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Journal of Applied Mathematics and Physics

Dynamics of a Quantum Dissipative System Coupled with an Oscillator

Emmanouil George Thrapsaniotis

Published Jan 1, 2024• 0 citations
Publisher

Abstract

We study the dynamics of a quantum dissipative system. Besides its linear coupling with a harmonic bath modelling the dissipation, we suppose that it is coupled with an oscillator with an interaction of the form s 2 x 2 . In our study, we integrate over the bath and the oscillator, extract the corresponding influence functionals and then solve the system’s sign problem. We apply the theory to the case of a double well and study the time evolution of the expectation value of the position.

DOI
10.4236/jamp.2024.124091

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We study the dynamics of a quantum dissipative system. Besides its linear coupling with a harmonic bath modelling the dissipation, we suppose that it is coupled with an oscillator with an interaction of the form s 2 x 2 . In our study, we integrate over the bath and the oscillator, extract the corresponding influence functionals and then solve the system’s sign problem. We apply the theory to the case of a double well and study the time evolution of the expectation value of the position.
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We develop a perturbation scheme to treat the dynamics of a quantum Brownian particle (coordinate xxx) coupled nonlinearly to a bath of oscillators (coordinates qn{q}_{n}qn​) with an interaction action in the form $\ensuremath{\lambda}f(x){q}_{n}^{k}$. We derive the influence functionals for the k=2,3,4k=2, 3, 4k=2,3,4 cases to order ${\ensuremath{\lambda}}^{2}$ and derive the master equations for the special cases of local dissipation and white noise, as well as the general cases of nonlocal dissipation and colored noise for f(x)=xandx2f(x)=x \mathrm{and} {x}^{2}f(x)=xandx2. We show that a generalized fluctuation-dissipation relation exists between the lthl\mathrm{th}lth-order noise kernels of the kthk\mathrm{th}kth-order coupling and their corresponding dissipation kernels.
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