Date of Award

8-31-2014

Document Type

Campus Access Thesis

Degree Name

Master of Science (MS)

Department

Physics, Applied

First Advisor

Bala Sundaram

Second Advisor

Kurt Jacobs

Third Advisor

Stephen Arnason

Abstract

Recent advances in quantum adiabatic shortcuts give hope for creating novel quantum technologies. In this thesis, Ehrenfest Dynamics and Heisenberg operator equations are proposed as a general way to examine the dynamics of a system when an external parameter of the Hamiltonian changes in time. Since the Heisenberg Operator equations result in an infinite hierarchy set of equation for an arbitrary Hamiltonian a second order cummulant truncation of the potential is used. The idea being proposed here is that this method is accurate as long as the Hamiltonian changes over short times. The test case used was a particle in a box. For cases where the initial condition of the particle is a stationary state it is shown that the second order truncation completely breaks down for any symmetric potential. When starting with non stationary states, the method seems to fail for our given test case. Whether this failure is in the numerics of the simulation or elsewhere is left as an open question.

Comments

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