Eur. Phys. J. B 18, 633-643 (2000)
https://doi.org/10.1007/s100510070012

Non-Markovian relaxation in an open quantum system

Polynomial approach to the solution of the quantum master equation

Institut für Physik der Humboldt-Universität zu Berlin, Hausvogteiplatz 5-7, 10117 Berlin, Germany

Corresponding author: ^a mancal@physik.hu-berlin.de

Received: 12 April 2000
Revised: 2 September 2000
Published online: 15 December 2000

Abstract

Non-Markovian dynamics in open quantum systems is characterized by a time-non-locality in the equation of motion valid for the reduced density operator. An expansion of this density matrix equation with respect to Laguerre polynomials is used to tackle the time-non-locality. The applicability and the numerical limitations of the method are discussed in detail. In order to illuminate the characteristics of non-Markovian dynamics the reference example is studied of a single quantum degree of freedom moving in a harmonic potential and being embedded in a heat bath. If interpreted as the photoinduced dynamics of nuclear motion in polyatomic molecules we can suggest two clear signatures of non-Markovian dynamics observable in ultrafast optical experiments, firstly a pronounced and somewhat irregular oscillatory behavior of the vibrational level populations, and secondly a separation of the vibrational wavepacket into a double-structure.