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

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

Embedding the affine complement of three intersecting lines in a finite projective plane

An (r, 1)–design is a pair (V, F) where V is a ν–set and F is a family of non-null subsets of V (b in number) which satisfy the following. (1) Every pair of distinct members of V is contained in precisely one member of F. (2) Every member of V occurs in precisely r members of F. A pseudo parallel complement PPC(n, α) is an (n+1, 1)–design with ν=n2−αn and b≦n2+n−α in which there are at least n−α a blocks of size n. A pseudo intersecting complement PIC(n, α) is an (n+1, 1)–design with ν=n2−αn+α−1 and b≦n2+n−α in which there are at least n−α+1 blocks of size n−1. It has previously been shown that for α≦4, every PIC(n, α) can be embedded in a PPC(n, α−1) and that for n>(α4−2α3+2α2+α−2)/2, every PPC(n, α) can be embedded in a finite projective plane of order n. In this paper we investigate the case of α=3 and show that any PIC(n, 3) is embeddable in a PPC(n,2) provided n≧14

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

Phases of granular segregation in a binary mixture

We present results from an extensive experimental investigation into granular segregation of a shallow binary mixture in which particles are driven by frictional interactions with the surface of a vibrating horizontal tray. Three distinct phases of the mixture are established viz; binary gas (unsegregated), segregation liquid and segregation crystal. Their ranges of existence are mapped out as a function of the system's primary control parameters using a number of measures based on Voronoi tessellation. We study the associated transitions and show that segregation can be suppressed is the total filling fraction of the granular layer, $C$, is decreased below a critical value, $C_{c}$, or if the dimensionless acceleration of the driving, $\gamma$, is increased above a value $\gamma_{c}$.Comment: 12 pages, 12 figures, submitted to Phys. Rev.

Acute inhibition of MEK suppresses congenital melanocytic nevus syndrome in a murine model driven by activated NRAS and Wnt signaling

Congenital melanocytic nevus (CMN) syndrome is the association of pigmented melanocytic nevi with extra-cutaneous features, classically melanotic cells within the central nervous system, most frequently caused by a mutation of NRAS codon 61. This condition is currently untreatable and carries a significant risk of melanoma within the skin, brain, or leptomeninges. We have previously proposed a key role for Wnt signaling in the formation of melanocytic nevi, suggesting that activated Wnt signaling may be synergistic with activated NRAS in the pathogenesis of CMN syndrome. Some familial pre-disposition suggests a germ-line contribution to CMN syndrome, as does variability of neurological phenotypes in individuals with similar cutaneous phenotypes. Accordingly, we performed exome sequencing of germ-line DNA from patients with CMN to reveal rare or undescribed Wnt-signaling alterations. A murine model harboring activated NRASQ61K and Wnt signaling in melanocytes exhibited striking features of CMN syndrome, in particular neurological involvement. In the first model of treatment for this condition, these congenital, and previously assumed permanent, features were profoundly suppressed by acute post-natal treatment with a MEK inhibitor. These data suggest that activated NRAS and aberrant Wnt signaling conspire to drive CMN syndrome. Post-natal MEK inhibition is a potential candidate therapy for patients with this debilitating condition

Classification of phase transitions of finite Bose-Einstein condensates in power law traps by Fisher zeros

We present a detailed description of a classification scheme for phase transitions in finite systems based on the distribution of Fisher zeros of the canonical partition function in the complex temperature plane. We apply this scheme to finite Bose-systems in power law traps within a semi-analytic approach with a continuous one-particle density of states $\Omega(E)\sim E^{d-1}$ for different values of $d$ and to a three dimensional harmonically confined ideal Bose-gas with discrete energy levels. Our results indicate that the order of the Bose-Einstein condensation phase transition sensitively depends on the confining potential.Comment: 7 pages, 9 eps-figures, For recent information on physics of small systems see "http://www.smallsystems.de

Classical Limit of Demagnetization in a Field Gradient

We calculate the rate of decrease of the expectation value of the transverse component of spin for spin-1/2 particles in a magnetic field with a spatial gradient, to determine the conditions under which a previous classical description is valid. A density matrix treatment is required for two reasons. The first arises because the particles initially are not in a pure state due to thermal motion. The second reason is that each particle interacts with the magnetic field and the other particles, with the latter taken to be via a 2-body central force. The equations for the 1-body Wigner distribution functions are written in a general manner, and the places where quantum mechanical effects can play a role are identified. One that may not have been considered previously concerns the momentum associated with the magnetic field gradient, which is proportional to the time integral of the gradient. Its relative magnitude compared with the important momenta in the problem is a significant parameter, and if their ratio is not small some non-classical effects contribute to the solution. Assuming the field gradient is sufficiently small, and a number of other inequalities are satisfied involving the mean wavelength, range of the force, and the mean separation between particles, we solve the integro- partial differential equations for the Wigner functions to second order in the strength of the gradient. When the same reasoning is applied to a different problem with no field gradient, but having instead a gradient to the z-component of polarization, the connection with the diffusion coefficient is established, and we find agreement with the classical result for the rate of decrease of the transverse component of magnetization.Comment: 22 pages, no figure

Comparison of Astrand VO2 Max Prediction to a Graded Leg Ergometry VO2 Max Test in Endurance Athletes

Please refer to the pdf version of the abstract located adjacent to the title

Numerical study of the spherically-symmetric Gross-Pitaevskii equation in two space dimensions

We present a numerical study of the time-dependent and time-independent Gross-Pitaevskii (GP) equation in two space dimensions, which describes the Bose-Einstein condensate of trapped bosons at ultralow temperature with both attractive and repulsive interatomic interactions. Both time-dependent and time-independent GP equations are used to study the stationary problems. In addition the time-dependent approach is used to study some evolution problems of the condensate. Specifically, we study the evolution problem where the trap energy is suddenly changed in a stable preformed condensate. In this case the system oscillates with increasing amplitude and does not remain limited between two stable configurations. Good convergence is obtained in all cases studied.Comment: 9 latex pages, 7 postscript figures, To appear in Phys. Rev.