6,248 research outputs found
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 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
On Distributed Power Control for Uncoordinated Dual Energy Harvesting Links: Performance Bounds and Near-Optimal Policies
In this paper, we consider a point-to-point link between an energy harvesting
transmitter and receiver, where neither node has the information about the
battery state or energy availability at the other node. We consider a model
where data is successfully delivered only in slots where both nodes are active.
Energy loss occurs whenever one node turns on while the other node is in sleep
mode. In each slot, based on their own energy availability, the transmitter and
receiver need to independently decide whether or not to turn on, with the aim
of maximizing the long-term time-average throughput. We present an upper bound
on the throughput achievable by analyzing a genie-aided system that has
noncausal knowledge of the energy arrivals at both the nodes. Next, we propose
an online policy requiring an occasional one-bit feedback whose throughput is
within one bit of the upper bound, asymptotically in the battery size. In order
to further reduce the feedback required, we propose a time-dilated version of
the online policy. As the time dilation gets large, this policy does not
require any feedback and achieves the upper bound asymptotically in the battery
size. Inspired by this, we also propose a near-optimal fully uncoordinated
policy. We use Monte Carlo simulations to validate our theoretical results and
illustrate the performance of the proposed policies.Comment: 8 page
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
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
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