Dynamical path integral calculations for condensed phase processes

As is well known, the computational effort in quantum mechanics grows exponentially with system size. Thus a typical computation of an interesting many-body problem quickly becomes prohibitive. In this work, we try to circumvent this exponential scaling by treating a few degrees of freedom explicitly (i.e. the system) while integrating out the rest of the degrees of freedom (i.e. the bath). For a bath of harmonic oscillators, this integration procedure is well known and we apply this result to problems of charge transfer across molecules by summing over statistically significant system paths. If we have a generic bath composed of classical like particles interacting with the system of interest, the classical behavior of the bath influences the quantum mechanical behavior of the system. Thus we arrive at a rigorous quantum-classical path integral formulation which we believe has very promising applications in chemistry and biology.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2013

Author dc:creator

• Lambert-Garrido, Roberto

Contributors dc:contributor

• Makri, Nancy
• Stack, John D.
• Cooper, S. Lance
• Makins, Naomi C.R.

• Path Integral
• Influence Functionals
• Molecular Wires
• Quantum-Classical Dynamics

Statement dc:rights

• Copyright 2013 Roberto Lambert-Garrido

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/44244

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/44244