Novikov, Alexey
[Verfasser:in]
;
Schreiber, Michael
[Gutachter:in];
Hoffmann, Karl Heinz
[Gutachter:in];
Pelster, Axel
[Gutachter:in]Technische Universität Chemnitz
Path integral formulation of dissipative quantum dynamics
Beschreibung:
In this thesis the path integral formalism is applied to the calculationof the dynamics of dissipative quantum systems. The time evolution of a system of bilinearly coupled bosonic modes istreated using the real-time path integral technique incoherent-state representation. This method is applied to a damped harmonic oscillatorwithin the Caldeira-Leggett model. In order to get the stationarytrajectories the corresponding Lagrangian function is diagonalized andthen the path integrals are evaluated by means of the stationary-phasemethod. The time evolution of thereduced density matrix in the basis of coherent states is given in simpleanalytic form for weak system-bath coupling, i.e. the so-calledrotating-wave terms can be evaluated exactly but the non-rotating-waveterms only in a perturbative manner. The validity range of therotating-wave approximation is discussed from the viewpoint of spectralequations. In addition, it is shown that systemswithout initial system-bath correlations can exhibit initial jumps in thepopulation dynamics even for rather weak dissipation.Only with initialcorrelations the classical trajectories for the system coordinate can berecovered.The path integral formalism in a combined phase-space and coherent-staterepresentation is applied to the problem of curve-crossing dynamics.Thesystem of interest is described by two coupled one-dimensional harmonicpotential energy surfaces interacting with a heat bath. The mapping approach is used to rewrite theLagrangian function of the electronic part of the system.Using theFeynman-Vernon influence-functional method the bath is eliminated whereasthe non-Gaussian part of the path integral is treated using theperturbation theory in the small coordinate shift betweenpotential energy surfaces. The vibrational and the population dynamics is considered in a lowest order of the perturbation.The dynamics of aGaussian wave packet is analyzed along a one-dimensional reactioncoordinate.Also the damping rate of coherence in the electronic part of the relevant systemis evaluated within the ordinary and variational perturbation theory.The analytic expressions for the rate functions are obtained in the low and high temperature regimes.