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Stone, Michael Park, Kee-Su 2012-06-04T17:50:12Z 2012-06-04T17:50:12Z 10000-01-01 2001 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. Submitted by Elizabeth Kent (eckent2@illinois.edu) on 2012-06-04T17:50:12Z No. of bitstreams: 1 2001_Park.pdf: 5225596 bytes, checksum: decad24a0037cbb4f5030e1b2fdf1d93 (MD5) Made available in DSpace on 2012-06-04T17:50:12Z (GMT). No. of bitstreams: 1 2001_Park.pdf: 5225596 bytes, checksum: decad24a0037cbb4f5030e1b2fdf1d93 (MD5) Previous issue date: 2001 Restriction data tranferred 2014-07-01T11:34:32-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: thesis Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Elizabeth Kent (eckent2@illinois.edu) on 2012-06-04T17:50:12Z Item is restricted indefinitely. thesis U of I Only 4539147 http://hdl.handle.net/2142/31330 en ©2001 Kee-Su Park magnetic molecular systems quantum tunneling Semiclassical Propagators for Quantum Coherent States and Applications of Extra Quantum Phase to Large-spin Tunneling of Magnetic Molecules Dissertation / Thesis text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.