scholarly journals Spectral resolution of the Liouvillian of the Lindblad master equation for a harmonic oscillator

2010 ◽  
Vol 51 (7) ◽  
pp. 072107 ◽  
Author(s):  
Daigo Honda ◽  
Hiromichi Nakazato ◽  
Motoyuki Yoshida
Keyword(s):  
Harmonic Oscillator ◽  
Master Equation ◽  
Spectral Resolution ◽  
Lindblad Master Equation

Solvability of the Caldeira–Leggett model

2020 ◽  
Vol 98 (7) ◽  
pp. 683-688
Author(s):  
Smail Bougouffa ◽  
Lazhar Bougoffa
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Harmonic Oscillator ◽  
Master Equation ◽  
Wigner Distribution ◽  
Partial Differential ◽  
Coupled Differential Equations

In this paper, we illustrate the use of the method of the characteristics in various dissipative models of a single harmonic oscillator. The master equation governing the process can be transformed to a partial differential equation on the Wigner distribution, which in turn can be split to a system of coupled differential equations. We present a useful technique that can be used to separate the system without increasing the order and then the solutions can be obtained. The obtained solutions are used to calculate the average of energy observable of the system. This procedure can be extended to solve some other complex similar problems.

TIME-DEPENDENT BOGOLIUBOV TRANSFORMATIONS AND THE DAMPED HARMONIC OSCILLATOR

1993 ◽  
Vol 08 (21) ◽  
pp. 1999-2009
Author(s):  
P. SHANTA ◽  
S. CHATURVEDI ◽  
V. SRINIVASAN ◽  
F. MANCINI
Keyword(s):  
Harmonic Oscillator ◽  
Master Equation ◽  
Time Dependent ◽  
Damped Harmonic Oscillator ◽  
Bogoliubov Transformations ◽  
Non Equilibrium

We derive the master equation for a damped harmonic oscillator, for any α, using time-dependent Bogoliubov transformations of non-equilibrium thermofield dynamics. This investigation naturally leads us to a physically and mathematically meaningful parametrization of the Bogoliubov matrix.

Sign in / Sign up

Export Citation Format

Share Document