Equation of state of an interacting Bose gas at finite temperature: A path-integral Monte Carlo study

S. Pilati, K. Sakkos, J. Boronat, J. Casulleras, and S. Giorgini

Phys. Rev. A 74, 043621 – Published 27 October 2006

Abstract

By using exact path-integral Monte Carlo methods we calculate the equation of state of an interacting Bose gas as a function of temperature both below and above the superfluid transition. The universal character of the equation of state for dilute systems and low temperatures is investigated by modeling the interatomic interactions using different repulsive potentials corresponding to the same $s$ -wave scattering length. The results obtained for the energy and the pressure are compared to the virial expansion for temperatures larger than the critical temperature. At very low temperatures we find agreement with the ground-state energy calculated using the diffusion Monte Carlo method.

Received 27 July 2006

DOI:https://doi.org/10.1103/PhysRevA.74.043621

Authors & Affiliations

S. Pilati¹, K. Sakkos², J. Boronat², J. Casulleras², and S. Giorgini¹

¹Dipartimento di Fisica, Università di Trento and CRS-BEC INFM, I-38050 Povo, Italy
²Departament de Física i Enginyeria Nuclear, Campus Nord B4-B5, Universitat Politècnica de Catalunya, E-08034 Barcelona, Spain

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Issue

Vol. 74, Iss. 4 — October 2006

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Images

Figure 1
(Color online) Energy per particle and pressure of a Bose gas in the normal phase as a function of temperature. The gas parameter is $n a^{3} = 10^{- 6}$ . Solid symbols (blue online) refer to $E ∕ N - 3 k_{B} T ∕ 2$ : HS potential (circles), SS potential (diamonds). Open symbols (red online) refer to $P ∕ n - k_{B} T$ : HS potential (circles), SS potential (diamonds). Statistical error bars are smaller than the size of the symbols. The virial expansion (21) is represented by lines (blue online): HS potential (solid line), SS potential (long-dashed line). The virial expansion (20) is represented by lines (red online): HS potential (short-dashed line), SS potential (dotted line).Reuse & Permissions
Figure 2
(Color online) Energy per particle and pressure of a Bose gas in the normal phase as a function of the temperature for $n a^{3} = 10^{- 4}$ . Same notation as in Fig. 1, except for the results of the energy for the NP potential, shown here as squares (blue online). Whenever not shown, the error bars are smaller than the symbol sizes.Reuse & Permissions
Figure 3
(Color online) Energy per particle and pressure of a Bose gas in the normal phase as a function of the temperature for $n a^{3} = 10^{- 2}$ . Same notation as in Figs. 1, 2. Error bars are smaller than the symbol sizes.Reuse & Permissions
Figure 4
(Color online) Energy per particle and pressure of a Bose gas in the superfluid phase as a function of temperature. The gas parameter is $n a^{3} = 10^{- 6}$ . Solid symbols (blue online) refer to $E ∕ N$ : HS potential (circles), SS potential (diamonds). Open symbols (red online) refer to $P ∕ n$ : HS potential (circles), SS potential (diamonds). Statistical error bars are smaller than the size of the symbols. The horizontal bar (green online) corresponds to the ground-state energy per particle $E_{0} ∕ N$ of a HS gas calculated using DMC. The lines correspond to a noninteracting gas: the solid line (blue online) refers to the energy per particle and the dashed line (red online) to the pressure.Reuse & Permissions
Figure 5
(Color online) Energy per particle and pressure of a Bose gas in the superfluid phase as a function of the temperature for $n a^{3} = 10^{- 4}$ . Same notation as in Fig. 4, except for the results of the energy for the NP potential, shown here as squares (blue online). Whenever not shown, the error bars are smaller than the symbol sizes.Reuse & Permissions
Figure 6
(Color online) Energy per particle and pressure of a Bose gas in the superfluid phase as a function of the temperature for $n a^{3} = 10^{- 2}$ . Same notation as in Figs. 4, 5. Error bars are smaller than the symbol sizes.Reuse & Permissions

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