short-report - Reversible Simulation and Visualization of...

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Unformatted text preview: Reversible Simulation and Visualization of Quantum Evolution DoRon B. Motter CIS4914 Senior Project Department of CISE University of Florida Advisor: Dr. Michael P. Frank, email: mpf@cise.ufl.edu Department of CISE University of Florida, Gainesville, FL 32611 Date of Talk: 9 Aug 2000 Abstract Current techniques in quantum simulations are often used to provide insight into a variety of particle interaction phenomena. These techniques are varied and in recent times have become highly specialized. However, the focus of this project is a more general technique: the finite difference method. Unlike other techniques in quantum simulation, a certain form of finite difference scheme has been previously shown to be computationally reversible ([Hey1999] pp.337-348). It is this scheme that is analyzed and simulated. A simulation application was written in Java based on this scheme. The results of simulations are presented and analyzed. Display using the HSB (Hue, Saturation, Brightness) color space in two dimensions is done as well. The main result of the mathematical analysis is a proof of convergence and stability for this finite difference scheme. We have been able to show this scheme is consistent, convergent, and stable under certain conditions. This analytical result is in good agreement with simulation. A more complete summary of the analysis is documented in a separate report. 1. Introduction Several techniques are commonly used for simulation of quantum effects. However, the simulation of a system that is physically reversible is not often done in a computationally reversible way. The finite difference scheme analyzed here is interesting since it has been shown to be reversible computationally. Reversible computations be implemented in thermodynamically reversible hardware, increasing energy efficiency. The finite difference method is a common, general idea of discretizing a differential equation so that it can be simulated numerically. For simulations of quantum particle evolution, the differential equation to be discretized is the Schrdinger equation. Previous work has been done in showing this system to be computationally reversible. For the reversible finite difference scheme, a formal analysis of its consistency, convergence, and stability are summarized in this report. In addition, an extension of this scheme into multidimensional systems is presented. A Java simulation of this finite difference scheme is used to verify many results experimentally and investigate other issues. Different visualization methods are explored in Java as well. 1.1 Problem Domain Although the reversible discretization of the Schrdinger equation has been known for some time, certain properties about it remained uninvestigated formally. The goals of this project are to characterize the numerical properties of this simulation and provide different methods for visualization of the output....
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short-report - Reversible Simulation and Visualization of...

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