Theoretical methods for the study of quantum dynamics

Chen, Jonathan E.

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https://hdl.handle.net/2142/16094 Copy

Description

Title

Theoretical methods for the study of quantum dynamics

Author(s)

Chen, Jonathan E.

Issue Date

2010-05-19T18:34:42Z

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

Makri, Nancy

Doctoral Committee Chair(s)

Makri, Nancy

Committee Member(s)

• Luthey-Schulten, Zaida A.
• Bond, Stephen
• Vishveshwara, Smitha

Department of Study

Chemistry

Discipline

Chemical Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• quantum dynamics
• correlation functions
• semiclassical approximation
• quantum trajectories
• Bohmian trajectories
• Monte Carlo
• forward-backward semiclassical dynamics
• forward-backward quantum dynamics
• sign problem
• Hamilton's law of varying action

Abstract

Several theoretical methods for the computation of quantum dynamical quantities are formulated, implemented, and applied, in the overall context of overcoming the exponential scaling property of quantum mechanics. The convergence of the approximate forward-backward semiclassical dynamics (FBSD) method has been accelerated by working with only the imaginary part of the real-time position and momentum time correlation functions. Simple manipulations allow the computationally favorable limit of a single factorization (“bead”) of the Boltzmann operator to yield greatly improved results. Numerical examples for a one-dimensional anharmonic oscillator and Lennard-Jones fluids are presented. Bohm's trajectory formulation of quantum mechanics is an exact mapping of the time-dependent Schrödinger equation onto classical fluid dynamics, plus one extra term responsible for all non-classical effects, the dreaded quantum potential. A computational procedure has been introduced to stably solve Bohm’s hydrodynamic equations of motion in the forward-backward quantum dynamics (FBQD) formulation of time correlation functions, and applied to one-dimensional bound systems at zero and low temperature. A key step in the formulation of this procedure was the use of Hamilton's law of varying action, a generalization of Hamilton’s principle of stationary action applicable to initial-value problems. This has resulted in the first reported synthetic computation of non-stationary quantum trajectories for a fully anharmonic oscillator. Success in one dimension has laid the groundwork for future extension to a rigorous quantum-classical scheme, which is briefly discussed. Other unpublished methods for obtaining time correlation functions and propagators in quantum dynamics are also discussed.

Graduation Semester

2010-5

Permalink

http://hdl.handle.net/2142/16094

Copyright and License Information

Copyright 2010 Jonathan E. Chen

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