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The Problems of Rural Reindustrialization: A Case Study of Monroe, Massachusetts
Owing to the departure of the mill industry from rural New England, many small towns have suffered erosion of their economic base. These towns and villages face a declining population, vacant mills, and an aging work force. Monroe, Massachusetts, is an example of the problems of rural reindustrialization. This article concludes that state intervention is required for the restoration of productivity
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Contains reports on three research projects.Lincoln Laboratory (Purchase Order DDL-B187)United States Department of the ArmyUnited States Department of the NavyUnited States Department of the Air Force (Contract AF19(122)-458
Exclusion Statistics in a two-dimensional trapped Bose gas
We briefly explain the notion of exclusion statistics and in particular
discuss the concept of an ideal exclusion statistics gas. We then review a
recent work where it is demonstrated that a {\em two-dimensional} Bose gas with
repulsive delta function interactions obeys ideal exclusion statistics, with a
fractional parameter related to the interaction strength.Comment: 10 pages, RevTeX. Proceedings of the Salerno workshop "Theory of
Quantum Gases and Quantum Coherence", to appear in a special issue of J.Phys.
B, Dec. 200
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
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
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
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
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.
Transverse spin dynamics in a spin-polarized Fermi liquid
The linear equations for transverse spin dynamics in weakly polarised
degenerate Fermi liquid with arbitrary relationship between temperature and
polarization are derived from Landau-Silin phenomenological kinetic equation
with general form of two-particle collision integral. The temperature and
polarization dependence of the spin current relaxation time is established. It
is found in particular that at finite polarization transverse spin wave damping
has a finite value at T=0. The analogy between temperature dependences of spin
waves attenuation and ultrasound absorption in degenerate Fermi liquid at
arbitrary temperature is presented. We also discuss spin-polarized Fermi liquid
in the general context of the Fermi-liquid theory and compare it with "Fermi
liquid" with spontaneous magnetization.Comment: 10 page
Bose-Einstein condensation in a two-dimensional, trapped,interacting gas
We study Bose-Einstein condensation phenomenon in a two-dimensional (2D)
system of bosons subjected to an harmonic oscillator type confining potential.
The interaction among the 2D bosons is described by a delta-function in
configuration space. Solving the Gross-Pitaevskii equation within the two-fluid
model we calculate the condensate fraction, ground state energy, and specific
heat of the system. Our results indicate that interacting bosons have similar
behavior to those of an ideal system for weak interactions.Comment: LaTeX, 4 pages, 4 figures, uses grafik.sty (included), to be
published in Phys. Rev. A, tentatively scheduled for 1 October 1998 (Volume
58, Number 4
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