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.
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
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks an ...
and
boson particles. The method is often applied to calculate thermodynamic properties such as the
internal energy
The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...
, heat capacity,
or
free energy.
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), the more quantum (and the less classical) the result is. However, for some properties the correction may cause model predictions to initially become less accurate than neglecting them if a small number of path descriptors are included. At some point the number of descriptors is sufficiently large and the corrected model begins to converge smoothly to the correct quantum answer.
Because it is a statistical sampling method, PIMC can take
anharmonicity fully into account, and because it is quantum, it takes into account important quantum effects such as
tunneling and
zero-point energy (while neglecting the
exchange interaction in some cases).
The basic framework was originally formulated within the canonical ensemble, but has since been extended to include the
grand canonical ensemble and the
microcanonical ensemble. Its use has been extended to fermion systems as well as systems of bosons.
An early application was to the study of liquid helium. Numerous applications have been made to other systems, including liquid water and the hydrated electron. The algorithms and formalism have also been mapped onto non-quantum mechanical problems in the field of
financial modeling, including
option pricing.
See also
*
Path integral molecular dynamics
*
Quantum algorithm
In quantum computing, a quantum algorithm is an algorithm which runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical (or non-quantum) algorithm is a finite sequ ...
References
External links
Path Integral Monte Carlo Simulation
Quantum chemistry
Quantum Monte Carlo
Quantum information theory
Quantum algorithms
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