Semiclassical Propagators for Quantum Coherent States and Applications of Extra Quantum Phase to Large-spin Tunneling of Magnetic Molecules

A continuous path integral is used to obtain the semiclassical expressions of quantum propagators by means of coherent states in the holomorphic representation together with the appropriate boundary conditions. It allows us to express the total actions including boundary terms, classical trajectories, and extra phases in the stationary phase approximation. In particular, in the semiclassical expression for the quantum spin propagator, we pay attention to the extra quantum phase discovered by Solari and Kochetov. It is shown that this extra phase is related to an anomaly in the fluctuation determinant. It is verified that once this extra phase is included, the semiclassical propagator leads to the correct short time behaviour to O(T²), and shows its consistency under dissection of the path. In the application to the instanton methods, the extra quantum phase yields the correct formula for the tunnel splitting including both the exponential factor and the prefactor. The quantum phase leads to the correct spectrum with a shift of the spin quantum number by 1/2. We apply the semiclassical propagators and the tunnel splitting to a few models in magnetic molecular systems. It is shown that the formula gives the correct exponential factor and prefactors for quantum tunneling of a large spin if the extra quantum phase is taken into account.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2012

Author dc:creator

• Park, Kee-Su

Contributors dc:contributor

• Stone, Michael

• magnetic molecular systems
• quantum tunneling

Statement dc:rights

• ©2001 Kee-Su Park

Language dc:language

en

Identifier

4539147

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/31330