Connecting dissipation and noncommutativity: A Bateman system case study

Quantum effects on a pair of Bateman oscillators embedded in an ambient noncommutative space (Moyal plane) is analyzed using both path integral and canonical quantization schemes within the framework of Hilbert-Schmidt operator formulation. We adopt a method which is distinct from the one which empl...

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Bibliographic Details
Published in:arXiv.org 2018-03
Main Authors: Pal, Sayan Kumar, Nandi, Partha, Chakraborty, Biswajit
Format: Article
Language:English
Subjects:
Damping
Dissipation factor
Embedded systems
Measurement
Operators (mathematics)
Oscillators
Online Access:Get full text
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Summary:Quantum effects on a pair of Bateman oscillators embedded in an ambient noncommutative space (Moyal plane) is analyzed using both path integral and canonical quantization schemes within the framework of Hilbert-Schmidt operator formulation. We adopt a method which is distinct from the one which employs 't Hooft's scheme of quantization, carried out earlier in the literature where the ambient space was taken to be commutative. Our quantization shows that we end up finally again with a Bateman system except that the damping factor undergoes renormalization. The corresponding expression shows that the renormalized damping factor can be non-zero even if "bare" one is zero to begin with. Conversely, the noncommuatative parameter \(\theta\), taken to be a free one now, can be fine-tuned to get a vanishing renormalized damping factor. This indicates a duality between dissipative commutative theory and non-dissipative noncommutative theory.
ISSN:2331-8422
DOI:10.48550/arxiv.1803.03334