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

2015 ◽  
Vol 438 ◽  
pp. 340-354 ◽  
Author(s):  
Jonas F.G. Santos ◽  
Alex E. Bernardini ◽  
Catarina Bastos
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Free Particles ◽  
Quantum Rotors ◽  
Space Noncommutativity

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 TRACE OF PHASE-SPACE NONCOMMUTATIVITY IN RESPONSE OF A FREE PARTICLE TO LINEARIZED GRAVITATIONAL WAVES

2013 ◽  
Vol 28 (35) ◽  
pp. 1350161 ◽  
Author(s):  
SUNANDAN GANGOPADHYAY ◽  
ANIRBAN SAHA ◽  
SWARUP SAHA
Keyword(s):  
Phase Space ◽  
Gravitational Waves ◽  
Cross Correlation ◽  
Free Particle ◽  
Momentum Scale ◽  
Specific Frequency ◽  
Global Nature ◽  
Space Noncommutativity ◽  
Correlation Procedure ◽  
Noncommutative Parameter

Interaction of linearized gravitational waves with a otherwise free particle has been studied quantum mechanically in a noncommutative (NC) phase-space to examine whether the particle's response to the gravitational wave gets modified due to spatial and/or momentum noncommutativity. The result shows that momentum noncommutativity introduces a oscillatory noise with a specific frequency determined by the fundamental momentum scale and particle mass. Because of the global nature of the phase-space noncommutativity such noise will have similar characteristics for all detector sites and thus will stand out in a data cross-correlation procedure. If detected, this noise will provide evidence of momentum noncommutativity and also an estimation of the relevant noncommutative parameter.

scholarly journals A VARIATIONAL FORMULATION OF SYMPLECTIC NONCOMMUTATIVE MECHANICS

2007 ◽  
Vol 04 (05) ◽  
pp. 789-805 ◽  
Author(s):  
IGNACIO CORTESE ◽  
J. ANTONIO GARCÍA
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Variational Principle ◽  
Configuration Space ◽  
Variational Formulation ◽  
Noncommutative Space ◽  
First Order ◽  
Dynamical Properties ◽  
Definition Of ◽  
Space Noncommutativity

The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to understand the inherent space noncommutativity, we propose a variational principle for noncommutative dynamical systems in configuration space, based on results of our previous work [18]. We hope that this variational formulation in configuration space can be of help to elucidate the definition of some global and dynamical properties of classical and quantum noncommutative space.

Invariance Groups in Classical and Quantum Mechanics

1973 ◽  
Vol 28 (3-4) ◽  
pp. 538-540 ◽  
Author(s):  
D. J. Simms
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Energy Levels ◽  
Classical Mechanics ◽  
Symmetry Groups ◽  
Casimir Invariants ◽  
Classical Phase Space ◽  
Invariance Groups ◽  
Classical And Quantum Mechanics

AbstractThis is a report on some new relations and analogies between classical mechanics and quantum mechanics which arise out of the work of Kostant and Souriau. Topics treated are i) the role of symmetry groups; ii) the notion of elementary system and the role of Casimir invariants; iii) energy levels; iv) quantisation in terms of geometric data on the classical phase space. Some applications are described.

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