Studies in dynamics

Citation

Wang, Neng E. (1995) Studies in dynamics. Master's thesis, California Institute of Technology. doi:10.7907/j1ch-3v41. https://resolver.caltech.edu/CaltechETD:etd-10292007-104923

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. In this thesis, three parts of my work are reported. The first part of the work was done with Prof. Rudy Marcus, the second and third parts of the work were done with Prof. Bill Goddard. Here I would like to summarize the results from each part briefly. In the first part, we propose doing Scanning Tunneling Microscopy(STM) current calculations with a new model in the spheroidal coordinate system. The tip is modeled as a hyperboloid. The electrostatic potential part of this model is solved exactly. The free electron model of the whole system is also solved exactly. In the second part, we found that the Nose Canonical Molecular Dynamics, the most commonly used CMD method, leads to the wrong heat capacity for the system and hence is inconsistent with the thermodynamics. To solve this problem, we propose Two Nose variable Dynamics by changing the dimensionality of the Nose variable s and its conjugate [...] from one- to two-dimension. In the third part, The exact expression for the quantum statistical partition function in the canonical ensemble is given. The physical interpretation of each term for N-particle system is discussed. The new formula is applied to the weakly degenerate quantum ideal case. By analyzing each term in the expansion, it is possible that this canonical partition function can be applied to cases where both quantum correlation effects and particle interactions are important.

Thesis Files