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 $\kappa$ 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 $\kappa$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 $t$ of length $n$ to report the occurrences of a query pattern $p$ containing $m$ characters and $j$ wildcards. Let $occ$ be the number of occurrences of $p$ in $t$, and $\sigma$ the size of the alphabet. We obtain the following results. - A linear space index with query time $O(m+\sigma^j \log \log n + occ)$. This significantly improves the previously best known linear space index by Lam et al. [ISAAC 2007], which requires query time $\Theta(jn)$ in the worst case. - An index with query time $O(m+j+occ)$ using space $O(\sigma^{k^2} n \log^k \log n)$, where $k$ 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