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Journal of Optics B Quantum and Semiclassical Optics

A method for calculating two-time correlation functions in the quantum trajectory approach

A. Karpati, Петер Адам, József Janszky

Published Mar 1, 2004• 0 citations
Publisher

Abstract

We developed a technique for calculating two-time correlation functions based on a quantum trajectory approach. Our method requires the simulation of the evolution of a given set of density matrices only once. The evaluation can be carried out from the density matrix data obtained for any quantities, time arguments and initial conditions. The computational efficiency of the method is estimated and an example of application is presented.

DOI
10.1088/1464-4266/6/3/013

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We developed a technique for calculating two-time correlation functions based on a quantum trajectory approach. Our method requires the simulation of the evolution of a given set of density matrices only once. The evaluation can be carried out from the density matrix data obtained for any quantities, time arguments and initial conditions. The computational efficiency of the method is estimated and an example of application is presented.
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Using the positive P-representation of the density matrix, we develop an algorithm for calculating the quantum many-body nonlinear response functions of a system of bosons driven impulsively by external fields. The formalism maps the quantum time evolution of N boson degrees of freedom into a stochastic dynamics of 4N classical degrees of freedom. The first- and the third-order response functions are calculated by propagating the parameters of the P-representation using a set of coupled Langevin equations with multiplicative noise. These parameters serve as classical variables. Two classical ways for computing the response functions are presented. In the nonequilibrium method, an observable is calculated for weak impulsive pulses, and the response functions are obtained by taking its derivatives with respect to the pulse amplitudes. In the alternative, equilibrium simulation, the response functions are expressed in terms of time-correlation functions involving the P-representation parameters and stability matrices representing the perturbation of the trajectories. The stability matrices can be propagated simultaneously with the Langevin equations for the parameters. The formalism is generalized for a many-body boson system coupled to a harmonic bath.