11,865 research outputs found
Ground States for Diffusion Dominated Free Energies with Logarithmic Interaction
Replacing linear diffusion by a degenerate diffusion of porous medium type is
known to regularize the classical two-dimensional parabolic-elliptic
Keller-Segel model. The implications of nonlinear diffusion are that solutions
exist globally and are uniformly bounded in time. We analyse the stationary
case showing the existence of a unique, up to translation, global minimizer of
the associated free energy. Furthermore, we prove that this global minimizer is
a radially decreasing compactly supported continuous density function which is
smooth inside its support, and it is characterized as the unique compactly
supported stationary state of the evolution model. This unique profile is the
clear candidate to describe the long time asymptotics of the diffusion
dominated classical Keller-Segel model for general initial data.Comment: 30 pages, 2 figure
Nonuniversal Effects in the Homogeneous Bose Gas
Effective field theory predicts that the leading nonuniversal effects in the
homogeneous Bose gas arise from the effective range for S-wave scattering and
from an effective three-body contact interaction. We calculate the leading
nonuniversal contributions to the energy density and condensate fraction and
compare the predictions with results from diffusion Monte Carlo calculations by
Giorgini, Boronat, and Casulleras. We give a crude determination of the
strength of the three-body contact interaction for various model potentials.
Accurate determinations could be obtained from diffusion Monte Carlo
calculations of the energy density with higher statistics.Comment: 24 pages, RevTex, 5 ps figures, included with epsf.te
Nonuniversal Effects in the Homogeneous Bose Gas
Effective field theory predicts that the leading nonuniversal effects in the
homogeneous Bose gas arise from the effective range for S-wave scattering and
from an effective three-body contact interaction. We calculate the leading
nonuniversal contributions to the energy density and condensate fraction and
compare the predictions with results from diffusion Monte Carlo calculations by
Giorgini, Boronat, and Casulleras. We give a crude determination of the
strength of the three-body contact interaction for various model potentials.
Accurate determinations could be obtained from diffusion Monte Carlo
calculations of the energy density with higher statistics.Comment: 24 pages, RevTex, 5 ps figures, included with epsf.te
Spin-charge coupling in quantum wires at zero magnetic field
We discuss an approximation for the dynamic charge response of nonlinear
spin-1/2 Luttinger liquids in the limit of small momentum. Besides accounting
for the broadening of the charge peak due to two-holon excitations, the
nonlinearity of the dispersion gives rise to a two-spinon peak, which at zero
temperature has an asymmetric line shape. At finite temperature the spin peak
is broadened by diffusion. As an application, we discuss the density and
temperature dependence of the Coulomb drag resistivity due to long-wavelength
scattering between quantum wires.Comment: 16 pages, 5 figures. This is an extended version of "Coulomb drag
from spin-charge coupling at zero magnetic field
Dissipative dynamics of a kink state in a Bose-condensed gas
We develop a theory of dissipative dynamics of a kink state in a
finite-temperature Bose-condensed gas. We find that due to the interaction with
the thermal cloud the kink state accelerates towards the velocity of sound and
continuously transforms to the ground-state condensate. We calculate the
life-time of a kink state in a trapped gas and discuss possible experimental
implications.Comment: 4 pages, RevTe
Models of the Knee in the Energy Spectrum of Cosmic Rays
The origin of the knee in the energy spectrum of cosmic rays is an
outstanding problem in astroparticle physics. Numerous mechanisms have been
proposed to explain the structure in the all-particle spectrum. In the article
basic ideas of several models are summarized, including diffusive acceleration
of cosmic rays in shock fronts, acceleration via cannonballs, leakage from the
Galaxy, interactions with background particles in the interstellar medium, as
well as new high-energy interactions in the atmosphere. The calculated energy
spectra and mean logarithmic masses are compiled and compared to results from
direct and indirect measurements.Comment: 30 pages, 20 figures accepted by Astroparticle Physics captions of
figures 1-3 clarified, references adde
Biexcitons in two-dimensional systems with spatially separated electrons and holes
The binding energy and wavefunctions of two-dimensional indirect biexcitons
are studied analytically and numerically. It is proven that stable biexcitons
exist only when the distance between electron and hole layers is smaller than a
certain critical threshold. Numerical results for the biexciton binding
energies are obtained using the stochastic variational method and compared with
the analytical asymptotics. The threshold interlayer separation and its
uncertainty are estimated. The results are compared with those obtained by
other techniques, in particular, the diffusion Monte-Carlo method and the
Born-Oppenheimer approximation.Comment: 11 pages, 7 figure
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