Beyond spontaneously broken symmetry in Bose-Einstein condensates

Spontaneous symmetry breaking (SSB) for Bose-Einstein condensates cannot treat phase off-diagonal effects, and thus not explain Bell inequality violations. We describe another situation that is beyond a SSB treatment: an experiment where particles from two (possibly macroscopic) condensate sources are used for conjugate measurements of the relative phase and populations. Off-diagonal phase effects are characterized by a "quantum angle" and observed via "population oscillations", signaling quantum interference of macroscopically distinct states (QIMDS).Comment: 10 pages 4 figure

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

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

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

Quantum-limited mass flow of liquid 3^{3}He

We consider theoretically the possibility of observing unusual quantum fluid behavior in liquid $^{3}$He and solutions of $^{3}$He in $^{4}$He systems confined to nano-channels. In the case of pure ballistic flow at very low temperature conductance will be quantized in units of $2m^{2}/h$. We show that these steps should be sensitive to increases in temperature. We also use of a random scattering matrix simulation to study flow with diffusive wall scattering. Universal conductance fluctuations analogous to those seen in electron systems should then be observable. Finally we consider the possibility of the cross-over to a one-dimensional system at sufficiently low temperature where the system could form a Luttinger liquid

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

Highly-resolved three-dimensional velocity measurements via dual-plane stereo particle image velocimetry (DSPIV) in turbulent flows

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76106/1/AIAA-2002-290-824.pd

Dual-plane stereo particle image velocimetry measurements of velocity gradient tensor fields in turbulent shear flow. I. Accuracy assessments

Results are presented from quantitative assessments of the accuracy of velocity gradients measured by a dual-plane stereo particle image velocimetry (DSPIV) technique that allows direct, highly resolved, nonintrusive measurements of all nine simultaneous components of the velocity gradient tensor fields ∂ui/∂xj∂ui∕∂xj at the quasi-universal intermediate and small scales of turbulent shear flows. The present results systematically determine the sources of errors in DSPIV measurements and the resulting accuracy of velocity gradients obtained from such measurements. Intrinsic errors resulting from asymmetric stereo imaging are found by synthetic particle imaging to be no larger than 0.8%. True particle imaging in finite-thickness light sheets is found from single-plane imaging tests to produce net errors in measured velocity differences of 6% for in-plane components and 10% for out-of-plane components. Further errors from limits on the accuracy of independent dual light sheet generation and positioning are found from coincident-plane imaging tests to produce overall errors of 9% and 16% in the in-plane and out-of-plane velocity differences. Practical DSPIV velocity gradient component measurements are found from separated-plane imaging tests in a turbulent shear flow to show excellent similarity in on-diagonal (i = j)(i=j) and off-diagonal (i ≠ j)(i≠j) components of ∂ui/∂xj∂ui∕∂xj, as well as mean-square gradient values showing agreement within 1%–4% of ideal isotropic limit values. The resulting measured divergence values are consistent with overall rms errors obtained from the coincident-plane imaging tests. Collectively, these results establish the accuracy with which all nine simultaneous components of the velocity gradient tensor fields ∂ui/∂xj∂ui∕∂xj can be obtained from DSPIV measurements at the quasi-universal intermediate and small scales of turbulent shear flows.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87388/2/035101_1.pd

Dual-plane stereo particle image velocimetry measurements of velocity gradient tensor fields in turbulent shear flow. II. Experimental results

Results are presented from highly resolved dual-plane stereo particle image velocimetry (DSPIV) measurements for the structure, statistics, similarity, and scaling of all nine simultaneous components of the velocity gradient tensor fields ∂ui/∂xj∂ui∕∂xj on the quasi-universal intermediate and small scales of turbulent shear flows. Measurements were obtained at three combinations of the outer-scale Reynolds number ReδReδ and the local mean shear rate SS in the fully developed self-similar far field of a turbulent jet, and thus reflect the combined effects of the large-scale structure, spatial inhomogeneities, and anisotropies inherent in such a flow. Conditions addressed in this study correspond to local outer-scale Reynolds numbers Reδ = 6,000Reδ=6,000 and 30,000 and local mean shear values Sδ/uc = 0Sδ∕uc=0 and 1.7, corresponding to Taylor-scale Reynolds numbers Reλ ≈ 44Reλ≈44 and 113 and shear rates Sk/ε = 0Sk∕ε=0 and 2.1. Gradient fields investigated here include the individual velocity gradient component fields, the strain rate component fields and the associated principal strain rates, the vorticity component fields and their orientations with respect to the principal strain axes, the enstrophy and enstrophy production rate fields, and the true kinetic energy dissipation rate field. Results normalized on both inner- and outer-scale variables are presented to allow interpretation relative to the similarity and scaling implied by classical turbulence theory. For both ReδReδ values at S = 0S=0, results show that most aspects of these gradient fields are essentially in agreement with the predictions from homogeneous isotropic turbulence, while for S ≠ 0S≠0 there are significant and consistent departures from isotropy. Results also provide direct measurements of the exponential scaling factors in the left and right tails of the velocity gradient distributions, as well as quantification of the inner (viscous) length scales in the enstrophy and dissipation rate fields. In addition, strong evidence for multifractal scale similarity at length scales greater than about twice the viscous length λνλν is found in both the enstrophy and dissipation rate fields.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87499/2/035102_1.pd