantum mechanics on a phase space with the same deformed Heisenberg algebra, there are mathematical and conceptual differences which we discuss.

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Towards an Observable Test of Noncommutative Quantum Mechanics

Ukrainian Journal of Physics ◽

10.15407/ujpe64.11.983 ◽

2019 ◽

Vol 64 (11) ◽

pp. 983 ◽

Cited By ~ 1

Author(s):

Liang Shi-Dong ◽

T. Harko

Keyword(s):

Quantum Mechanics ◽

Phase Space ◽

Quantum Physics ◽

Planck Scale ◽

Noncommutative Phase Space ◽

A Value ◽

Noncommutative Quantum Mechanics ◽

Noncommutative Spacetime ◽

Aharonov Bohm ◽

Noncommutative Quantum

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.

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Aspects of phase-space noncommutative quantum mechanics

Physics Letters B ◽

10.1016/j.physletb.2015.08.024 ◽

2015 ◽

Vol 750 ◽

pp. 6-11 ◽

Cited By ~ 36

Author(s):

O. Bertolami ◽

P. Leal

Keyword(s):

Quantum Mechanics ◽

Phase Space ◽

Noncommutative Quantum Mechanics ◽

Noncommutative Quantum

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Fractional Zero-Point Angular Momenta in Noncommutative Quantum Mechanics

Zeitschrift für Naturforschung A ◽

10.1515/zna-2016-0191 ◽

2016 ◽

Vol 71 (9) ◽

pp. 823-829

Author(s):

Si-Jia Liu ◽

Yu-Fei Zhang ◽

Zheng-Wen Long ◽

Jian Jing

Keyword(s):

Magnetic Field ◽

Quantum Mechanics ◽

Phase Space ◽

Dimensionless Parameter ◽

Zero Point ◽

Angular Momenta ◽

Noncommutative Quantum Mechanics ◽

Planar Phase ◽

Aharonov Bohm ◽

Noncommutative Quantum

AbstractThe charged particle confined by a harmonic potential in a noncommutative planar phase space interacting with a homogeneous dynamical magnetic field and Aharonov-Bohm potentials is studied. We find that the canonical orbital angular momenta of the reduced models, which are obtained by setting the mass and a dimensionless parameter to zero, take fractional values. These fractional angular momenta are not only determined by the flux inside the thin long solenoid but also affected by the noncommutativities of phase space.

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COMMUTATOR ANOMALY IN NONCOMMUTATIVE QUANTUM MECHANICS

Modern Physics Letters A ◽

10.1142/s0217732306020585 ◽

2006 ◽

Vol 21 (39) ◽

pp. 2971-2976 ◽

Cited By ~ 7

Author(s):

SAYIPJAMAL DULAT ◽

KANG LI

Keyword(s):

Quantum Mechanics ◽

Phase Space ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Uncertainty Relation ◽

Uncertainty Relations ◽

Noncommutative Phase Space ◽

Noncommutative Quantum Mechanics ◽

Physical Observable ◽

Noncommutative Quantum

In this paper, the Schrödinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space–space and space–momentum as well as momentum–momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical observable operators in NCQM are discussed.

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