TY - JOUR
T1 - Quantum behavior of general time-dependent quadratic systems linearly coupled to a bath
AU - Twamley, J.
PY - 1993
Y1 - 1993
N2 - In this paper we solve for the quantum propagator of a general time-dependent system quadratic in both position and momentum, linearly coupled to an infinite bath of harmonic oscillators. We work in the regime where the quantum optical master equation is valid. We map this master equation to a Schrödinger equation on super-Hilbert space and utilize Lie-algebraic techniques to solve for the dynamics in this space. We then map back to the original Hilbert space to obtain the solution of the quantum dynamics. The Lie-algebraic techniques used are preferable to the standard Wei-Norman methods in that only coupled systems of first-order ordinary differential equations and purely algebraic equations need only be solved. We look at two examples.
AB - In this paper we solve for the quantum propagator of a general time-dependent system quadratic in both position and momentum, linearly coupled to an infinite bath of harmonic oscillators. We work in the regime where the quantum optical master equation is valid. We map this master equation to a Schrödinger equation on super-Hilbert space and utilize Lie-algebraic techniques to solve for the dynamics in this space. We then map back to the original Hilbert space to obtain the solution of the quantum dynamics. The Lie-algebraic techniques used are preferable to the standard Wei-Norman methods in that only coupled systems of first-order ordinary differential equations and purely algebraic equations need only be solved. We look at two examples.
UR - http://www.scopus.com/inward/record.url?scp=5544324114&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.48.2627
DO - 10.1103/PhysRevA.48.2627
M3 - Article
VL - 48
SP - 2627
EP - 2633
JO - Physical Review A: covering atomic, molecular, and optical physics and quantum information
JF - Physical Review A: covering atomic, molecular, and optical physics and quantum information
SN - 2469-9926
IS - 4
ER -