Dynamical path integral calculations for condensed phase processes

Lambert-Garrido, Roberto

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https://hdl.handle.net/2142/44244 Copy

Description

Title

Dynamical path integral calculations for condensed phase processes

Author(s)

Lambert-Garrido, Roberto

Issue Date

2013-05-24T22:05:20Z

Director of Research (if dissertation) or Advisor (if thesis)

Makri, Nancy

Doctoral Committee Chair(s)

Stack, John D.

Committee Member(s)

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

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

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

Abstract

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.

Graduation Semester

2013-05

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

Copyright and License Information

Copyright 2013 Roberto Lambert-Garrido

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