Validity of the Hohenberg Theorem for a Generalized Bose-Einstein Condensation in Two Dimensions

Several authors have considered the possibility of a generalized Bose-Einstein condensation (BEC) in which a band of low states is occupied so that the total occupation number is macroscopic, even if the occupation number of each state is not extensive. The Hohenberg theorem (HT) states that there is no BEC into a single state in 2D; we consider its validity for the case of a generalized condensation and find that, under certain conditions, the HT does not forbid a BEC in 2D. We discuss whether this situation actually occurs in any theoretical model system.Comment: 6 pages, Latex, JLTP class, accepted by Jour. Low Temp. Phys., Quantum Fluids and Solids Conference QFS200

Some fundamental fracture mechanisms applicable to advanced filament reinforced composites

Stress analysis and fracture mechanisms of advanced fiber reinforced composite

Investigation of the reinforcement of ductule metals with strong, high modulus discontinuous, brittle fibers Quarterly report, 1 May - 1 Aug. 1968

Factors affecting tensile strength of ductile metals reinforced with short, brittle fiber

Theory of cooling by flow through narrow pores

We consider the possibility of adding a stage to a dilution refrigerator to provide additional cooling by ``filtering out'' hot atoms. Three methods are considered: 1) Effusion, where holes having diameters larger than a mean-free path allow atoms to pass through easily; 2) Particle waveguide-like motion using very narrow channels that greatly restrict the quantum states of the atoms in a channel. 3) Wall-limited diffusion through channels, in which the wall scattering is disordered so that local density equilibrium is established in a channel. We assume that channel dimension are smaller than the mean-free path for atom-atom interactions. The particle waveguide and the wall-limited diffusion methods using channels on order of the de Broglie wavelength give cooling. Recent advances in nano-filters give this method some hope of being practical.Comment: 10 pages, 3 figures. Corrected typos and made some minor wording change

Shot noise of interference between independent atomic systems

We study shot (counting) noise of the amplitude of interference between independent atomic systems. In particular, for the two interfering systems the variance of the fringe amplitude decreases as the inverse power of the number of particles per system with the coefficient being a non-universal number. This number depends on the details of the initial state of each system so that the shot noise measurements can be used to distinguish between such states. We explicitly evaluate this coefficient for the two cases of the interference between bosons in number states and in broken symmetry states. We generalize our analysis to the interference of multiple independent atomic systems. We show that the variance of the interference contrast vanishes as the inverse power of the number of the interfering systems. This result, implying high signal to noise ratio in the interference experiments, holds both for bosons and for fermions.Comment: 5 pages, 1 figure, final version, added a simple quantum-mechanical argument why two independent condensates with fixed number of particles in each must interfere in a generic experimental setu

Absence of Fragmentation in Two-Dimensional Bose-Einstein Condensation

We investigate the possibility that the BEC-like phenomena recently detected on two-dimensional finite trapped systems consist of fragmented condensates. We derive and diagonalize the one-body density matrix of a two-dimensional isotropically trapped Bose gas at finite temperature. For the ideal gas, the procedure reproduces the exact harmonic-oscillator eigenfunctions and the Bose distribution. We use a new collocation-minimization method to study the interacting gas in the Hartree-Fock approximation and obtain a ground-state wavefunction and condensate fraction consistent with those obtained by other methods. The populations of the next few eigenstates increase at the expense of the ground state but continue to be negligible; this supports the conclusion that two-dimensional BEC is into a single state.Comment: 6 pages, 1 figur

Imperfect Homoclinic Bifurcations

Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics observed in the circuit can be understood by reference to imperfect homoclinic bifurcations without constructing an explicit mathematical model of the system.Comment: 8 pages, 11 figures, submitted to PR

Anisotropic Spin Diffusion in Trapped Boltzmann Gases

Recent experiments in a mixture of two hyperfine states of trapped Bose gases show behavior analogous to a spin-1/2 system, including transverse spin waves and other familiar Leggett-Rice-type effects. We have derived the kinetic equations applicable to these systems, including the spin dependence of interparticle interactions in the collision integral, and have solved for spin-wave frequencies and longitudinal and transverse diffusion constants in the Boltzmann limit. We find that, while the transverse and longitudinal collision times for trapped Fermi gases are identical, the Bose gas shows diffusion anisotropy. Moreover, the lack of spin isotropy in the interactions leads to the non-conservation of transverse spin, which in turn has novel effects on the hydrodynamic modes.Comment: 10 pages, 4 figures; submitted to PR

Instability in a Two-Dimensional Dilute Interacting Bose System

The formalism of Ursell operators provides a self-consistent integral equation for the one-particle reduced operator. In three dimensions this technique yields values of the shift in the Bose-Einstein condensation (BEC) transition temperature, as a function of the scattering length, that are in good agreement with those of Green’s function and quantum Monte Carlo methods. We have applied the same equations to a uniform two-dimensional system and find that, as we alter the chemical potential, an instability develops so that the self-consistent equations no longer have a solution. This instability, which seems to indicate that interactions restore a transition, occurs at a non-zero value of an effective chemical potential. The non-linear equations are limited to temperatures greater than or equal to Tc, so that they do not indicate the nature of the new stable state, but we speculate concerning whether it is a Kosterlitz-Thouless state or a “smeared” BEC, which might avoid any violation of the Hohenberg theorem, as described in an accompanying paper