# Path-integral Monte Carlo study of particles obeying quantum mechanics and classical statistics

## Abstract

Ultracold atomic systems have been of great research interest in the past, with more recent attention being paid to systems of mixed species. In this work, we carry out nonperturbative path-integral Monte Carlo (PIMC) simulations of $N$ distinguishable particles at finite temperature, which can be thought of as an ultracold atomic system containing $N$ distinct species. We use the PIMC approach to calculate thermodynamic properties of particles interacting via hard-sphere and hard-cavity potentials. The first problem we study is a two-particle system interacting via a hard-sphere and hard-cavity interaction in order to test the effectiveness of two approximations for the thermal density matrix corresponding to these potentials. We then apply the PIMC method to a system of many hard-sphere particles under periodic boundary conditions at varying temperature in order to calculate the energy per particle, pressure, and specific heat of the system. We examine how finite-size effects impact the results of PIMC simulations of hard-sphere particles and when the thermodynamic limit has been reached. Finally, our results provide microscopic benchmarks for a system containing distinguishable particles, which can be thought of as a limiting case for ultracold atomic systems of mixed species.

- Authors:

- Univ. of Guelph, ON (Canada). Dept. of Physics

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1523837

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review A

- Additional Journal Information:
- [ Journal Volume: 96; Journal Issue: 4]; Journal ID: ISSN 2469-9926

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Dawkins, William G., and Gezerlis, Alexandros. Path-integral Monte Carlo study of particles obeying quantum mechanics and classical statistics. United States: N. p., 2017.
Web. doi:10.1103/PhysRevA.96.043619.
```

```
Dawkins, William G., & Gezerlis, Alexandros. Path-integral Monte Carlo study of particles obeying quantum mechanics and classical statistics. United States. doi:10.1103/PhysRevA.96.043619.
```

```
Dawkins, William G., and Gezerlis, Alexandros. Wed .
"Path-integral Monte Carlo study of particles obeying quantum mechanics and classical statistics". United States. doi:10.1103/PhysRevA.96.043619. https://www.osti.gov/servlets/purl/1523837.
```

```
@article{osti_1523837,
```

title = {Path-integral Monte Carlo study of particles obeying quantum mechanics and classical statistics},

author = {Dawkins, William G. and Gezerlis, Alexandros},

abstractNote = {Ultracold atomic systems have been of great research interest in the past, with more recent attention being paid to systems of mixed species. In this work, we carry out nonperturbative path-integral Monte Carlo (PIMC) simulations of $N$ distinguishable particles at finite temperature, which can be thought of as an ultracold atomic system containing $N$ distinct species. We use the PIMC approach to calculate thermodynamic properties of particles interacting via hard-sphere and hard-cavity potentials. The first problem we study is a two-particle system interacting via a hard-sphere and hard-cavity interaction in order to test the effectiveness of two approximations for the thermal density matrix corresponding to these potentials. We then apply the PIMC method to a system of many hard-sphere particles under periodic boundary conditions at varying temperature in order to calculate the energy per particle, pressure, and specific heat of the system. We examine how finite-size effects impact the results of PIMC simulations of hard-sphere particles and when the thermodynamic limit has been reached. Finally, our results provide microscopic benchmarks for a system containing distinguishable particles, which can be thought of as a limiting case for ultracold atomic systems of mixed species.},

doi = {10.1103/PhysRevA.96.043619},

journal = {Physical Review A},

number = [4],

volume = [96],

place = {United States},

year = {2017},

month = {10}

}

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