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 Schrödinger equation. Many QMC variants under various acronyms exist. We propose to classify them as follows:
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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 Schrödinger equation. Many QMC variants known under various acronyms exist in the literature. We propose here to classify them as follows:
 
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<li> Zero-temperature (T=O) and Finite-temperature (T diff 0) QMC methods
 
<li> Zero-temperature (T=O) and Finite-temperature (T diff 0) QMC methods

Revision as of 17:38, 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 known under various acronyms exist in the literature. We propose here 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