arXiv:1908.01187

Lindblad dynamics of the damped and forced quantum harmonic oscillator

H. J. Korsch

Published Aug 3, 2019• 2 citations

Abstract

The quantum dynamics of a damped and forced harmonic oscillator is investigated in terms of a Lindblad master equation. Elementary algebraic techniques are employed allowing for example to analyze the long time behavior, i.e. the quantum limit cycle. The time evolution of various expectation values is obtained in closed form as well as the entropy and the Husimi phase space distribution. We also discuss the related description in terms of a non-Hermitian Hamiltonian.

DOI: 10.48550/arxiv.1908.01187

Related papers

Lindblad dynamics of the damped and forced quantum harmonic oscillator: General solution

H. J. Korsch

The quantum dynamics of a damped and forced harmonic oscillator described by a Lindblad master equation is analyzed. The master equation is converted into a matrix-vector representation and the resulting non-Hermitian Schrödinger equation is solved by Lie-algebraic techniques allowing the construction of the general solution for the density operator.

arXiv:1909.03206Sep 7, 20190 citations

Analytic solutions to various dissipation models of the simple and driven quantum harmonic oscillator

Pablo Carlos López Vázquez, Roberto Santos Silva

We obtain analytic solutions to various models of dissipation of the quantum harmonic oscillator, employing a simple method in the Wigner function Fourier transform description of the system; and study as an exemplification, the driven open quantum harmonic oscillator. The environmental models we use are based on optical master equations for the zero and finite temperature bath and whose open dynamics are described by a Lindblad master equation, and also we use the Caldeira-Leggett model for the high temperature limit, in the the under damped an the over damped case. Under the Wigner Fourier transform or chord function as it has been called, it becomes particularly simple to solve the dynamics of the open oscillator in the sense that the dynamics of the system are reduced to the application of an evolution matrix related to the damped motion of the oscillator.

arXiv:1801.05943Jan 18, 20182 citations

From Closed to Open Quantum Systems

Alexander Eichler, Oded Zilberberg

Abstract In this chapter, we generalize our treatment of quantum systems by allowing them to be coupled to an environment at a finite temperature, similar to what we discussed for classical systems in chapter 4. The time evolution of many open quantum system can be calculated using the Lindblad master equation. We study various effects of the thermal environment on the quantum harmonic oscillator, and then continue to include driving by an external force

Sep 26, 20230 citations

Effective description of the quantum damped harmonic oscillator: revisiting the Bateman dual system

Carlos Raul Javier Valdez, Héctor H. Hernández, Guillermo Chacón‐Acosta

Abstract In this work, we present a quantization scheme for the damped harmonic oscillator (QDHO) using a framework known as momentous quantum mechanics. Our method relies on a semiclassical dynamical system derived from an extended classical Hamiltonian, where the phase-space variables are given by expectation values of observables and quantum dispersions. The significance of our study lies in its potential to serve as a foundational basis for the effective description of open quantum systems (OQS), and the description of dissipation in quantum mechanics. By employing the Bateman’s dual model as the initial classical framework, and undergoing quantization, we demonstrate that our description aligns exceptionally well with the well-established Lindblad master equation for the QDHO. Furthermore, the robust formulation of our approach suggests a broad applicability in the context of OQS, extending implementations into more general systems, making it a versatile and powerful tool to study diverse phenomena.

arXiv:2309.02689Physica ScriptaFeb 10, 20253 citations

Husimi Dynamics Generated by non-Hermitian Hamiltonians

Katherine Holmes, Wasim Rehman, Simon Malzard +1 more

The dynamics generated by non-Hermitian Hamiltonians are often less intuitive than those of conventional Hermitian systems. Even for models as simple as a complexified harmonic oscillator, the dynamics for generic initial states shows surprising features. Here we analyze the dynamics of the Husimi distribution in a semiclassical limit, illuminating the foundations of the full quantum evolution. The classical Husimi evolution is composed of two factors: (i) the initial Husimi distribution evaluated along phase-space trajectories and (ii) the final value of the norm corresponding to each phase-space point. Both factors conspire to lead to intriguing dynamical behaviors. We demonstrate how the full quantum dynamics unfolds on top of the classical Husimi dynamics for two instructive examples.

arXiv:2212.03719Physical Review LettersApr 11, 202310 citations

Algebraic Structure of a Master Equation with Generalized Lindblad Form

Kazuyuki Fujii

The quantum damped harmonic oscillator is described by the master equation with usual Lindblad form. The equation has been solved completely by us in arXiv: 0710.2724 [quant-ph]. To construct the general solution a few facts of representation theory based on the Lie algebra su(1,1) were used. In this paper we treat a general model described by a master equation with generalized Lindblad form. Then we examine the algebraic structure related to some Lie algebras and construct the interesting approximate solution. Quantum Computation (Computer) is one of main subjects in Quantum Physics. To realize it we must overcome severe problems arising from Decoherence, so we need to study Quantum Open System to control decoherence (if possible). This paper is a series of [1] and [2], and we study dynamics of a quantum open system. First we explain our purpose in a short manner. See [3] as a general introduction to this subject. ∗E-mail address:

Nov 20, 20123 citations