A Canonical Approach to the Quantization of the Damped Harmonic Oscillator
classification
🪐 quant-ph
hep-th
keywords
approachanalysiscanonicaldampedhamiltonianharmonicoscillatorquantization
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We provide a new canonical approach for studying the quantum mechanical damped harmonic oscillator based on the doubling of degrees of freedom approach. Explicit expressions for Lagrangians of the elementary modes of the problem, characterising both forward and backward time propagations are given. A Hamiltonian analysis, showing the equivalence with the Lagrangian approach, is also done. Based on this Hamiltonian analysis, the quantization of the model is discussed.
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Spin-Induced Non-Markovian Time-Crystal-Like Dynamics and Fractal Scaling in the Bateman Dual Oscillator
Spin-induced deformation in the Bateman dual oscillator framework yields non-Markovian reduced dynamics with persistent oscillations and fractal scaling that mimic time crystals in a globally unitary quantum system.
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