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中国科学通报：英文版

Superfluid density of two-dimensional weakly interacting boson system at zero temperature

He, Peisong, Fan Fan, Yuwei

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

我们在弱联合区域用一个环不安理论在零温度与弱二身体的排斥相互作用计算一个二维的波色子系统的超流体密度。波色子域被拿在在真实空格的连续统形式，并且相互作用被在波色子之间的距离的一个函数接近。我们发现一个环变化稍微减少古典水平的超流体密度。超流体密度被波色子粒子的团乘的冷凝物密度接近。

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我们在弱联合区域用一个环不安理论在零温度与弱二身体的排斥相互作用计算一个二维的波色子系统的超流体密度。波色子域被拿在在真实空格的连续统形式，并且相互作用被在波色子之间的距离的一个函数接近。我们发现一个环变化稍微减少古典水平的超流体密度。超流体密度被波色子粒子的团乘的冷凝物密度接近。
The recent study of He and You [P.-S. He and W.-L. You, Int. J. Mod. Phys. B26, 1250107 (2012)] on the relation between superfluid and condensate densities in a two-dimensional weakly interacting Boson system assumed a δ(x − x′) interaction between two particles at sites x and x′. The main purpose of this article is to point out the sensitivity of the conclusions of He and You to the choice of interaction. Thus, it is known for logarithmic interactions that one can have superfluidity without a condensate. Finally, some related ideas are mentioned in relation to superfluidity in liquid 4 He at exceedingly low temperatures.
We have developed a microscopic theory of superfluidity in a two-dimensional, slightly nonideal Bose gas. The theory is rooted in the fact that a number of bosons are concentrated in the small momentum region at low temperatures when the interaction is weak, in spite of the fact that there is no Bose condensate in the two-dimensional case when T≠0. This fact lets us reduce the description of the system from one employing creation ak+ and annihilation ak operators for bosons to one based on combinations of these operators ρk and φk(ρk = S−1Σqaq+aq+k, φk· = −(i/ns) Σ(kq/k2 + l)aq+aq+k, where n is the boson density, and S is the area of the system). The description in terms of ρk and φk is simple because the hamiltonian is quadratic with respect to ρk and φk. The operators ρk and φk can also be used to express the occupation number Nk = ak+ak and current operators. We find the elementary excitation spectrum (which is identical to the Bogolyubov spectrum) and the momentum distribution of the bosons. We calculate the normal density due to thermal oscillations in the Bose gas and to interactions with impurity centers in the substrate.
The refinement and the combination of laser cooling and evaporative cooling in dilute systems of alkali atoms lead to the achievement of Bose-Einstein condensation in 1995. Nowadays there is a fruitful interplay between theoretical and experimental results: in this context, the study of uniform Bose gases plays an important role in the comprehension of the static and dynamic properties of a bosonic system. Here we use quantum field theory, within the approach of functional integration, to study an homogeneous system of weakly-interacting bosonic cold atoms. After characterizing their thermodynamical properties, we derive - at a gaussian level - the number density and the superfluid density in three and in two spatial dimensions, expressed as functions of the condensate density and the temperature. Since the equations derived are valid for a generic interaction potential, we implement these formulas for bosons with a zero-range interaction, providing also an extension of these results with the inclusion of a finite-range interaction.
We compute the superfluid density of a two-dimensional boson system with weak two-body repulsive interactions at zero temperature using one-loop perturbation theory in the weak coupling region. The boson fields are taken to be in continuum form in real space, and the interactions are approximated by a δ function of the distance between the bosons. We find that the one-loop fluctuations slightly decrease the superfluid density of a classical level. The superfluid density is approximated by the condensate density multiplied by the mass of the boson particle.
In dieser Arbeit erörtern wir ein eindimensionales Lieb Liniger Modell für Bosonen mit einem zusätzlichen Zufallspotenzial. Für dieses Modell von schwach wechselwirkendem Bosegas wurde von Seiringer, Yngvason und Zagrebnov gezeigt, dass für N nach unendlich, wobei N die Anzahl an Teilchen bezeichnet, die Gross Pitaevskii Energie zur quantenmechanischen Energie konvergiert. Weiters wurde gezeigt, dass für den Vielteilchenlimes vollständige Bose Einstein Kondensation (BEC) existiert. Für die Diskussion von Superfluidität, ist eine genauere Analyse der Gross Pitaevskii Dichte nötig und für bestimmte Limiten wird diese Analyse in dieser Arbeit durchgeführt. Im Speziellen können wir zeigen, dass für schwache Wechselwirkung keine Superfluidität im Limes existiert, auch wenn Bose Einstein Kondensation vorkommt. Andererseits können wir zeigen, dass es einen Parameterbereich gibt, in dem vollständige Superfluidität stattfindet. Daher fordert die Existenz von Superfluidität stärkere Voraussetzungen als die Existenz von BEC, in diesem eindimensionalen Modell. In derselben Arbeit von Seiringer, Yngvason und Zagrebnov wurde gezeigt, dass in einem speziellen Parameterbereich, ein deterministischer Limes für die Gross Pitaevskii Energie existiert welche von dem Zufallspotenzial abhängt. In dieser Arbeit erweitern wir diesen Beweis um Abschätzungen für die Konvergenz in Wahrscheinlichkeit. Weiters beweisen wir, dass es möglich ist, diese Konvergenz auch für ein Bernoulli Zufallspotenzial zu erreichen.