Spin-polarized hydrogen: A weakly interacting boson gas

These lectures on a gas of spin-polarized hydrogen discuss the developments in this field up to the latest results. First, hydrogen is treated as a stable non-recombining gas and many fundamental properties such as Bose-Einstein condensation (BEC), the two-dimensional Kosterlitz-Thouless transition to superfluidity, and interactions with helium are discussed. In the second section the experimental production and handling of spin-polarized hydrogen is treated. This includes theoretical and experimental discussions of two- and three-body recombination as well as relaxation, both in the normal and condensate phase. These processes have so far prevented the experimental observation of degenerate quantum effects, as they either limit the density or the temperatures of samples. In the final section several experimental ideas for BEC, currently under development, are discussed. These include the magnetostatic trap, the microwave trap, compression of hydrogen as bubbles in helium, compression with magnetic field gradients, and the use of the Lyman- laser source in the study of atomic hydrogen.Presented by Isaac F. Silvera.     

On some effects in a system of two interacting Josephson junctions

We consider two long, weakly interacting Josephson junctions in an external magnetic field. A uniformly distributed direct current applied to the system excites the movement of a vortex chain within each junction. The weak interaction between the vortex chains results in monochromatical radiation from the system and some peculiarities in theI–V curve.     

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.     

Indirect detection of weakly interacting massive particles

Several experiments are performing searches for dark matter in the Galaxy in the form of weakly interacting massive particles (WIMPs). A major search technique is to look for secondary particles originating from the annihilation of pairs of WIMPs at various locations in the Galaxy. The nature of the experiment depends on the species of secondary particle searched for. This paper outlines the motivation for such searches and describes the present experimental status. Existing data from searches from positron, anti-proton, gamma-ray and neutrino detectors will be presented, together with details of future experiments under construction.     

Dynamical susceptibility of weakly interacting ferromagnetic nanoclusters

The ac-susceptibility of weakly interacting ferromagnetic nanoclusters located at the vertices of a periodic lattice in a static applied field is calculated using a perturbation theory. The samples are nonspherical which gives rise to predominant shape effects due to dipolar interactions. The effects observed on the maximum of the two components of the dynamical susceptibility when increasing the strength of the dipolar interactions are opposite for prolate and oblate samples. It is also shown that a static applied field can invert these effects. The peak position of the out-of-phase component of the ac-susceptibility shifts towards lower temperatures with increasing the strength of the dipolar interactions in most cases in agreement with previous numerical studies on isotropic systems. It is shown that the opposite behaviour can be observed in the high damping case because of a sample shape effect.     

X-ray focusing with lobster-eye optics: a comparison of theory with experiment

We report an experimental investigation and comparison with simulation of the x-ray focusing of a flat, square profile microchannel plate. We use x rays with an energy of ~1.5 keV from a laser-produced plasma. The images were recorded with x-ray film. We find the focal structure to be consistent with theoretical expectations. The angular resolution of the focus is 0.96 mrad, which is a major improvement over previous results. The measured peak intensity gain is 27 ± 4, which is ~33% of that for a perfect optic.     

The density distribution of a weakly interacting bose gas in an external potential

The Gross-Pitaevskii equations are generalized to finite temperatures by means of the self-consistent Hartree-Fock and Bogolyubov approximations that are derived through a variational principle for the optimal set of one-particle eigenstates. A number of sample density profiles are provided for spin-polarized atomic hydrogen when the external potential depends on thez coordinate onlySupported by the National Science Foundation under grant # DMR-80-20429 and by the Sloan Foundation.     

II. Locally enhanced spin fluctuations viewed within the Wilson theory. Comparison with the Kondo problem

We give here the details of a brief report given elsewhere and based on the study developed in the previous paper (I). We begin by citing the analogy between the behavior of a ferromagnet above its Curie temperature and an itinerant strongly interacting set of fermions at 0 K. We show that this analogy holds beyond the well-known mean-field results. We then develop a calculation similar to the Wilson theory of phase transitions, using a Lagrangian established in paper I for locally interacting fermions and shown to be comparable to the Wilson Lagrangian. We find that the renormalized local enhancement on a nearly magnetic impurity has the same form as in mean-field theory but with a renormalized local interaction actually weaker than the Hartree-Fock one. We conclude that the stable fixed point in that theory should correspond to a vanishing local interaction between the fermions. This last result is compared with the stable fixed pointJ=?∞ of the Kondo problem. In the present case the theory of local paramagnons appears to actually be a weak coupling theory. A contrast between the problems of local spin fluctuations and uniform ones is also pointed out.     

On the theory of the Kondo effect

The Kondo effect is investigated by methods developed in the theory of fields with strong coupling. Renormalizability relations analogous to the scaling laws in the theory of second-order phase transitions are found. The behavior of the scattering amplitude of an electron by an impurity is analyzed as a function of the electron energy. Formulas are derived for the resistance as a function of the temperature and for the magnetic moment as a function of the magnetic field and temperature. For the antiferromagnetic interaction sign the resistance tends to a constant and the magnetic moment to zero asT 0 according to power laws with universal exponents that depend only on the spin of the impurity. For sufficiently large spin the susceptibility tends to infinity asT 0.     

Kinetics of phase transition in ideal and weakly interacting bose gas

The time evolution of a Bose system passing through the critical point is considered. The solution of the nonlinear integrodifferential equation that governs the kinetics demonstrates that the new phase formation proceeds by the set of essentially nonequilibrium states. The phase transition in an ideal Bose gas is of first order and can be completed att= only if there are no nuclei of the new phase at the beginning of the cooling process. With nuclei the Bose condensate formation takes a finite time. A Bose gas with interaction between Bose particles exhibits a second-order phase transition with a finite time of new phase formation even without nuclei. The time evolution of an energy spectrum of a Bose system following the variation of its distribution function is considered and it is shown that the appearance of superfluidity coincides with the instant of Bose condensate formation.     

Control of a weakly perturbed Lagrangian system with a guaranteed escape rate

This paper considers a problem of controlling a weakly perturbed Lagrangian system so as to keep it within a reference domain on a pregiven time interval. Escape from this domain is associated with failure of the system. The criterion of interest is the rate of escape, and the task is to design a controller ensuring a noise-independent escape rate (in the small noise limit) of the controlled system. We treat this problem in the context of control against large deviations in weakly perturbed dissipative systems. As this paper demonstrates, for Lagrangian systems, in contrast to the great majority of large deviation problems, an explicit logarithmic asymptotic of the escape rate can be found. An explicit formula allows us to define the parameters of a regulator guaranteeing weak dependence of the escape rate on the noise strength. The regulator consists of two units, nonlinear velocity feedback with the parameters depending on the noise strength and state feedback, independent of noise. The first unit stabilizes the system and ensures a noise-independent asymptotics of the logarithmic escape rate; the second unit is designed to modify the exit location on the boundary of the reference domain. Applications of these results to stabilization and tracking models illustrate the theory.     

Marginal behavior of a Fermi system interacting with bosonic excitations

We calculated the self-energy of a Fermi system interacting with bosonic excitation. If the bosonic system is near instability, the imaginary part of the self-energy which measures the lifetime of quasiparticles is of the order of ((p)- _F ) which is typical for a marginal Fermi liquid. Such a behavior can appear for three- and two-dimensional Fermi systems.     

Nuclear alignment in a Kondo system as a very low temperature thermometer

Cu doped with less than 1 ppm Mn⁵⁴ appears to offer a number of advantages as a -ray anisotropy thermometer in the temperature range 1 to 20 mK. In order to use such a thermometer it is necessary to know how the hyperfine field at the Mn⁵⁴ nuclei varies with temperature and with applied field. We have studied this -ray anisotropy and find that the hyperfine field is independent of temperature in the range 4 mK <T<10 mK. Further, we have determined the hyperfine field to ±5% as a function of applied field in the range 60 Oe<H _a<1200 Oe. The latter data may be used to determine a Kondo temperature of 64±2 mK for this system.Work performed under the auspices of the U.S. Atomic Energy Commission.     

Design of a compliant-cylinder-type fiber-optic accelerometer: theory and experiment

Experimental and theoretical research was carried out in order to establish the dependence of the performance of a compliant-cylinder-based fiber-optic accelerometer on the geometry and elastic properties of the transducer cylinders. The sensitivity and the natural frequency of the sensor were measured as a function of the ratio ε = (inner cylinder diameter)/(outer cylinder diameter). Two transducer materials with different elastic properties, a silicone rubber (Ecosil) and a polyetheretherketone polymer (PEEK 450G), were examined. It was found that with decreasing ε the sensitivity increases in the case of Ecosil and decreases in the case of PEEK. In both cases the natural frequency increases with decreasing ε. A simple analytical model was developed in order to explain this behavior qualitatively. The model takes into account the contributions to the effective stiffness from both the cylinder material and the fiber wrapped around the cylinder. The model is useful for the design of such types of accelerometer.     

Stability of a system of interacting cracks

In the absence of crack branching, a system of straight cracks may interact and their growth regime may become unstable in the sense that some cracks may grow faster at a certain critical state, or even snap into a longer length, while other cracks may stop growing, or even snap closed.When the crack extension involves Modes I, II, and III, and the fracture criterion is defined by a critical value for the total energy release rate, necessary and sufficient conditions are developed for both the stability of a given regime, and for unstable crack growth.     

Analysis of the parquet theory for the Kondo problem

The equations of the parquet theory for the Kondo problem are analyzed. The integral equation of the vertex function is recast as a differential equation and a fundamental relation characterizing the function responsible for Kondo divergence is derived. It is shown that the Kondo divergence occurs at a branch point which explicitly reveals the difference between ferromagnetic and anti-ferromagnetic couplings. That the scattering amplitude obeys a power law is also deduced.     

Specific heat discontinuity of a proximity-effect sandwich system containing Kondo impurities

The theoretical work of Matsuura, Ichinose, and Nagaoka on the Kondo effect in superconductors and McMillan's tunneling model are applied to a proximity-effect sandwich system containing Kondo impurities. Analytic expressions for the renormalized Green's functions of superconducting and normal-metal electrons are given as functions of the system composition. It is found that as the thicknesses become large, the specific heat discontinuity changes continuously from the Müller-Hartmann-Zittartz value for the magnetic cases to the Ichinose value for the nonmagnetic ones. For small values of the layer thickness, and with the films in proximity, our results can be used to calculate the specific heat jump at the transition temperature numerically.