Path integral Monte Carlo
Encyclopedia
Path integral Monte Carlo (PIMC)is a quantum Monte Carlo
method in the path integral formulation
of quantum mechanics
.
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
or free energy
.
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).
Quantum Monte Carlo
Quantum Monte Carlo is a large class of computer algorithms that simulate quantum systems with the idea of solving the quantum many-body problem. They use, in one way or another, the Monte Carlo method to handle the many-dimensional integrals that arise...
method in the path integral formulation
Path integral formulation
The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics...
of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
.
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
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
and boson
Boson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
particles). The theory usually is applied to calculate thermodynamic properties such as the
internal energy
Internal energy
In thermodynamics, the internal energy is the total energy contained by a thermodynamic system. It is the energy needed to create the system, but excludes the energy to displace the system's surroundings, any energy associated with a move as a whole, or due to external force fields. Internal...
or free energy
Thermodynamic free energy
The thermodynamic free energy is the amount of work that a thermodynamic system can perform. The concept is useful in the thermodynamics of chemical or thermal processes in engineering and science. The free energy is the internal energy of a system less the amount of energy that cannot be used to...
.
As with all Monte Carlo method
Monte Carlo method
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...
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
Exchange interaction
In physics, the exchange interaction is a quantum mechanical effect without classical analog which increases or decreases the expectation value of the energy or distance between two or more identical particles when their wave functions overlap...
usually).