Coupled oscillators in non-commutative phase space: Path integral approach

. We present the path integral techniques in a non-commutative phase space and illustrate the calculation in the case of an exact problem of the coupled oscillator in two dimensions. The non-commutativity, with respect to Poisson (classical) and Heisenberg (quantum) brackets, in this phase space, is...

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Bibliographic Details
Published in:European physical journal plus 2019-08, Vol.134 (8), p.396, Article 396
Main Authors: Khiari, L., Boudjedaa, T., Makhlouf, A., Meftah, M. T.
Format: Article
Language:English
Subjects:
Applied and Technical Physics
Atomic
Commutativity
Complex Systems
Condensed Matter Physics
Euclidean space
Harmonic oscillators
Linear transformations
Mathematical analysis
Mathematical and Computational Physics
Molecular
Optical and Plasma Physics
Oscillators
Physics
Physics and Astronomy
Quantum field theory
Quantum physics
Regular Article
Spacetime
Theoretical
Theoretical physics
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Summary:. We present the path integral techniques in a non-commutative phase space and illustrate the calculation in the case of an exact problem of the coupled oscillator in two dimensions. The non-commutativity, with respect to Poisson (classical) and Heisenberg (quantum) brackets, in this phase space, is governed by two small constant parameters. They characterize the geometric deformation of this space. The path integral is formulated in a mixed representation due to the non-commutativity of the coordinates on one hand and those of the momentum on the other hand. Using a canonical linear transformation in this non-commutative phase space, we retrieve the commutative phase space properties by which the study becomes more suitable. The case of the non-commutative coupled harmonic oscillator in two dimensions is treated and the thermodynamics properties of the assembly of such oscillators are derived too.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/i2019-12770-3