Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation

@article{citeulike:1921022, abstract = {We develop a formulation of quantum damping theory in which the explicit nature of inputs from a heat bath; and of outputs into it; is taken into account. Quantum Langevin equations are developed; in which the Langevin forces are the field operators corresponding to the input modes. Time-reversed equations exist in which the Langevin forces are the output modes; and the sign of damping is reversed. Causality and boundary conditions relating inputs to system variables are developed. The concept of ‘‘quantum white noise’’ is formulated; and the formal relationship between quantum Langevin equations and quantum stochastic differential equations (SDE’s) is established. In analogy to the classical formulation; there are two kinds of SDE’s: the Ito and the Stratonovich forms. Rules are developed for converting from one to the other. These rules depend on the nature of the quantum white noise; which may be squeezed. The SDE’s developed are shown to be exactly equivalent to quantum master equations; and rules are developed for computing multitime-ordered correlation functions with use of the appropriate master equation. With use of the causality and boundary conditions; the relationship between correlation functions of the output and those of the system and the input is developed. It is possible to calculate what kind of output statistics result; provided that one knows the input statistics and provided that one can compute the system correlation functions.}, author = {Gardiner, C. W. and Collett, M. J. }, citeulike-article-id = {1921022}, doi = {http://dx.doi.org/10.1103/PhysRevA.31.3761}, journal = {Physical Review A}, keywords = {master-equation, stochastic-differential-equations}, month = {June}, number = {6}, pages = {3761+}, posted-at = {2007-11-15 09:30:07}, priority = {2}, publisher = {American Physical Society}, title = {Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation}, url = {http://dx.doi.org/10.1103/PhysRevA.31.3761}, volume = {31}, year = {1985} }

TY - JOUR ID - citeulike:1921022 L3 - citeulike-article-id:1921022 TI - Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation JF - Physical Review A VL - 31 IS - 6 SP - 3761 PB - American Physical Society N2 - We develop a formulation of quantum damping theory in which the explicit nature of inputs from a heat bath; and of outputs into it; is taken into account. Quantum Langevin equations are developed; in which the Langevin forces are the field operators corresponding to the input modes. Time-reversed equations exist in which the Langevin forces are the output modes; and the sign of damping is reversed. Causality and boundary conditions relating inputs to system variables are developed. The concept of ‘‘quantum white noise’’ is formulated; and the formal relationship between quantum Langevin equations and quantum stochastic differential equations (SDE’s) is established. In analogy to the classical formulation; there are two kinds of SDE’s: the Ito and the Stratonovich forms. Rules are developed for converting from one to the other. These rules depend on the nature of the quantum white noise; which may be squeezed. The SDE’s developed are shown to be exactly equivalent to quantum master equations; and rules are developed for computing multitime-ordered correlation functions with use of the appropriate master equation. With use of the causality and boundary conditions; the relationship between correlation functions of the output and those of the system and the input is developed. It is possible to calculate what kind of output statistics result; provided that one knows the input statistics and provided that one can compute the system correlation functions. KW - master-equation KW - stochastic-differential-equations AU - Gardiner, CW AU - Collett, MJ PY - 1985/06// UR - http://dx.doi.org/10.1103/PhysRevA.31.3761 ER -