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Caffarel at 15:42, 25 October 2010

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Caffarel at 16:43, 24 October 2010

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Caffarel at 16:42, 24 October 2010

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Caffarel at 16:40, 24 October 2010

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Caffarel: nt

2010-10-24T16:21:15Z

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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 Schroedinger equation. There exist many variants of QMC known under various acronyms. The various approaches may be classified as follows:
<ul>
<li> T=O and T diff 0 QMC
<li>Continuous or discrete configuration space
<li> Quantum statistics: boltzamon, fermion, and boson.
</ul>

@@ Line 1: / Line 1: @@
 Quantum Monte Carlo methods are powerful probabilistic approaches for computing quantum averages of a N-body quantum system described by a Schr&ouml;dinger equation. Many QMC variants known under various acronyms exist in the literature. We propose here to classify them as follows:
-<ul>
-<li> Zero-temperature (T=O) and Finite-temperature (T diff 0) QMC methods
+* Zero-temperature (T=O) and Finite-temperature (T diff 0) QMC methods
-<li> QMC defined in continuous or discrete (lattice) configuration space
+* QMC defined in continuous or discrete (lattice) configuration space
-<li>  QMC for Boltzmanon, Fermion, or Boson particles.
+* 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 corresponding to electronic structure theory conditions.

@@ Line 8: / Line 8: @@
 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 corresponding to electronic structure theory conditions.
-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 particular statistics. Second, we shall say a few words about the generalization to arbitrary number of dimensions d (actually, d=3N where N is the number of electrons). It is a nice aspect of the vast majority of Monte Carlo methods that such a generalization is in general trivial. Finally, we shall consider how to introduce into QMC the specific constraints due to the Pauli principle.
+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 particular statistics. Second, we shall say a few words about the generalization to arbitrary number d of dimensions (actually, d=3N where N is the number of electrons). Remark that it is a nice aspect of the vast majority of Monte Carlo methods that such a generalization does not bring additional difficulties. Finally, we shall consider how to introduce into QMC the specific constraints due to the Pauli principle.
 I. T=0 QMC for a continuous one-dimensional system with no specific symmetry constraints

@@ Line 8: / Line 8: @@
 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 corresponding to electronic structure theory conditions.
-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 in general trivial. Finally, we shall consider how to introduce into QMC the specific constraints due to the Pauli principle.
+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 particular statistics. Second, we shall say a few words about the generalization to arbitrary number of dimensions d (actually, d=3N where N is the number of electrons). It is a nice aspect of the vast majority of Monte Carlo methods that such a generalization is in general trivial. Finally, we shall consider how to introduce into QMC the specific constraints due to the Pauli principle.
 I. T=0 QMC for a continuous one-dimensional system with no specific symmetry constraints

@@ Line 8: / Line 8: @@
 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 corresponding to electronic structure theory conditions.
-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.
+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 in general trivial. Finally, we shall consider how to introduce into QMC the specific constraints due to the Pauli principle.
 I. T=0 QMC for a continuous one-dimensional system with no specific symmetry constraints

@@ Line 6: / Line 6: @@
 </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 what follows a self-contained presentation of QMC is proposed. We shall concentrate on the T=0 QMC approaches defined in a continuous space corresponding to electronic structure theory conditions.
 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

@@ Line 1: / Line 1: @@
+Quantum Monte Carlo methods are powerful probabilistic approaches for computing quantum averages of a N-body quantum system described by a Schr&oum;dinger equation. There exist many variants of QMC known under various acronyms. We propose to classify the various approaches as follows:
 <ul>
-<li> T=O and T diff 0 QMC
+<li> Zero-temperature (T=O) and finite-temperature QMC methods
-<li>Continuous or discrete configuration space
+<li> QMC defined in continuous or discrete (latticve) configuration space
-<li> Quantum statistics: boltzamon, fermion, and boson.
+<li>  QMC for Boltzmanon, Fermion, or Boson particles.
 </ul>