Connecting dissipation and noncommutativity: A Bateman system case study Article Swipe
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· 2018
· Open Access
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· DOI: https://doi.org/10.1103/physreva.97.062110
· OA: W2793513789
Quantum effects on a pair of Bateman oscillators embedded in an ambient\nnoncommutative space (Moyal plane) is analyzed using both path integral and\ncanonical quantization schemes within the framework of Hilbert-Schmidt operator\nformulation. We adopt a method which is distinct from the one which employs 't\nHooft's scheme of quantization, carried out earlier in the literature where the\nambient space was taken to be commutative. Our quantization shows that we end\nup finally again with a Bateman system except that the damping factor undergoes\nrenormalization. The corresponding expression shows that the renormalized\ndamping factor can be non-zero even if "bare" one is zero to begin with.\nConversely, the noncommuatative parameter $\\theta$, taken to be a free one now,\ncan be fine-tuned to get a vanishing renormalized damping factor. This\nindicates a duality between dissipative commutative theory and non-dissipative\nnoncommutative theory.\n
