Path integral Monte Carlo

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Path integral Monte Carlo (PIMC) is a quantum Monte Carlo method used to solve quantum statistical mechanics problems numerically within the path integral formulation. The application of Monte Carlo methods to path integral simulations of condensed matter systems was first pursued in a key paper by John A. Barker.[1][2]

The method is typically (but not necessarily) applied under the assumption that symmetry or antisymmetry under exchange can be neglected, i.e., identical particles are assumed to be quantum Boltzmann particles, as opposed to fermion and boson particles. The method is often applied to calculate thermodynamic properties[3] such as the internal energy,[4] heat capacity,[5] or free energy.[6][7] As with all Monte Carlo method based approaches, a large number of points must be calculated.

In principle, as more path descriptors are used (these can be "replicas", "beads," or "Fourier coefficients," depending on what strategy is used to represent the paths),

tunneling and zero-point energy (while neglecting the exchange interaction in some cases).[6]

The basic framework was originally formulated within the canonical ensemble,[9] but has since been extended to include the grand canonical ensemble[10] and the microcanonical ensemble.[11] Its use has been extended to fermion systems[12] as well as systems of bosons.[13]

An early application was to the study of liquid helium.

option pricing.[17]

See also

References

  1. doi:10.1063/1.437829
    .
  2. doi:10.1103/RevModPhys.89.035003
    . Retrieved May 13, 2022.
  3. ^ Topper, Robert Q. (1999). "Adaptive path-integral Monte Carlo methods for accurate computation of molecular thermodynamic properties". Advances in Chemical Physics. 105: 117–170. Retrieved May 12, 2022.
  4. doi:10.1063/1.1460861
    .
  5. ^
    doi:10.1063/1.1493184
    .
  6. ^
    doi:10.1063/1.1529682
    .
  7. PMID 16080726
    .
  8. doi:10.1063/1.448081
    . Retrieved May 13, 2022.
  9. ^ Feynman, Richard P.; Hibbs, Albert R. (1965). Quantum Mechanics and Path Integrals. New York: McGraw-Hill.
  10. doi:10.1063/1.474874
    .
  11. S2CID 15896126
    .
  12. S2CID 14845299
    . Retrieved May 13, 2022.
  13. S2CID 218570984
    . Retrieved May 13, 2022.
  14. doi:10.1103/RevModPhys.67.279
    .
  15. S2CID 44166408
    . Retrieved May 12, 2022.
  16. doi:10.1063/1.452429
    . Retrieved May 12, 2022.
  17. doi:10.1016/j.physa.2021.126231
    . Retrieved May 13, 2022.

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