# The many-body Wigner Monte Carlo method for time-dependent ab-initio quantum simulations

## Abstract

The aim of ab-initio approaches is the simulation of many-body quantum systems from the first principles of quantum mechanics. These methods are traditionally based on the many-body Schrödinger equation which represents an incredible mathematical challenge. In this paper, we introduce the many-body Wigner Monte Carlo method in the context of distinguishable particles and in the absence of spin-dependent effects. Despite these restrictions, the method has several advantages. First of all, the Wigner formalism is intuitive, as it is based on the concept of a quasi-distribution function. Secondly, the Monte Carlo numerical approach allows scalability on parallel machines that is practically unachievable by means of other techniques based on finite difference or finite element methods. Finally, this method allows time-dependent ab-initio simulations of strongly correlated quantum systems. In order to validate our many-body Wigner Monte Carlo method, as a case study we simulate a relatively simple system consisting of two particles in several different situations. We first start from two non-interacting free Gaussian wave packets. We, then, proceed with the inclusion of an external potential barrier, and we conclude by simulating two entangled (i.e. correlated) particles. The results show how, in the case of negligible spin-dependent effects, the many-body Wigner Montemore »

- Authors:

- Publication Date:

- OSTI Identifier:
- 22382112

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 273; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; DISTRIBUTION FUNCTIONS; MANY-BODY PROBLEM; MONTE CARLO METHOD; POTENTIALS; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; QUANTUM SYSTEMS; SCHROEDINGER EQUATION; SPIN; TIME DEPENDENCE

### Citation Formats

```
Sellier, J.M., E-mail: jeanmichel.sellier@parallel.bas.bg, and Dimov, I.
```*The many-body Wigner Monte Carlo method for time-dependent ab-initio quantum simulations*. United States: N. p., 2014.
Web. doi:10.1016/J.JCP.2014.05.039.

```
Sellier, J.M., E-mail: jeanmichel.sellier@parallel.bas.bg, & Dimov, I.
```*The many-body Wigner Monte Carlo method for time-dependent ab-initio quantum simulations*. United States. doi:10.1016/J.JCP.2014.05.039.

```
Sellier, J.M., E-mail: jeanmichel.sellier@parallel.bas.bg, and Dimov, I. Mon .
"The many-body Wigner Monte Carlo method for time-dependent ab-initio quantum simulations". United States. doi:10.1016/J.JCP.2014.05.039.
```

```
@article{osti_22382112,
```

title = {The many-body Wigner Monte Carlo method for time-dependent ab-initio quantum simulations},

author = {Sellier, J.M., E-mail: jeanmichel.sellier@parallel.bas.bg and Dimov, I.},

abstractNote = {The aim of ab-initio approaches is the simulation of many-body quantum systems from the first principles of quantum mechanics. These methods are traditionally based on the many-body Schrödinger equation which represents an incredible mathematical challenge. In this paper, we introduce the many-body Wigner Monte Carlo method in the context of distinguishable particles and in the absence of spin-dependent effects. Despite these restrictions, the method has several advantages. First of all, the Wigner formalism is intuitive, as it is based on the concept of a quasi-distribution function. Secondly, the Monte Carlo numerical approach allows scalability on parallel machines that is practically unachievable by means of other techniques based on finite difference or finite element methods. Finally, this method allows time-dependent ab-initio simulations of strongly correlated quantum systems. In order to validate our many-body Wigner Monte Carlo method, as a case study we simulate a relatively simple system consisting of two particles in several different situations. We first start from two non-interacting free Gaussian wave packets. We, then, proceed with the inclusion of an external potential barrier, and we conclude by simulating two entangled (i.e. correlated) particles. The results show how, in the case of negligible spin-dependent effects, the many-body Wigner Monte Carlo method provides an efficient and reliable tool to study the time-dependent evolution of quantum systems composed of distinguishable particles.},

doi = {10.1016/J.JCP.2014.05.039},

journal = {Journal of Computational Physics},

issn = {0021-9991},

number = ,

volume = 273,

place = {United States},

year = {2014},

month = {9}

}