Dissipative quantum trajectories in complex space: Damped harmonic oscillator

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• 作者：Chia-Chun Chou ^{ccchou@mx.nthu.edu.tw" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Dissipative quantum trajectory ; Logarithmic nonlinear Schrö ; dinger equation ; Quantum Hamilton&ndash ; Jacobi equation ; Damped harmonic oscillator ; Dissipative system
• 刊名：Annals of Physics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：373
• 期：Complete
• 页码：325-345
• 全文大小：1755 K

文摘

Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.