172 research outputs found
Flat coordinates and dilaton fields for three--dimensional conformal sigma models
Riemannian coordinates for flat metrics corresponding to three--dimensional
conformal Poisson--Lie T--dualizable sigma models are found by solving partial
differential equations that follow from the transformations of the connection
components. They are then used for finding general forms of the dilaton fields
satisfying the vanishing beta equations of the sigma models.Comment: 16 pages, no figure
Nucleation Rate of Hadron Bubbles in Baryon-Free Quark-Gluon Plasma
We evaluate the factor appearing in Langer's expression for the
nucleation rate extended to the case of hadron bubbles forming in zero baryon
number cooled quark-gluon plasma. We consider both the absence and presence of
viscosity and show that viscous effects introduce only small changes in the
value of Comment: 9 pages, revtex, no figures Full postscript version available at via
the WWW at http://nucth.physics.wisc.edu/preprints/ or by via from
ftp://nucth.physics.wisc.edu/pub/preprints/mad-nt-95-06.p
Relic Gravitational Waves and Their Detection
The range of expected amplitudes and spectral slopes of relic (squeezed)
gravitational waves, predicted by theory and partially supported by
observations, is within the reach of sensitive gravity-wave detectors. In the
most favorable case, the detection of relic gravitational waves can be achieved
by the cross-correlation of outputs of the initial laser interferometers in
LIGO, VIRGO, GEO600. In the more realistic case, the sensitivity of advanced
ground-based and space-based laser interferometers will be needed. The specific
statistical signature of relic gravitational waves, associated with the
phenomenon of squeezing, is a potential reserve for further improvement of the
signal to noise ratio.Comment: 25 pages, 9 figures included, revtex. Based on a talk given at
"Gyros, Clocks, and Interferometers: Testing General Relativity in Space"
(Germany, August 99
Is the mean-field approximation so bad? A simple generalization yelding realistic critical indices for 3D Ising-class systems
Modification of the renormalization-group approach, invoking Stratonovich
transformation at each step, is proposed to describe phase transitions in 3D
Ising-class systems. The proposed method is closely related to the mean-field
approximation. The low-order scheme works well for a wide thermal range, is
consistent with a scaling hypothesis and predicts very reasonable values of
critical indices.Comment: 4 page
The Hydrodynamics of M-Theory
We consider the low energy limit of a stack of N M-branes at finite
temperature. In this limit, the M-branes are well described, via the AdS/CFT
correspondence, in terms of classical solutions to the eleven dimensional
supergravity equations of motion. We calculate Minkowski space two-point
functions on these M-branes in the long-distance, low-frequency limit, i.e. the
hydrodynamic limit, using the prescription of Son and Starinets
[hep-th/0205051]. From these Green's functions for the R-currents and for
components of the stress-energy tensor, we extract two kinds of diffusion
constant and a viscosity. The N dependence of these physical quantities may
help lead to a better understanding of M-branes.Comment: 1+19 pages, references added, section 5 clarified, eq. (72) correcte
String Indexing for Patterns with Wildcards
We consider the problem of indexing a string of length to report the
occurrences of a query pattern containing characters and wildcards.
Let be the number of occurrences of in , and the size of
the alphabet. We obtain the following results.
- A linear space index with query time .
This significantly improves the previously best known linear space index by Lam
et al. [ISAAC 2007], which requires query time in the worst case.
- An index with query time using space , where is the maximum number of wildcards allowed in the pattern.
This is the first non-trivial bound with this query time.
- A time-space trade-off, generalizing the index by Cole et al. [STOC 2004].
We also show that these indexes can be generalized to allow variable length
gaps in the pattern. Our results are obtained using a novel combination of
well-known and new techniques, which could be of independent interest
Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation
A method is proposed for a self-consistent evaluation of the coupling
constant in the Gross-Pitaevskii equation without involving a pseudopotential
replacement. A renormalization of the coupling constant occurs due to medium
effects and the trapping potential, e.g. in quasi-1D or quasi-2D systems. It is
shown that a simplified version of the Hartree-Fock-Bogoliubov approximation
leads to a variational problem for both the condensate and a two-body wave
function describing the behaviour of a pair of bosons in the Bose-Einstein
condensate. The resulting coupled equations are free of unphysical divergences.
Particular cases of this scheme that admit analytical estimations are
considered and compared to the literature. In addition to the well-known cases
of low-dimensional trapping, cross-over regimes can be studied. The values of
the kinetic, interaction, external, and release energies in low dimensions are
also evaluated and contributions due to short-range correlations are found to
be substantial.Comment: 15 pages, ReVTEX, no figure
Vortex states in binary mixture of Bose-Einstein condensates
The vortex configurations in the Bose-Einstein condensate of the mixture of
two different spin states |F=1,m_f=-1> and |2,1> of ^{87}Rb atoms corresponding
to the recent experiments by Matthews et. al. (Phys. Rev. Lett. 83, 2498
(1999)) are considered in the framework of the Thomas-Fermi approximation as
functions of N_2/N_1, where N_1 is the number of atoms in the state |1,-1> and
N_2 - in the state |2,1>. It is shown that for nonrotating condensates the
configuration with the |1,-1> fluid forming the shell about the |2,1> fluid
(configuration "a") has lower energy than the opposite configuration
(configuration "b") for all values of N_2/N_1. When the |1,-1> fluid has net
angular momentum and forms an equatorial ring around the resting central
condensate |2,1>, the total energy of the system is higher than the ground
energy, but the configuration "a" has lower energy than the configuration "b"
for all N_2/N_1. On the other hand, when the |2> fluid has the net angular
momentum, for the lowest value of the angular momentum \hbar l (l=1) there is
the range of the ratio N_2/N_1 where the configuration "b" has lower energy
than the configuration "a". For higher values of the angular momentum the
configuration "b" is stable for all values of N_2/N_1.Comment: minor changes, references adde
Landau-Khalatnikov two-fluid hydrodynamics of a trapped Bose gas
Starting from the quantum kinetic equation for the non-condensate atoms and
the generalized Gross-Pitaevskii equation for the condensate, we derive the
two-fluid hydrodynamic equations of a trapped Bose gas at finite temperatures.
We follow the standard Chapman-Enskog procedure, starting from a solution of
the kinetic equation corresponding to the complete local equilibrium between
the condensate and the non-condensate components. Our hydrodynamic equations
are shown to reduce to a form identical to the well-known Landau-Khalatnikov
two-fluid equations, with hydrodynamic damping due to the deviation from local
equilibrium. The deviation from local equilibrium within the thermal cloud
gives rise to dissipation associated with shear viscosity and thermal
conduction. In addition, we show that effects due to the deviation from the
diffusive local equilibrium between the condensate and the non-condensate
(recently considered by Zaremba, Nikuni and Griffin) can be described by four
frequency-dependent second viscosity transport coefficients. We also derive
explicit formulas for all the transport coefficients. These results are used to
introduce two new characteristic relaxation times associated with hydrodynamic
damping. These relaxation times give the rate at which local equilibrium is
reached and hence determine whether one is in the two-fluid hydrodynamic
region.Comment: 26 pages, 3 postscript figures, submitted to PR
Quantum correction to the Kubo formula in closed mesoscopic systems
We study the energy dissipation rate in a mesoscopic system described by the
parametrically-driven random-matrix Hamiltonian H[\phi(t)] for the case of
linear bias \phi=vt. Evolution of the field \phi(t) causes interlevel
transitions leading to energy pumping, and also smears the discrete spectrum of
the Hamiltonian. For sufficiently fast perturbation this smearing exceeds the
mean level spacing and the dissipation rate is given by the Kubo formula. We
calculate the quantum correction to the Kubo result that reveals the original
discreteness of the energy spectrum. The first correction to the system
viscosity scales proportional to v^{-2/3} in the orthogonal case and vanishes
in the unitary case.Comment: 4 pages, 3 eps figures, REVTeX
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