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Abstract
We derive the two-dimensional equation of state for a bosonic system of ultracold atoms interacting with a finite-range effective interaction. Within a functional integration approach, we employ a hydrodynamic parameterization of the bosonic field to calculate the superfluid equations of motion and the zero-temperature pressure. The ultraviolet divergences, naturally arising from the finite-range interaction, are regularized with an improved dimensional regularization technique.
Highlights
A fluid perspective on the study of bosonic gases made of ultracold atoms may have originated in the pioneering work of Landau [1], who correctly described the superfluid behavior of He-4 as observed in his experiments [2]
Historical results for a two-dimensional Bose gas were obtained by Schick, who calculated the thermodynamics of a gas of hard-spheres [9], improved by Popov derivation of the equation of state for a weakly-interacting superfluid [10]
We provide an alternative derivation of the zero-temperature equation of state by adopting an explicit superfluid parametrization of the bosonic field
Summary
A fluid perspective on the study of bosonic gases made of ultracold atoms may have originated in the pioneering work of Landau [1], who correctly described the superfluid behavior of He-4 as observed in his experiments [2]. From those years, several technical advances allowed a precise experimental control of the atomic gases, culminating in the achievement of Bose–Einstein condensation in 1995 [3,4,5]. We develop an improved dimensional regularization technique to regularize the zero-temperature pressure of a bosonic quantum fluid, whose particles interact with a finite-range interaction
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