A Fermion-like description of condensed Bosons in a trap

A Bose-Einstein condensate of atoms, trapped in an axially symmetric harmonic potential, is considered. By averaging the spatial density along the symmetry direction over a length that preserves the aspect ratio, the system may be mapped on to a zero temperature noninteracting Fermi-like gas. The ``mock fermions'' have a state occupancy factor $(>>1)$ proportional to the ratio of the coherance length to the ``hard-core'' radius of the atom. The mapping reproduces the ground state properties of the condensate, and is used to estimate the vortex excitation energy analytically. The ``mock-fermion'' description predicts some novel collective excitation in the condensed phase.Comment: 11 pages, REVTE

Haldane Exclusion Statistics and the Boltzmann Equation

We generalize the collision term in the one-dimensional Boltzmann-Nordheim transport equation for quasiparticles that obey the Haldane exclusion statistics. For the equilibrium situation, this leads to the ``golden rule'' factor for quantum transitions. As an application of this, we calculate the density response function of a one-dimensional electron gas in a periodic potential, assuming that the particle-hole excitations are quasiparticles obeying the new statistics. We also calculate the relaxation time of a nuclear spin in a metal using the modified golden rule.Comment: version accepted for publication in J. of Stat. Phy

Re-equilibration after quenches in athermal martensites:Conversion-delays for vapour to liquid domain-wall phases

Entropy barriers and ageing states appear in martensitic structural-transition models, slowly re-equilibrating after temperature quenches, under Monte Carlo dynamics. Concepts from protein folding and ageing harmonic oscillators turn out to be useful in understanding these nonequilibrium evolutions. We show how the athermal, non-activated delay time for seeded parent-phase austenite to convert to product-phase martensite, arises from an identified entropy barrier in Fourier space. In an ageing state of low Monte Carlo acceptances, the strain structure factor makes constant-energy searches for rare pathways, to enter a Brillouin zone `golf hole' enclosing negative energy states, and to suddenly release entropically trapped stresses. In this context, a stress-dependent effective temperature can be defined, that re-equilibrates to the quenched bath temperature.Comment: 11 pages, 12 figures. Under process with Phys. Rev. B (2015

Ground state fluctuations in finite Fermi and Bose systems

We consider a small and fixed number of fermions (bosons) in a trap. The ground state of the system is defined at T=0. For a given excitation energy, there are several ways of exciting the particles from this ground state. We formulate a method for calculating the number fluctuation in the ground state using microcanonical counting, and implement it for small systems of noninteracting fermions as well as bosons in harmonic confinement. This exact calculation for fluctuation, when compared with canonical ensemble averaging, gives considerably different results, specially for fermions. This difference is expected to persist at low excitation even when the fermion number in the trap is large.Comment: 20 pages (including 1 appendix), 3 postscript figures. An error was found in one section of the paper. The corrected version is updated on Sep/05/200

End wall flows in rotors and stators of a single stage compressor

A computer code for solving the parabolized Navier-Stokes equations for internal flows was developed. Oscillations that develop in the calculation procedure are discussed. The measurements made in the hub and annulus wall boundary layers are summarized. The flow in the hub wall boundary layer, starting ahead of the inlet guide vanes to the inlet of the rotor is traced

Magnetic phenomena at and near nu =1/2 and 1/4: theory, experiment and interpretation

I show that the hamiltonian theory of Composite Fermions (CF) is capable of yielding a unified description in fair agreement with recent experiments on polarization P and relaxation rate 1/T_1 in quantum Hall states at filling nu = p/(2ps+1), at and near nu = 1/2 and 1/4, at zero and nonzero temperatures. I show how rotational invariance and two dimensionality can make the underlying interacting theory behave like a free one in a limited context.Comment: Latex 4 pages, 2 figure

Cold atoms at unitarity and inverse square interaction

Consider two identical atoms in a spherical harmonic oscillator interacting with a zero-range interaction which is tuned to produce an s-wave zero-energy bound state. The quantum spectrum of the system is known to be exactly solvable. We note that the same partial wave quantum spectrum is obtained by the one-dimensional scale-invariant inverse square potential. Long known as the Calogero-Sutherland-Moser (CSM) model, it leads to Fractional Exclusion Statistics (FES) of Haldane and Wu. The statistical parameter is deduced from the analytically calculated second virial coefficient. When FES is applied to a Fermi gas at unitarity, it gives good agreement with experimental data without the use of any free parameter.Comment: 11 pages, 3 figures, To appear in J. Phys. B. Atomic, Molecular and Optical Physic