Damped quantum harmonic oscillator
A. Isar, A. Sandulescu

TL;DR
This paper analyzes the Lindblad theory for the damped quantum harmonic oscillator, providing generalized constraints, explicit representations, and solutions for moments and distributions, unifying various master equations and exploring their properties.
Contribution
It generalizes the constraints on diffusion coefficients, explicitly derives representations of the Lindblad equation, and unifies different master equations under a common framework.
Findings
Master equations are particular cases of the Lindblad equation.
Quasiprobability distributions are Gaussian in steady state.
Variances are consistent across different quasiprobability representations.
Abstract
In the framework of the Lindblad theory for open quantum systems the damping of the harmonic oscillator is studied. A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the master equation for the damped quantum oscillator is presented; the Schr\"odinger and Heisenberg representations of the Lindblad equation are given explicitly. On the basis of these representations it is shown that various master equations for the damped quantum oscillator used in the literature are particular cases of the Lindblad equation and that the majority of these equations are not satisfying the constraints on quantum mechanical diffusion coefficients. Analytical expressions for the first two moments of coordinate and momentum are also obtained by using the characteristic function of the Lindblad master equation. The master equation is transformed into…
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Taxonomy
TopicsQuantum Information and Cryptography · Mechanical and Optical Resonators · Quantum Mechanics and Applications
