Relaxation processes in a condensed Bose gas

We develop, on the basis of the self-consistent mean-field approximation, the kinetic theory for a dilute Bose gas below the Bose-Einstein transition temperature. The collision operator in the Boltzmann equation is calculated by golden rule arguments, and the momentum and temperature dependences of the scattering rates are determined. As an application, we consider the relaxation of a nonequilibrium distribution of the quasiparticles. We discuss the relevance of our calculation for the (hypothetical) condensed state of spinpolarized hydrogen.Zur Erlangung der Lehrbefähigung für das Lehrgebiet Physik der Fakultät für Physik der Universität Karlsruhe vorgelegte Habilitationsschrift.     

Critical Velocity of a Superfluid Bose Gas Flowing in a Random Potential

We investigate the critical velocity of a weakly interacting Bose gas flowing in a random potential. By applying the Bogoliubov theory to a disordered Bose system with a steady flow, we determine the critical velocity for weak and moderate disorder. We also calculate the superfluid density and the condensate density as a function of the disorder strength and the flow velocity, and their behaviors near the critical velocity are discussed.     

Critical Velocities in Two-Component Superfluid Bose Gases

On the ground of the Landau criterion we study the behavior of critical velocities in a superfluid two-component Bose gas. It is found that under motion of the components with different velocities the velocity of each component should not be lower than a minimum phase velocity of elementary excitations (s ₋). The Landau criterion yields a relation between the critical velocities of the components (v _c1, v _c2). The velocity of one or even both components may exceed s ₋. The maximum value of the critical velocity of a given component can be reached when the other component does not move. The approach is generalized for a two-component condensate confined in a cylindrical harmonic potential.      

Transport coefficients in a dilute but condensed Bose gas

The kinetic equations for a dilute superfluid developed previously are used to derive the Landau-Khalatnikov two-fluid hydrodynamic equations. Explicit expressions for the associated transport coefficients are given for very low temperatures and for moderately low temperatures.     

The dynamics of three-mode coupling in a trapped Bose gas

ABSTRACT

Multiple mode couplings in topological coherent modes of Bose–Einstein condensate are considered, by introducing an external alternating (resonating) field in the system. This analysis is based on the analytical solutions of nonlinear Gross–Pitaevskii equation for a trapped Bose gas at nearly absolute zero temperature. The dynamics of fractional populations of the generated coherent modes are analysed, particularly for a three-level system in the limit of small to large detuning of the intermediate state. These coupled topological modes, though nonlinear, are analogous to a resonant atom and exhibit a variety of significant non-trivial phenomena (effects), like: dynamic phase transitions, interference patterns, critical phenomena, mode-locking and chaotic motion.     

First and second sound in a weakly interacting dilute Bose gas

An explicit expression for the density response function in the hydrodynamic region has been given by Hohenberg and Martin, starting from the two-fluid equations of motion for a superfluid. We use their results to calculate the first and second sound resonances in a weakly interacting, dilute Bose-condensed gas. We only consider the intermediate temperature region, where the effect of the interactions may be treated as a small correction (nV ₀«k _B T). We use the transport coefficients obtained by Kirkpatrick and Dorfman. As expected for a gas, the second sound mode has appreciable weight in the density-fluctuation spectrum.     

On Critical Velocity of Superfluid Bose Gas with Boundary Interactions

The existence of superfluidity in a 3D Bose-gas can depend on boundary interactions with container walls. We study a simple model where the dilute moving Bose-gas interacts with the walls via hard-core repulsion. Special boundary excitations are introduced, and their excitation spectrum is calculated within a semiclassical approximation. It turns out that the state of the moving Bose-gas is unstable with respect to the creation of these boundary excitations in the system gas + walls, i.e. the critical velocity vanishes in the semiclassical (Bogoliubov) approximation. Such a surface mode could exist in soft matter containers with flexible walls.     

High- and low-frequency behavior of response functions in a Bose condensed liquid

Recent studies of superfluid ⁴He have shown that it is useful to separate S(Q, ) into condensate and regular parts. We discuss the f-sum rule and the compressibility sum rule which the condensate part satisfies at T = 0K and at finite temperatures. Our work is based on the microscopic approach of Gavoret and Nozières, as amended by Nepomnyashchii and Nepomnyashchii. We also discuss the implications of the Wong-Gould sum rule for the condensate part of S(Q, ).This research was supported by a grant from NSERC, Canada.     

Particle number fluctuations in an ideal Bose gas

Abstract

We analyse occupation number fluctuations of an ideal Bose gas in a trap which is isolated from the environment with respect to particle exchange (canonical ensemble). We show that in contrast to the predictions of the grandcanonical ensemble, the counting statistics of particles in the trap ground state changes from monotonously decreasing above the condensation temperature to single-peaked below that temperature. For the exactly solvable case of a harmonic oscillator trapping potential in one spatial dimension we extract a Landau–Ginzburg functional which–despite the non-interacting nature of the system–displays the characteristic behaviour of a weakly interacting Bose gas. We also compare our findings with the usual treatment which is based on the grand-canonical ensemble. We show that for an ideal Bose gas neither the grand-canonical and canonical ensemble thermodynamically equivalent, nor the grand-canonical ensemble can be viewed as a small system in diffusive contact with a particle reservoir.     

Bogoliubov Theory for a Superfluid Bose Gas Flowing in a Random Potential: Stability and Critical Velocity

We investigate the stability and critical velocity of a weakly interacting Bose gas flowing in a random potential. By applying the Bogoliubov theory to a disordered Bose system with a steady flow, the condensate density and the superfluid density are determined as functions of the disorder strength, flow velocity, and temperature. The critical velocity, at which the steady flow becomes unstable, is calculated from the spectrum of hydrodynamic excitation. We also show that in two dimensions the critical velocity strongly depends on the system size.     

Critical conditions for instability of a charged drop moving in an electrostatic field

The pressure balance on the surface of a charged drop of the ideal incompressible liquid freely falling in a homogeneous electrostatic field are analyzed and the critical conditions for instability of the liquid surface are established. Satisfying the criteria found, the values of the drop charge, the electrostatic field strength, and the drop velocity relative to the medium coincide with those observed in thunderstorm clouds. Therefore, the proposed model conditions can be used as a basis in developing a hypothetical mechanism of lightning discharge initiation.     

Imaging of microscopic features of charged particle tracks in a low-pressure gas

An imaging system for measuring the spatial distribution of charged particle tracks in a low-pressure gas is presented. The method is based on an optically read out time projection chamber. Results of experiments with fast heavy ions are shown.     

Terahertz ionization of highly charged quantum posts in a perforated electron gas

"Quantum posts" are roughly cylindrical semiconductor nanostructures that are embedded in an energetically shallower "matrix" quantum well of comparable thickness. We report measurements of voltage-controlled charging and terahertz absorption of 30 nm thick InGaAs quantum wells and posts. Under flat-band (zero-electric field) conditions, the quantum posts each contain approximately six electrons, and an additional ~2.4 × 10(11) cm(-2) electrons populate the quantum well matrix. In this regime, absorption spectra show peaks at 3.5 and 4.8 THz (14 and 19 meV) whose relative amplitude depends strongly on temperature. These peaks are assigned to intersubband transitions of electrons in the quantum well matrix. A third, broader feature has a temperature-independent amplitude and is assigned to an absorption involving quantum posts. Eight-band k·p calculations incorporating the effects of strain and Coulomb repulsion predict that the electrons in the posts strongly repel the electrons in the quantum well matrix, "perforating" the electron gas. The strongest calculated transition, which has a frequency close to the center of the quantum post related absorption at 5 THz (20 meV), is an ionizing transition from a filled state to a quasi-bound state that can easily scatter to empty states in the quantum well matrix.     

Critical behavior of nonionic micellar solutions

The critical behavior of micellar solutions of triethylene glycol monon-hexylether in water has been investigated in view of the issue of critical-point universality for such systems close to their critical mixing point. The values of the critical exponents obtained in this work are in excellent agreement with the theoretical ones for three-dimensional Ising-like systems. The dynamical critical behavior is also discussed.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

How should the dynamics of an interacting degenerate Bose gas be described?

We show how a semiclassical representation of the atomic field may describe the interacting base gas at finite temperatures.     

Study of spin relaxation by a charged particle beam in a polarized 3He gas target

A model has been constructed for depolarization of a sample of polarized ³He by a charged particle beam. The predictions of this model have been tested experimentally for 0.25 to 1.0 μA of 3 MeV protons incident on a 0.5 to 5.0 Torr room-temperature target of polarized ³He. Good agreement has been found between the model and experiment.     

Methods for a Nonuniform Bose Gas

We review mathematical methods for the treatment of a system of Bose particles with nonuniform density. The use of the pseudopotential is explained, especially with respect to negative scattering lengths. It is emphasized that the delta-function potential produces no scattering in three dimensions, and should not be used in the Bogoliubov self-consistent field method, which is variational in nature. A common misuse of the Bogoliubov method at finite temperatures is pointed out. A Gaussian variational method is proposed.