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Quantum Simulation Using Path Integrals

  • M. Sprik
Chapter
  • 291 Downloads
Part of the NATO ASI Series book series (NSSE, volume 205)

Abstract

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.

Keywords

Quantum Effect Classical Isomorphism Quantum Particle Excess Electron Euclidean Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Feynman, R. P. and Hibbs, A. R. (1965) Quantum Mechanics and Path Integrals, McGraw-Hill, New YorkzbMATHGoogle Scholar
  2. 1a.
    Feynman, R. P. (1972) Statistical Mechanics, Addison-Wesley, Reading.Google Scholar
  3. 2.
    Schulman, L. S. (1981) Techniques and Applications of Path Integration, Wiley, New York.zbMATHGoogle Scholar
  4. 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
  5. 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
  6. 5.
    Sprik, M., Klein, M. L. and Chandler D. (1985) J. Chem. Phys. 83, 3042.ADSCrossRefGoogle Scholar
  7. 6.
    Pollok, E. L. and Ceperley, D. M. (1984) Phys. Rev. B 30, 2555.ADSCrossRefGoogle Scholar
  8. 7.
    Ceperley, D. M. and Pollock, E. L. (1986) Phys. Rev. Lett. 56, 351ADSCrossRefGoogle Scholar
  9. 7a.
    Pollock, E. L. and Ceperley, D. M. (1987) Phys. Rev. B 36, 8343.ADSCrossRefGoogle Scholar
  10. 8.
    Ceperley, D. M. and Jacucci, G. (1987) Phys. Rev. Lett. 58, 1648.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • M. Sprik
    • 1
  1. 1.IBM Research DivisionZurich Research LaboratoryRüschlikonSwitzerland

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