Forward-Backward Methods for Mixed System Dynamics
Bukhman, Edward
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https://hdl.handle.net/2142/84302
Description
Title
Forward-Backward Methods for Mixed System Dynamics
Author(s)
Bukhman, Edward
Issue Date
2008
Doctoral Committee Chair(s)
Makri, Nancy
Department of Study
Chemistry
Discipline
Chemistry
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Condensed Matter
Language
eng
Abstract
When a quantum system is inhomogeneous (comprised of two particle types, each one having different size and time scales) it is possible to achieve an optimal mix of accuracy and computational efficiency in the study of its dynamics by applying mixed methods---methods that treat the two subsystems differently. In particular, the observable system is treated by a method that fully preserves its quantum character, while the treatment of its environment, the bath, contains some simplifying assumptions. One such simplified treatment is the derivative Forward-Backward Semiclassical Dynamics (FBSD) method. FBSD has an important limitation in that its description of the dynamics of quantum systems is accurate only for short times, since the method proceeds by assigning quantum weights to classical trajectories, and is unable to describe systems which exhibit strong coherence. An extension of this method described in this work makes it possible to apply quantum propagation to the system while simultaneously applying FBSD propagation to the surrounding bath. There are two principal reasons why this extension is non-trivial. First, because FBSD uses a statistical (Monte-Carlo) methodology to perform the requisite integral, the method is optimal when the resulting observable can be particle-averaged with respect to the system components. When the system is inhomogeneous, such averaging is no longer possible, reducing the capability of the method. Second, because the system and the bath are coupled, yet are propagated by quantum and classical dynamics respectively, the description of the coupling determines the accuracy and the limitations of the method. In the work below, we proceed to solve these problems in the context of developing a mixed Quantum-FBSD method.
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