Quantum Simulation Using Path Integrals
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The aim of this contribution to the school is to give an elementary introduction to the use of the path integral formulation of quantum mechanics as a tool for the simulation of quantum systems. The implementation of path integration in statistical mechanics is known as the classical isomorphism. It enables us to obtain finite temperature quantum expectation values as averages over the fluctuations of an entirely classical system. The emphasis will be on understanding how quantum effects are described in terms of the classical isomorphism. In this context, we will treat several important technical issues, such as choosing the size of the classical isomorphic system and Monte Carlo sampling methods. Applications will be mentioned only to clarify and motivate the methodology. The source material for this lecture is taken from the textbooks of Refs. 1 and 2 and the chapter by David Chandler in Ref. 3.
KeywordsQuantum Effect Classical Isomorphism Quantum Particle Excess Electron Euclidean Time
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- 1a.Feynman, R. P. (1972) Statistical Mechanics, Addison-Wesley, Reading.Google Scholar
- 3.Chandler, D. (1990), in D. Levesque, J. P. Hansen and J. Linn-Justin (eds.), Theory of Quantum Processes in Liquids (Les Houches 1989, Liquids, Freezing and Glass Transitions), Elsevier, Amsterdam.Google Scholar
- 4.Coker, D. F. and Berne, B. J., (1990) in J.-P, Jay-Gerlin and C. Ferradini (eds.), Excess Electrons in Dielectric Media, Chemical Rubber Company Uniscience Press, Boca Raton, FL.Google Scholar