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

Nonlocal appearance of a macroscopic angular momentum

We discuss a type of measurement in which a macroscopically large angular momentum (spin) is "created" nonlocally by the measurement of just a few atoms from a double Fock state. This procedure apparently leads to a blatant nonconservation of a macroscopic variable - the local angular momentum. We argue that while this gedankenexperiment provides a striking illustration of several counter-intuitive features of quantum mechanics, it does not imply a non-local violation of the conservation of angular momentum.Comment: 10 pages, 1 figur

Giant viscosity enhancement in a spin-polarized Fermi liquid

The viscosity is measured for a Fermi liquid, a dilute $^3$He-$^4$He mixture, under extremely high magnetic field/temperature conditions ($B \leq 14.8$ T, $T \geq 1.5$ mK). The spin splitting energy $\mu B$ is substantially greater than the Fermi energy $k_B T_F$; as a consequence the polarization tends to unity and s-wave quasiparticle scattering is suppressed for $T \ll T_F$. Using a novel composite vibrating-wire viscometer an enhancement of the viscosity is observed by a factor of more than 500 over its low-field value. Good agreement is found between the measured viscosity and theoretical predictions based upon a $t$-matrix formalism.Comment: 4 pages, 4 figure

Low-Temperature Spin Diffusion in a Spin-Polarized Fermi Gas

We present a finite temperature calculation of the transverse spin-diffusion coefficient, $D_\bot$, in a dilute degenerate Fermi gas in the presence of a small external magnetic field, $H$. While the longitudinal diffusion coefficient displays the conventional low-temperature Fermi-liquid behavior, $D_\parallel \propto T^{-2}$, the corresponding results for $D_\bot$ show three separate regimes: (a) $D_\bot \sim H^{-2}$ for $T \ll H$; (b) $D_\bot \sim T^{-2}$, $D_\bot /D_\parallel \neq 1$ for $T \gg H$ and large spin-rotation parameter $\xi \gg 1$, and (c) $D_\bot = D_\parallel \propto T^{-2}$ for $T \gg H$ and $\xi \ll 1$. Our results are qualitatively consistent with the available experimental data in weakly spin-polarized $^3{\rm He}$ and $^3{\rm He} - ^4{\rm He}$ mixtures.Comment: 13 pages, REVTEX, 3 figures available upon request, RU-94-4

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

Exclusion Statistics in a trapped two-dimensional Bose gas

We study the statistical mechanics of a two-dimensional gas with a repulsive delta function interaction, using a mean field approximation. By a direct counting of states we establish that this model obeys exclusion statistics and is equivalent to an ideal exclusion statistics gas.Comment: 3 pages; minor changes in notation; typos correcte

Maximal length of trapped one-dimensional Bose-Einstein condensates

I discuss a Bogoliubov inequality for obtaining a rigorous bound on the maximal axial extension of inhomogeneous one-dimensional Bose-Einstein condensates. An explicit upper limit for the aspect ratio of a strongly elongated, harmonically trapped Thomas-Fermi condensate is derived.Comment: 6 pages; contributed paper for Quantum Fluids and Solids, Trento 2004, to appear in JLT

Does Nonrandom Nest Placement Imply Nonrandom Nest Predation?: a Reply

In response to the critique by Schmidt and Whelan (Condor 101 (4): 916-920, 1999), we find that the relationship between nest success and tree selectivity is dependent upon inclusion or exclusion of particular tree species, whether or not years are pooled, and the selectivity index used. We question their use of point estimates of nest success with extremely high variances, defend our index, question the application of the Chesson (1983) index to our data, and explain the need to analyze years separately. Bottomland hardwood forest systems are extremely variable; hydroperiods alter the suitability of nesting substrates, availability of alternative food, and behavior of predators and their prey. Given these features, actively searching for Acadian Flycatcher (Empidonax virescens) nests is seldom an efficient predator foraging strategy. Therefore, these predation events are best described as random; nests are principally encountered opportunistically by generalist predators while searching for other prey