Forward-Backward Methods for Mixed System Dynamics

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Chemistry

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Bukhman, Edward

Contributors dc:contributor

• Makri, Nancy

• Physics, Condensed Matter

Language dc:language

eng

Identifier

(MiAaPQ)AAI3337711

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/84302