Trapped bosons exhibit fundamental physical phenomena and are at the core of emerging quantum technologies. We present a method for simulating bosons using path integral molecular dynamics. The main difficulty in performing such simulations is enumerating all ring-polymer configurations, which arise due to permutations of identical particles. We show that the potential and forces at each time step can be evaluated by using a recurrence relation which avoids enumerating all permutations, while providing the correct thermal expectation values. The resulting algorithm scales cubically with system size. The method is tested and applied to bosons in a 2-dimensional (2D) trap and agrees with analytical results and numerical diagonalization of the many-body Hamiltonian. An analysis of the role of exchange effects at different temperatures, through the relative probability of different ring-polymer configurations, is also presented.
Keywords: bosons; cold atoms; molecular dynamics; path integrals.
Conflict of interest statement
The authors declare no competing interest.
From classical to quantum and back: Hamiltonian adaptive resolution path integral, ring polymer, and centroid molecular dynamics.J Chem Phys. 2017 Dec 28;147(24):244104. doi: 10.1063/1.5000701. J Chem Phys. 2017. PMID: 29289131
Droplets of Trapped Quantum Dipolar Bosons.Phys Rev Lett. 2016 Nov 11;117(20):205301. doi: 10.1103/PhysRevLett.117.205301. Epub 2016 Nov 10. Phys Rev Lett. 2016. PMID: 27886489
Cayley modification for strongly stable path-integral and ring-polymer molecular dynamics.J Chem Phys. 2019 Sep 28;151(12):124103. doi: 10.1063/1.5120282. J Chem Phys. 2019. PMID: 31575166
Recent developments in quantum Monte Carlo simulations with applications for cold gases.Rep Prog Phys. 2012 Sep;75(9):094501. doi: 10.1088/0034-4885/75/9/094501. Epub 2012 Aug 10. Rep Prog Phys. 2012. PMID: 22885729 Review.
Review of computer simulations of isotope effects on biochemical reactions: From the Bigeleisen equation to Feynman's path integral.Biochim Biophys Acta. 2015 Nov;1854(11):1782-94. doi: 10.1016/j.bbapap.2015.04.021. Epub 2015 Apr 30. Biochim Biophys Acta. 2015. PMID: 25936775 Review.