Path integral Monte Carlo

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. But, the answer might become less accurate initially as more beads are added, until a point where the method starts to converge to the correct quantum answer.[3] 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] and the microcanonical ensemble.[8]

With agent-based PIMC the perimeter and sum borderlines of objects can be calculated.[9][10]

See also

References
  1. Barker, J. A. (1979). "A quantum-statistical Monte Carlo method; path integrals with boundary conditions". The Journal of Chemical Physics. 70 (6): 2914–2918. 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. 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 (Submitted manuscript). 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.
  8. Freeman, David L; Doll, J. D (1994). "Fourier path integral Monte Carlo method for the calculation of the microcanonical density of states". The Journal of Chemical Physics. 101 (1): 848. arXiv:chem-ph/9403001. Bibcode:1994JChPh.101..848F. CiteSeerX 10.1.1.342.765. doi:10.1063/1.468087. S2CID 15896126.
  9. Wirth, E.; Szabó, G.; Czinkóczky, A. (June 8, 2016). "Measure Landscape Diversity with Logical Scout Agents". ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. XLI-B2: 491–495. Bibcode:2016ISPAr49B2..491W. doi:10.5194/isprs-archives-xli-b2-491-2016.
  10. Wirth E. (2015). Pi from agent border crossings by NetLogo package. Wolfram Library Archive


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.