An Extra Phase for Two-Mode Coherent States Displaced in Noncommutative Phase Space

2012 ◽  
Vol 29 (4) ◽  
pp. 041102
Author(s):  
Long Yan ◽  
Xun-Li Feng ◽  
Zhi-Ming Zhang ◽  
Song-Hao Liu
Keyword(s):  
Phase Space ◽  
Coherent States ◽  
Noncommutative Phase Space

ON DEFORMED BOSON ALGEBRA AND VACUUM PROJECTION OPERATOR ON NONCOMMUTATIVE PLANE

2013 ◽  
Vol 28 (07) ◽  
pp. 1350020
Author(s):  
GAO-FU LIU ◽  
HONG-LING LIU ◽  
GUANG-JIE GUO
Keyword(s):  
Phase Space ◽  
Projection Operator ◽  
Coherent States ◽  
Completeness Relation ◽  
Noncommutative Phase Space ◽  
Normal Ordering ◽  
Expansion Form ◽  
Noncommutative Plane

In the noncommutative phase space, a new mapping is proposed to express the noncommutative coordinate and momentum operators in terms of the ordinary coordinate and momentum operators under the case of large noncommutativity parameters (μν>1). Using this mapping matrix, the deformed boson operators can be expressed in terms of the ordinary boson operators. Thus, the normal ordering expansion form of vacuum projection operator is obtained. As an application, the completeness relation of the two-mode deformed coherent states is verified by using the vacuum projection operator.

THREE-DIMENSIONAL KLEIN–GORDON OSCILLATOR IN A BACKGROUND MAGNETIC FIELD IN NONCOMMUTATIVE PHASE SPACE

2012 ◽  
Vol 27 (10) ◽  
pp. 1250047 ◽  
Author(s):  
MAI-LIN LIANG ◽  
RUI-LIN YANG
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Coherent States ◽  
Semiclassical Limit ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Noncommutative Phase Space ◽  
Background Magnetic Field ◽  
Klein Gordon ◽  
Lowering Operators

In noncommutative phase space, wave functions and energy spectra are derived for the three-dimensional (3D) Klein–Gordon oscillator in a background magnetic field. The raising and lowering operators for this system are derived from the Heisenberg equations of motion for a 3D nonrelativistic oscillator. The coherent states are obtained as the eigenstates of the lowering operators and it is found that the coherent states are not the minimum uncertainty states due to the noncommutativity of the space. It is also pointed out that in the semiclassical limit, quantum matrix elements give solutions to the semiclassical equations.

scholarly journals Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
Author(s):  
Fabio Benatti ◽  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Classical Limit ◽  
Coherent States ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Wigner Functions ◽  
Quantum Mechanical Oscillators ◽  
Mechanical Oscillators ◽  
Space Noncommutativity

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

scholarly journals Algebraic Approach to Exact Solution of the (2 + 1)-Dimensional Dirac Oscillator in the Noncommutative Phase Space

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
H. Panahi ◽  
A. Savadi
Keyword(s):  
Exact Solution ◽  
Phase Space ◽  
Algebraic Approach ◽  
Wave Functions ◽  
Dirac Oscillator ◽  
Noncommutative Phase Space ◽  
Energy Eigenvalues ◽  
Good Agreement

We study the (2 + 1)-dimensional Dirac oscillator in the noncommutative phase space and the energy eigenvalues and the corresponding wave functions of the system are obtained through the sl(2) algebraization. It is shown that the results are in good agreement with those obtained previously via a different method.

scholarly journals Composite system in rotationally invariant noncommutative phase space

2018 ◽  
Vol 33 (07) ◽  
pp. 1850037 ◽  
Author(s):  
Kh. P. Gnatenko ◽  
V. M. Tkachuk
Keyword(s):  
Phase Space ◽  
Composite System ◽  
Particle System ◽  
Rotational Symmetry ◽  
Center Of Mass ◽  
Noncommutative Space ◽  
Effective Parameters ◽  
Noncommutative Phase Space ◽  
Noncommutative Algebra ◽  
Rotationally Invariant

Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of composite system reproduce noncommutative algebra for coordinates and momenta of individual particles. Also, on these conditions, the coordinates and the momenta of the center-of-mass satisfy noncommutative algebra with effective parameters of noncommutativity which depend on the total mass of the system and do not depend on its composition. Besides, it is shown that on these conditions the coordinates in noncommutative space do not depend on mass and can be considered as kinematic variables, the momenta are proportional to mass as it has to be. A two-particle system with Coulomb interaction is studied and the corrections to the energy levels of the system are found in rotationally invariant noncommutative phase space. On the basis of this result the effect of noncommutativity on the spectrum of exotic atoms is analyzed.

scholarly journals Quantum tetrachotomous states: Superposition of four coherent states on a line in phase space

2019 ◽  
Vol 99 (6) ◽  
Author(s):  
Namrata Shukla ◽  
Naeem Akhtar ◽  
Barry C. Sanders
Keyword(s):  
Phase Space ◽  
Coherent States

scholarly journals Thermodynamical properties of graphene in noncommutative phase–space

2014 ◽  
Vol 349 ◽  
pp. 402-410 ◽  
Author(s):  
Victor Santos ◽  
R.V. Maluf ◽  
C.A.S. Almeida
Keyword(s):  
Phase Space ◽  
Noncommutative Phase Space ◽  
Thermodynamical Properties

Reply to  Comment on   Semiclassical approximations in phase space with coherent states   

2002 ◽  
Vol 35 (44) ◽  
pp. 9493-9497 ◽  
Author(s):  
M Baranger ◽  
M A M de Aguiar ◽  
F Keck ◽  
H J Korsch ◽  
B Schellhaa 
Keyword(s):  
Phase Space ◽  
Coherent States ◽  
Semiclassical Approximations

COHERENT STATES WITHOUT GROUPS: QUANTIZATION ON NONHOMOGENEOUS MANIFOLDS

1993 ◽  
Vol 08 (18) ◽  
pp. 1735-1738 ◽  
Author(s):  
JOHN R. KLAUDER
Keyword(s):  
Phase Space ◽  
Coherent State ◽  
Wide Class ◽  
Coherent States ◽  
Path Integrals ◽  
Killing Vector ◽  
Single Variable ◽  
Holomorphic Representation ◽  
Representation Spaces ◽  
State Path

A wide class of single-variable holomorphic representation spaces are constructed that are associated with very general sets of coherent states defined without the use of transitively acting groups. These representations and states are used to define coherent-state path integrals involving phase-space manifolds having one Killing vector but a quite general curvature otherwise.

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