Path integral Monte Carlo

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Path integral Monte Carlo (PIMC) is a quantum Monte Carlo method in the path integral formulation of quantum statistical mechanics.[1]

The equations often are applied assuming that quantum exchange does not matter (the particles are assumed to be Boltzmann particles, not the physically realistic fermion and boson particles). The theory usually is applied to calculate thermodynamic properties such as the internal energy,[2] heat capacity,[3] or free energy.[4][5] As with all Monte Carlo method based approaches, a large number of points must be calculated. As more "replicas" are used to integrate the path integral, the more quantum and the less classical the result is. Because it is a statistical sampling method, PIMC takes into account all the anharmonicity, and because it is quantum, it takes into account all quantum effects (with the exception of the exchange interaction usually).[4] An early application was to the study of liquid helium.[6] It has been extended to include the grand canonical ensemble[7]

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References[edit]

  1. ^ Barker, J. A. (1979). "A quantum-statistical Monte Carlo method; path integrals with boundary conditions". The Journal of Chemical Physics 70 (6): 2914–2911. Bibcode:1979JChPh..70.2914B. doi:10.1063/1.437829. 
  2. ^ Glaesemann, Kurt R.; Fried, Laurence E. (2002). "An improved thermodynamic energy estimator for path integral simulations". The Journal of Chemical Physics 116 (14): 5951–5955. Bibcode:2002JChPh.116.5951G. doi:10.1063/1.1460861. 
  3. ^ Glaesemann, Kurt R.; Fried, Laurence E. (2002). "Improved heat capacity estimator for path integral simulations". The Journal of Chemical Physics 117 (7): 3020–3026. Bibcode:2002JChPh.117.3020G. doi:10.1063/1.1493184. 
  4. ^ a b Glaesemann, Kurt R.; Fried, Laurence E. (2003). "A path integral approach to molecular thermochemistry". The Journal of Chemical Physics 118 (4): 1596–1602. Bibcode:2003JChPh.118.1596G. doi:10.1063/1.1529682. 
  5. ^ Glaesemann, Kurt R.; Fried, Laurence E. (2005). "Quantitative molecular thermochemistry based on path integrals". The Journal of Chemical Physics 123 (3): 034103. Bibcode:2005JChPh.123c4103G. doi:10.1063/1.1954771. PMID 16080726. 
  6. ^ Ceperley, D. M. (1995). "Path integrals in the theory of condensed helium". Reviews of Modern Physics 67 (2): 279–355. Bibcode:1995RvMP...67..279C. doi:10.1103/RevModPhys.67.279. 
  7. ^ Wang, Q.; Johnson, J. K.; Broughton, J. Q. (1997). "Path integral grand canonical Monte Carlo". The Journal of Chemical Physics 107 (13): 5108–5117. Bibcode:1997JChPh.107.5108W. doi:10.1063/1.474874. 

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