In this thesis the path integral formalism is applied to the calculation
of the dynamics of dissipative quantum systems.
The time evolution of a system of bilinearly coupled bosonic modes is
treated using the real-time path integral technique in
coherent-state representation.
This method is applied to a damped harmonic oscillator
within the Caldeira-Leggett model.
In order to get the stationary
trajectories the corresponding Lagrangian function is diagonalized and
then the path integrals are evaluated by means of the stationary-phase
method. The time evolution of the
reduced density matrix in the basis of coherent states is given in simple
analytic form for weak system-bath coupling, i.e. the so-called
rotating-wave terms can be evaluated exactly but the non-rotating-wave
terms only in a perturbative manner. The validity range of the
rotating-wave approximation is discussed from the viewpoint of spectral
equations. In addition, it is shown that systems
without initial system-bath correlations can exhibit initial jumps in the
population dynamics even for rather weak dissipation. Only with initial
correlations the classical trajectories for the system coordinate can be
recovered.
The path integral formalism in a combined phase-space and coherent-state
representation is applied to the problem of curve-crossing dynamics. The
system of interest is described by two coupled one-dimensional harmonic
potential energy surfaces interacting with a heat bath.
The mapping approach is used to rewrite the
Lagrangian function of the electronic part of the system. Using the
Feynman-Vernon influence-functional method the bath is eliminated whereas
the non-Gaussian part of the path integral is treated using the
perturbation theory in the small coordinate shift between
potential energy surfaces.
The vibrational and the population dynamics is considered in a lowest order of the perturbation.
The dynamics of a
Gaussian wave packet is analyzed along a one-dimensional reaction
coordinate.
Also the damping rate of coherence in the electronic part of the relevant system
is evaluated within the ordinary and variational perturbation theory.
The analytic expressions for the rate functions are obtained in
the low and high temperature regimes.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:18309 |
| Date | 13 May 2005 |
| Creators | Novikov, Alexey |
| Contributors | Schreiber, Michael, Hoffmann, Karl Heinz, Pelster, Axel, Technische Universität Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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