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Soviet Journal of Low Temperature Physics

Characteristics of superfluid flow along a substrate with impurities

S. I. Shevchenko

Published Feb 1, 1983• 3 citations
Publisher

Abstract

It is shown that the normal component generated by substrate impurities represents a fluid mass associated with the impurity centers, while the normal Landau density is a mass connected to thermal fluctuations in the density of the fluid. Based on this interpretation of the normal component, a semiphenomenological method is proposed for describing superfluid flows. For a weakly nonideal Bose gas and low impurity concentration, a microscopic theory of superfluid flow along a substrate with impurities is constructed without assuming the presence of a Bose condensate in the system. The wave function of the ground state of the system, the density distribution near an impurity center, and the density-density correlation function are found. The response of the system to rotation of the substrate is calculated and the normal density, generated by impurities at T = 0, is determined.

DOI
10.1063/10.0030829

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It is shown that the normal component generated by substrate impurities represents a fluid mass associated with the impurity centers, while the normal Landau density is a mass connected to thermal fluctuations in the density of the fluid. Based on this interpretation of the normal component, a semiphenomenological method is proposed for describing superfluid flows. For a weakly nonideal Bose gas and low impurity concentration, a microscopic theory of superfluid flow along a substrate with impurities is constructed without assuming the presence of a Bose condensate in the system. The wave function of the ground state of the system, the density distribution near an impurity center, and the density-density correlation function are found. The response of the system to rotation of the substrate is calculated and the normal density, generated by impurities at T = 0, is determined.
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.
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.
It has been proposed in recent years that an impurity moving in a superfluid will experience drag forces even below the Landau critical velocity [1–3]. Quantum fluctuations that are present in superfluid systems at zero temperature can scatter from impurities present in the fluid. If the impurity is moving, there will be an asymmetric Doppler shift associated with the scattered waves, which will result in a net drag force. This challenges the long-accepted notion of dissipationless flow in superfluids. Analytical estimates of this drag force in superfluid Bose-Einstein condensates using Bogoliubov methods have found a non-zero drag force, resulting from the most sensible choice of boundary conditions in an infinite system. Through stochastic simulations of the 1D Bose gas under the truncated Wigner formalism, we verify the existence of this sub-critical drag force and quantify the drag forces present. We will also determine whether dissipationless flow can be recovered in finite sized systems.
The possibility of delocalization of particles in a quantum crystal at the nucleus of a dislocation and the transition of delocalized particles into a superfluid state are predicted. A theory is constructed for the one-dimensional superfluidity of a slightly nonideal Bose gas. The effect of impurities on the superfluid density is studied and it is shown that impurities do not destroy the superfluidity, but rather make an additional contribution to the normal component, different from zero even at T = 0. The flow of the superfluid current through a weak link is studied. It is established that in spite of the fact that there is no long-range order in the one-dimensional case, a superfluid current will flow through a weak link without dissipation. Some experimental manifestations of dislocation superfluidity are discussed.
The theory of the condensate of a weakly interacting Bose gas is developed. The condensate is described by a wavefunction ψ(x, t) normalized to the number of particles. It obeys a nonlinear self-consistent field equation. The solution in the presence of a rigid wall with the boundary condition of vanishing wavefunction involves a de Broglie length. This length depends on the mean potential energy per particle. The self-consistent field term keeps the density uniform except in localized spatial regions. In the hydrodynamical version, a key role is played by the quantum potential. A theory of quantized vortices and of general potential flows follows immediately. In contrast to classical hydrodynamics, the cores of vortices are completely determined by the de Broglie length and all energies are finite. Nonstationary disturbances of the condensate correspond to phonons, rotons, vortex waves etc. They can exchange momentum with rigid boundaries. This is compatible with the vanishing of the wavefunction at a boundary. This condition fully determines the dynamics of the system. These points are illustrated by considering the motion of a foreign ion in a Bose gas, a rotating container of fluid, and the Landau criterion for superfluidity.
A finite one-dimensional microscopic model of a superfluid is presented. The model consists of interacting Bose particles with an additional impurity particle confined to a ring. Both semiclassical and exact quantum calculations reveal dissipationless motion of impurity with increased effective mass due to its interaction with the excitations of Bose fluid. It is shown that both the excitation spectrum of Bose fluid and the excitation spectrum of impurity can be analyzed using the structure of the ground state of the system.