Properties of the random force in coupled nonlinear Langevin equations

1992 ◽  
Vol 45 (12) ◽  
pp. 8957-8960 ◽  
Author(s):  
P. Mazur
Keyword(s):  
Random Force ◽  
Langevin Equations ◽  
Nonlinear Langevin Equations

QUANTUM STOCHASTIC EQUATIONS FOR A NON-LINEAR DAMPED OSCILLATOR

1993 ◽  
Vol 07 (09) ◽  
pp. 623-631 ◽  
Author(s):  
T. SAITO ◽  
T. ARIMITSU
Keyword(s):  
Master Equation ◽  
Conventional Treatment ◽  
Random Force ◽  
Quantum Systems ◽  
Langevin Equations ◽  
Unified Framework ◽  
Thermo Field Dynamics ◽  
Non Linear ◽  
Damping Theory ◽  
Damped Oscillator

A unified framework of stochastic differential equations for quantum systems, formulated within Non-Equilibrium Thermo Field Dynamics (NETFD), is applied to a model of non-linear damped oscillator. The quantum stochastic Liouville equation and the quantum Langevin equations (both of Ito and Stratonovich type), which are consistent with the corresponding master equation, are written down explicitly in the case of a non-conventional treatment. This solves Kubo's third problem: how one can obtain the correlations of random force operators for the Langevin equation compatible with the master equation derived by the non-conventional treatment of the damping theory.

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