Difference between revisions of "Much more about QMC here"
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| − | Quantum Monte Carlo methods are powerful probabilistic approaches for computing quantum averages of a N-body quantum system described by a Schr& | + | Quantum Monte Carlo methods are powerful probabilistic approaches for computing quantum averages of a N-body quantum system described by a Schrödinger equation. Many QMC variants under various acronyms exist. We propose to classify them as follows: |
<ul> | <ul> | ||
| − | <li> Zero-temperature (T=O) and | + | <li> Zero-temperature (T=O) and Finite-temperature (T diff 0) QMC methods |
| − | <li> QMC defined in continuous or discrete ( | + | <li> QMC defined in continuous or discrete (lattice) configuration space |
<li> QMC for Boltzmanon, Fermion, or Boson particles. | <li> QMC for Boltzmanon, Fermion, or Boson particles. | ||
</ul> | </ul> | ||
| + | |||
| + | In what follows a self-contained presentation of QMC is proposed. We shall concentrate on the T=0 QMC approaches defined in a continuous space since such conditions correspond to electronic structure theory. | ||
| + | |||
| + | In order to make easier the presentation, we shall first consider the case of a one-dimensional system defined in a continuous space and no fermionic statistics. Second, we shall say a few words about the generalization to arbitrary number of dimensions (actually, 3N where N is the number of electrons). It is a nice aspect of Monte Carlo methods that such a generalization is easy and does not bring specific difficulties. Finally, we shall consider how to introduce the specific constraints due to the Pauli principle. | ||
| + | |||
| + | I. T=0 QMC for a continuous one-dimensional system with no specific symmetry constraints | ||
Revision as of 17:36, 24 October 2010
Quantum Monte Carlo methods are powerful probabilistic approaches for computing quantum averages of a N-body quantum system described by a Schrödinger equation. Many QMC variants under various acronyms exist. We propose to classify them as follows:
- Zero-temperature (T=O) and Finite-temperature (T diff 0) QMC methods
- QMC defined in continuous or discrete (lattice) configuration space
- QMC for Boltzmanon, Fermion, or Boson particles.
In what follows a self-contained presentation of QMC is proposed. We shall concentrate on the T=0 QMC approaches defined in a continuous space since such conditions correspond to electronic structure theory.
In order to make easier the presentation, we shall first consider the case of a one-dimensional system defined in a continuous space and no fermionic statistics. Second, we shall say a few words about the generalization to arbitrary number of dimensions (actually, 3N where N is the number of electrons). It is a nice aspect of Monte Carlo methods that such a generalization is easy and does not bring specific difficulties. Finally, we shall consider how to introduce the specific constraints due to the Pauli principle.
I. T=0 QMC for a continuous one-dimensional system with no specific symmetry constraints
