Path integral formulation: Difference between revisions
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#R. P. Feynman and A. R. Hibbs, Path-integrals and Quantum Mechanics (McGraw-Hill, New York, 1965) | #R. P. Feynman and A. R. Hibbs, Path-integrals and Quantum Mechanics (McGraw-Hill, New York, 1965) | ||
#R. P. Feynman, Statistical Mechanics (Benjamin, Reading, Mass., 1972) | #R. P. Feynman, Statistical Mechanics (Benjamin, Reading, Mass., 1972) | ||
# | #[http://dx.doi.org/10.1063/1.441588 David Chandler and Peter G. Wolynes "Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids", Journal of Chemical Physics '''74''' pp. 4078-4095 (1981)] | ||
#B. J. Berne and | #[http://dx.doi.org/10.1146/annurev.pc.37.100186.002153 B. J. Berne and D. Thirumalai "On the Simulation of Quantum Systems: Path Integral Methods", Annual Review of Physical Chemistry '''37''' pp. 401-424 (1986)] | ||
#D. M. Ceperley, | #[http://dx.doi.org/10.1103/RevModPhys.67.279 D. M. Ceperley "Path integrals in the theory of condensed helium", Reviews of Modern Physics '''67''' 279 - 355 (1995)] | ||
====Applications==== | ====Applications==== | ||
Phase transitions, quantum dynamics, centroids etc. | Phase transitions, quantum dynamics, centroids etc. | ||
#J. R. Melrose and K. Singer, | #[http://dx.doi.org/10.1080/00268978900100811 J. R. Melrose and K. Singer "An investigation of supercooled Lennard-Jones argon by quantum mechanical and classical Monte Carlo simulation", Molecular Physics '''66''' 1203-1214 (1989)] | ||
# | #[http://dx.doi.org/10.1063/1.467175 Jianshu Cao and Gregory A. Voth "The formulation of quantum statistical mechanics based on the Feynman path centroid density. I. Equilibrium properties", Journal of Chemical Physics '''100''' pp. 5093-5105 (1994)] | ||
# | #[http://dx.doi.org/10.1063/1.470898 Jianshu Cao and Gregory A. Voth "Semiclassical approximations to quantum dynamical time correlation functions", Journal of Chemical Physics '''104''' pp. 273-285 (1996)] | ||
#C. Chakravarty and R. M. Lynden-Bell, | #[http://dx.doi.org/10.1063/1.479666 Rafael Ramírez and Telesforo López-Ciudad "The Schrödinger formulation of the Feynman path centroid density", Journal of Chemical Physics '''111''' pp. 3339-3348 (1999)] | ||
#[http://dx.doi.org/10.1063/1.1316105 C. Chakravarty and R. M. Lynden-Bell "Landau free energy curves for melting of quantum solids", Journal of Chemical Physics '''113''' pp. 9239-9247 (2000)] | |||
[[Category: Monte Carlo]] | [[Category: Monte Carlo]] | ||
Revision as of 19:40, 16 October 2007
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General Reading
Reviews
- R. P. Feynman and A. R. Hibbs, Path-integrals and Quantum Mechanics (McGraw-Hill, New York, 1965)
- R. P. Feynman, Statistical Mechanics (Benjamin, Reading, Mass., 1972)
- David Chandler and Peter G. Wolynes "Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids", Journal of Chemical Physics 74 pp. 4078-4095 (1981)
- B. J. Berne and D. Thirumalai "On the Simulation of Quantum Systems: Path Integral Methods", Annual Review of Physical Chemistry 37 pp. 401-424 (1986)
- D. M. Ceperley "Path integrals in the theory of condensed helium", Reviews of Modern Physics 67 279 - 355 (1995)
Applications
Phase transitions, quantum dynamics, centroids etc.
- J. R. Melrose and K. Singer "An investigation of supercooled Lennard-Jones argon by quantum mechanical and classical Monte Carlo simulation", Molecular Physics 66 1203-1214 (1989)
- Jianshu Cao and Gregory A. Voth "The formulation of quantum statistical mechanics based on the Feynman path centroid density. I. Equilibrium properties", Journal of Chemical Physics 100 pp. 5093-5105 (1994)
- Jianshu Cao and Gregory A. Voth "Semiclassical approximations to quantum dynamical time correlation functions", Journal of Chemical Physics 104 pp. 273-285 (1996)
- Rafael Ramírez and Telesforo López-Ciudad "The Schrödinger formulation of the Feynman path centroid density", Journal of Chemical Physics 111 pp. 3339-3348 (1999)
- C. Chakravarty and R. M. Lynden-Bell "Landau free energy curves for melting of quantum solids", Journal of Chemical Physics 113 pp. 9239-9247 (2000)