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.
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.
Motivated by recent experiments on alkali gases in atom traps, a largely pedagogical account is given of the implications of the existence of a single-particle Bose-Einstein condensate for the phenomenon of superfluidity. The first conclusion is that, for alkalis in traps at the lowest temperatures, Bose-Einstein condensation coexists with superfluidity. Both experimental evidence and basic microscopic theory are reviewed in this context, with superfluidity in finite systems, quantized vortices and the threshold for breakdown of superfluidity all being referred to. The contrast between liquid 4He below the λ point and the alkali atom gases is then emphasized. Both exhibit superfluidity, but the manifestations of a Bose-Einstein condensate are quite different. For the atomic vapours, near to 100% of the atoms are condensed at the lowest temperatures, whereas from (i) neutron scattering and (ii) computer simulations in liquid 4He present evidence is that 7% is the condensate fraction. This leads finally into a brief discussion of superfluidity without a condensate, with specific reference to the two-dimensional Bose Coulomb gas. The main conclusion is that Bose-Einstein condensation and superfluidity are distinct consequences of deeper topological properties of the many-body wavefunction.
A well-known paradox in the theory of superfluidity is studied: superfluidity is linked to Bose condensation, but the superfluid density is always greater than the density of the Bose condensate. Based on the model of a weakly nonideal Bose gas, it is demonstrated that supercondensate particles, forming pairs which are correlated in momentum space—the two-particle condensate—make the missing contribution to the superfluid density. It is shown that in the case of slow spatial variations of superfluid flows it is possible to introduce a macroscopic wave function describing the entire superfluid component and not only the single-particle condensate. The characteristic features of weak superfluidity in Bose systems are studied and it is shown that the tunneling effect is a sensitive tool for studying the structure of the superfluid component. It is hypothesized that the superfluid component of real He II consists of the sum of one-, two-, three-, and many-particle condensates.
This chapter describes a system of interacting bosons at very low temperatures. For helium, the forces are relatively weak, while, because of its low mass, the zero-point oscillations of the individual atoms are large. The low temperature phase is called He II; the high temperature phase, He I. Indications of the existence of He II were already present in the early experiments of Kamerlingh Onnes. The "superfluidity" of He II was discovered independently, and essentially, simultaneously, by Kapitza and Allen and Misener, by studying the flow of liquid helium through a thin capillary. In the two-fluid model, superfluid He II is regarded as being composed of two fluids which are simultaneously present and mutually interpenetrating. The superfluid component is the condensate, the single condensed quantum state of the Bose liquid. The existence of superfluid flow through a narrow capillary is built into the theory.
Analyzing the basic dynamics of two bosons, interacting through a central force, we make three unequivocal conclusions: (i). Natural laws, demanding the ground state of a system to have least possible energy, forbid the existence of p = 0 condensate in a system of interacting bosons (SIB). (ii). The ground state of a SIB, with different number of particles having different momenta does not have least possible energy as it should be. (iii). All particles in the true ground state have identically equal energy, εo = h2/8md2, and equivalent momentum, qo = π/d. The real nature of Bose Einstein condensation (BEC) that exists in the superfluid state of a SIB is identified as the condensation of particles in a state of a pair of particles having equal and opposite momenta (q, -q) with center of mass momentum, K = 0 and q = π/d. We also discuss how experimental results pertaining to the existence of electron bubble and free rotation of molecules in helium droplets and clusters support the absence of p=0 condensate and how single particle basis (SPB), having an alliance with p=0 condensate, is inconsistent with certain physical realities of the system at low temperatures. These conclusions render strong support for our theory of superfluidity of a system like liquid 4He (Amer. J. Cond. Mat. Phys. 2, 32-52(2012).
We show that the condensate occupation of a superfluid Bose liquid quite generally exhibits anomalously large fluctuations at finite temperatures $T\ensuremath{\ne}0.$ In three dimensions, the variance $〈\ensuremath{\delta}{N}_{0}^{2}〉$ of the number N0 of particles in the condensate scales nonlinearly with volume V like T2V4/3 at low T, generalizing the result obtained by Giorgini, Pitaevskii, and Stringari for a weakly interacting Bose gas. In two dimensions there is only a quasicondensate whose fluctuations are of the same order as the mean value.
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.