Bose Fluid Research Articles

Fluctuation Theory of Nonequilibrium Fluid. I. A General Formalism of a Normal Fluid

We construct a quantum statistical theory for nonequilibrium hydrodynamic systems which is based on the collective description of a bose fluid. It is proposed that the fluctuations around the Onsager variables can be treated in terms of the collective coordinates which are the auxiliary variables grounded upon the existence of the adiabatic motions of the fluid. The nonlinear hydrodynamic equations are derived from a new stand point of view. A special attention has been put on the treatment of the reaction of heat bath to the hydrodynamic motions.

Theory of inhomogeneous quantum systems. I. Static properties of Bose fluids.

We develop a variational theory for the determination of the ground-state properties of an inhomogeneous Bose fluid at zero temperature. Euler-Lagrange equations are derived for the one- and two-body correlations, and systematic approximation methods are physically motivated. It is shown that the optimized variational method provides a self-consistent approximate summation of ladder and ring diagrams. Numerical applications are presented for the density profile, distribution functions, energy, and chemical potential of films of $^{4}\mathrm{He}$ atoms. Both the bulk and surface energies are calculated and found to be in fair agreement with experiments.

4He as a dilute bose gas

Superfluid 4 He films adsorbed on Vycor glass, which is a highly interconnected 3D substrate, provide an opportunity for the study of mobile 4 He atoms in the low density limit. This system shares many of the features of a low density 3D gas and can provide an experimental realization of a dilute weakly interacting Bose fluid.

Solution of an inverse problem: Maximum-overlap Jastrow function of the Lennard-Jones Bose fluid

We determine for the Lennard-Jones Bose fluid the Jastrow function that has the maximum overlap with the exact ground state as determined by the Green's-function Monte Carlo method. We solve the resulting inverse problem with an iterative predictor-corrector method using integral equations and Monte Carlo methods, respectively. The maximum-overlap Jastrow function gives also a good value for the energy.

Density-wave instability in the linear-response functions of liquidHe4and the charged-boson gas

Indications of the density-wave phase in two quantum Bose fluids, liquid $^{4}\mathrm{He}$ and the charged-boson gas, are found by calculating the linear-response functions, $\ensuremath{\chi}(k)$, of these systems using the Jastrow theory. In liquid $^{4}\mathrm{He}$ the linear-response function diverges at momentum $k\ensuremath{\sim}2.2$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ and the fluid density ${\ensuremath{\rho}}_{0}\ensuremath{\sim}0.028$ ${\mathrm{\AA{}}}^{\ensuremath{-}3}$ which is within the liquid-solid phase-transition region. A good agreement with measured $\ensuremath{\chi}(k)$ is obtained at the saturation density ${\ensuremath{\rho}}_{0}\ensuremath{\sim}0.02185$ ${\mathrm{\AA{}}}^{\ensuremath{-}3}$. In the charged-boson gas $\ensuremath{\chi}(k)$ diverges at ${r}_{s}\ensuremath{\sim}308$.

Critical Behavior of a Dilute Interacting Bose Fluid

The crossover from critical behavior to ideal Bose-gas behavior in a dilute, weakly interacting Bose fluid at low temperatures is shown to be described by a scaling function depending on the temperature, density, and dimensionality. The results are applied to the experimental measurements of Crooker et al. on the superfluid density of /sup 4/He in Vycor glass. The satisfactory agreement obtained lends support to the model of /sup 4/He in Vycor as a dilute, weakly interacting, three-dimensional Bose fluid.

Linear-response function of the quantum Bose fluid. Application to the charged-boson gas

The static-linear-response function $\ensuremath{\chi}(k)$ is derived for the quantum Bose fluid with the use of the hypernetted-chain approximation in the Jastrow theory. The pair-correlation function of the uniform system required as an input function is optimized within the same theory. The compressibility sum rule as well as the sequential and screening conditions are exactly fulfilled by construction. It is shown analytically that in the small-wavelength limit the leading correction in ${\ensuremath{\chi}}^{\ensuremath{-}1}(k)$ to the freeparticle kinetic energy is a constant $\frac{2}{3}\frac{{T}_{\mathrm{JF}}}{N}$, where ${T}_{\mathrm{JF}}$ is the Jackson-Feenberg kinetic energy. We have also developed a reliable numerical method which is used in the calculation of the linear-response function of the charged-boson gas at metallic densities.

High- and low-frequency behaviour of response functions in a Bose liquid: One-loop approximation

The filed-theoretic analysis of Wong and Gould for a Bose fluid is used to study response functions at arbitrary temperatures. Several rigorous identities are derived for density and momentum current response functions in the high- and low-frequency limits. These involve the condensate fraction n 0 and the superfluid density ϱ s . By explicit calculations using the one-loop diagrammatic approximation for the proper irreducible functions, these rigorous results are verified at finite temperatures. In particular, the zero-frequency Gavoret-Nozières relation, the high-frequency Wong-Gould f-sum rule, and the impulse approximation at high momentum transfers are all satisfied in this simple microscopic calculation. On the other hand, the superfluid f-sum rule is found not to be satisfied.

High- and low-frequency behaviour of response functions in a Bose liquid: One-loop approximation

Abstract The filed-theoretic analysis of Wong and Gould for a Bose fluid is used to study response functions at arbitrary temperatures. Several rigorous identities are derived for density and momentum current response functions in the high- and low-frequency limits. These involve the condensate fraction n 0 and the superfluid density ϱ s . By explicit calculations using the one-loop diagrammatic approximation for the proper irreducible functions, these rigorous results are verified at finite temperatures. In particular, the zero-frequency Gavoret-Nozieres relation, the high-frequency Wong-Gould f -sum rule, and the impulse approximation at high momentum transfers are all satisfied in this simple microscopic calculation. On the other hand, the superfluid f -sum rule is found not to be satisfied.

Renormalization theory of the interacting Bose fluid

We derive an approximate closed form for the infinitesimal generator of the renormalization group for the interacting Bose fluid. The Bose-condensed phase is treated by the method of Bogoliubov, and a simple scaling law is found for the condensate density. It is shown that the quantum-mechanical features are irrelevant close to the $\ensuremath{\lambda}$ line. This is demonstrated by calculating the critical behavior in $4\ensuremath{-}\ensuremath{\epsilon}$ dimensions to order $\ensuremath{\epsilon}$.

Paired-phonon analysis of impurities in bose fluids

The paired-phonon analysis for boson mixtures is employed in conjunction with the hypernetted-chain approximation to study the ground-state properties of an impurity embedded in liquid4He. Chemical potentials, volume coefficients and other thermodynamic quantities as well as some of the most interesting optimal correlation functions are calculated for various impurities interacting with the4He background atoms via Lennard-Jones potentials of differing strength.

Dynamics of Vortices in Bose Fluids and Classical Continuous Spin Models

Dynamics of two-dimensional (2d) vortices in Bose fluids governed by the Gross-Pitaevskii equation or the nonlinear Schrödinger equation and planar Heisenberg ferromagnets in an external field is studied. This is done by introducing a velocity potential corresponding to 2d point vortices and by assuming the time-dependence of field variables to occur only through the position of vortex cores. Equations of motion for these model systems are shown to be reducible to canonical equations of motion for 2d vortices which are identical in form to those for 2d point vortices in incompressible and inviscid fluids due to singularity natures of vortex cores. From the result for the integrability or the non-integrability of the motion of Euler vortices in 2d fluid dynamics, the non-integrability of the equations of motion for the systems are deduced. Discussions are also given on the dynamics of vortices in the 2d O(3)-nonlinear σ model and phonons in spin fluids associated with the classical XY model in an external field.

Renormalization group theory of the critical properties of the interacting bose fluid

Starting from a functional integral representation of the partition function we apply the renormalization group to the interacting Bose fluid. A closed form for the renormalization equation is derived and the critical exponents are calculated in 4-ϵ dimensions.

On the momentum distribution in Bose fluids

We comment on some properties of the momentum distribution in an interacting Bose fluid and its relation to the average kinetic energy per particle within the hypernetted chain approach.

Structure of the ground-state wave function of quantum fluids and "exact" numerical methods

The problem of how to extract information on the structure of the exact ground-state wave function of a Bose fluid from the results of Green's-function Monte Carlo computations is considered. Use of the criterion of maximum overlap of the exact ground state with an extended Jastrow function leads to certain equalities for correlation functions. By using methods borrowed from theories of classical fluids various schemes are proposed that permit the determination of the "best" Jastrow function. The case of Fermi statistics is also considered.

On the relation between the normal fluid density and the one particle Green function for Bose fluids

The normal fluid density is defined through the moment of inertia of a cylinder rotating about its axis, in the limit of infinitesimal angular velocity. The angular momentum may be calculated from the one particle Green function, and this leads to the relation between ρn and the Green function. We then consider an ensemble in which the fluid is constrained to irrotational flow. For statistical states which are “locally gauge invariant” we show that ρn, as defined previously, is identical to the full density. This demonstrates the connection between superfluidity and the breaking of local gauge symmetry. Finally, we apply the result to the gas of non-interacting quasi-particles and the fully interacting Bose fluid in the limit of very low temperatures. In both cases we reproduce the Landau expression for ρn in terms of the quasiparticle occupation numbers, and derive the well-known result for real superfluid helium that ρn ~ T4 as T→0.

Hypernetted Chain Theory of Charged Impurity

Applying the inhomogeneous hypernetted chain method we formulate the general impurity problem for a correlated Bose or Fermi fluid as a host. In the present paper we apply the method to an impurity in electron gas. From the Euler-Lagrange equation for the induced density one obtains the screening and cusp conditions. It turns out that these two conditions alone are sufficient to give accurate prediction for the positron annihilation in metals. We construct numerical solution for the Euler-Lagrange equation demanding the two conditions to be satisfied. The resulting energies compare well with existing field theoretical calculations for hydrogen and positronium impurities. The uniform limit approximation is used to derive an expression for the dielectric function. In the present theory the linear response to an external field is determined by one characteristic function which is calculable from the ground state quantities alone. Eliminating this function in favour of the dielectric function which is assumed to be known exactly we obtain an equation for the non linear density response which may have more general validity than the approximations made here suggest.

Effective Harmonic-Fluid Approach to Low-Energy Properties of One-Dimensional Quantum Fluids

A universal description of the low-energy properties of one-dimensional quantum fluids, based on a harmonic theory of long-wavelength density fluctuations with use of renormalized parameters, is outlined. The structure of long-distance correlations of a spinless fluid is obtained, showing the essential similarity of one-dimensional Bose and Fermi fluids. The results are illustrated by application to the one-dimensional Bose fluid with $\ensuremath{\delta}$-function interaction.

Three-Particle Correlations in the Ground State of a Bose Fluid

Three-Particle Correlations in the Ground State of a Bose Fluid

Sum rule relating pair fluctuations and the superfluid mass density in helium four

We derive a relation between the pairing function χ q, of which Ristig has recently made a variational calculation for 4He, and the contribution of pairing fluctuations to the superfluid mass density in a bose fluid. We have shown that the two fluid hydrodynamic equations are unchanged in the presence of a pair condensate, though the microscopic identification of ϱ s is changed.