Complex quantum trajectories for barrier scattering

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dc.contributor.advisorWyatt, Robert E. (Robert Eugene),en
dc.creatorRowland, Bradley Allen, 1979-en
dc.date.accessioned2008-08-29T00:12:02Zen
dc.date.accessioned2017-05-11T22:19:12Z
dc.date.available2008-08-29T00:12:02Zen
dc.date.available2017-05-11T22:19:12Z
dc.date.issued2007-12en
dc.description.abstractWe have directed much attention towards developing quantum trajectory methods which can accurately predict the transmission probabilities for a variety of quantum mechanical barrier scattering processes. One promising method involves solving the complex quantum Hamilton-Jacobi equation with the Derivative Propagation Method (DPM). We present this method, termed complex valued DPM (CVDPM(n)). CVDPM(n) has been successfully employed in the Lagrangian frame to accurately compute transmission probabilities on 'thick' one dimensional Eckart and Gaussian potential surfaces. CVDPM(n) is able to reproduce accurate results with a much lower order of approximation than is required by real valued quantum trajectory methods, from initial wave packet energies ranging from the tunneling case (E[subscript o]=0) to high energy cases (twice the barrier height). We successfully extended CVDPM(n) to two-dimensional problems (one translational degree of freedom representing an Eckart or Gaussian barrier coupled to a vibrational degree of freedom) in the Lagrangian framework with great success. CVDPM helps to explain why barrier scattering from "thick" barriers is a much more well posed problem than barrier scattering from "thin" barriers. Though results in these two cases are in very good agreement with grid methods, the search for an appropriate set of initial conditions (termed an 'isochrone) from which to launch the trajectories leads to a time-consuming search problem that is reminiscent of the rootsearching problem from semi-classical dynamics. In order to circumvent the isochrone problem, we present CVDPM(n) equations of motion which are derived and implemented in the arbitrary Lagrangian-Eulerian frame for a metastable potential as well as the Eckart and Gaussian surfaces. In this way, the isochrone problem can be circumvented but at the cost of introducing other computational difficulties. In order to understand why CVDPM may give better transmission probabilities than real valued counterparts, much attention we have been studying and applying numerical analytic continuation techniques to visualize complex-extended wave packets as well as the complex-extended quantum potential. Numerical analytic continuation techniques have also been used to analytically continue a discrete real-valued potential into the complex plane for CVDPM with very promising results.en
dc.description.departmentChemistryen
dc.description.departmentChemistry and Biochemistryen
dc.format.mediumelectronicen
dc.identifier.oclc233607316en
dc.identifier.urihttp://hdl.handle.net/2152/3811en
dc.language.isoengen
dc.rightsCopyright © is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.en
dc.subject.lcshQuantum trajectoriesen
dc.subject.lcshScattering (Physics)en
dc.subject.lcshHamilton-Jacobi equations--Numerical solutionsen
dc.subject.lcshLagrange equations--Numerical solutionsen
dc.titleComplex quantum trajectories for barrier scatteringen
dc.type.genreThesisen

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