Connecting dissipation and noncommutativity: A Bateman system case study

Abstract

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.

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Cited by in corpus (9)

• Two quantization approaches to the Bateman oscillator model
• Quantization of the damped harmonic oscillator based on a modified Bateman Lagrangian
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• Hyperbolic ring based formulation for thermo field dynamics, quantum dissipation, entanglement, and holography
• Emergent entropy of exotic oscillators and squeezing in three-wave mixing process
• Quantization of nonlinear non-Hamiltonian systems
• Particle Dynamics and Lie-algebraic type of Non-commutativity of space-time
• Classical Hamiltonian Systems with Balanced loss and gain
• Acceleration of particles in Schwarzschild and Kerr geometries