P. Szépfalusy

Multifractal spectra of multi-affine functions

Self-affine functions F(x) with multiscaling height correlations cq(x) ∼xqHq are described in terms of the standard multifractal formalism with a modified assumption for the partition. The corresponding quantities and expressions are shown to exhibit some characteristic differences from the standard ones. According to our calculations the f(α) type spectra are not uniquely determined by the Hq spectrum, but depend on the particular choice which is made for the dependence of N on x, where N is the number of points over which the average is taken. Our results are expected to be relevant in the analysis of signal type data obtained in experiments on systems with an underlying multiplicative process.

Hydrodynamic excitations of Bose Condensates in anisotropic traps

The collective excitations of Bose condensates in anisotropic axially symmetric harmonic traps are investigated in the hydrodynamic and Thomas-Fermi limit. We identify an additional conserved quantity, besides the axial angular momentum and the total energy, and separate the wave equation in elliptic coordinates. The solution is thereby reduced to the algebraic problem of diagonalizing finite dimensional matrices. The classical quasi-particle dynamics in the local density approximation for energies of the order of the chemical potential is shown to be chaotic.

Hydrodynamics of an n-component phonon system

The dynamic properties of an n-component phonon system in d dimensions, which serves as a model for a structural phase transition of second order, are investigated. The symmetry group of the hamiltonian is the group of orthogonal transformations O(n). For n ≥ 2 a continuous symmetry is broken for T Tc. In the ordered phase we find 2 (n − 1) propagating modes with linear dispersion and quadratic damping. Formally the hydrodynamics is similar in the isotropic Heisenberg ferromagnet (n = 2) or the isotropic antiferromagnet (n ≥ 3). The relaxing modes for T < Tc require special care. We study the critical dynamics by means of the dynamical scaling hypothesis and by a mode-coupling calculation, both of which give the critical dynamical exponent z = 12d. The results are compared with the 1/n expansion. It is shown that for large n there is a non-asymptotic region characterized by an effective exponent z = φ/2ν, where φ is the crossover exponent for a uniaxial perturbation, and ν the critical exponent of the correlation length.

Mapping the boundary of the first order finite temperature restoration of chiral symmetry in the (mπ-mK)-plane with a linear sigma model

The phase diagram of the three-flavor QCD is mapped out in the low mass corner of the (

Shifts and widths of collective excitations in trapped Bose gases determined by the dielectric formalism

{m}_{\ensuremath{\pi}}\ensuremath{-}{m}_{K}

Conserving and gapless model of the weakly interacting Bose gas

)-plane with help of the

Dynamic critical exponent of a Bose system to O(1/n)

S{U}_{L}(3)\ifmmode\times\else\texttimes\fi{}S{U}_{R}(3)

Finite-temperature excitations of Bose gases in anisotropic traps

linear sigma model (

Diffusion in Normal and Critical Transient Chaos

L\ensuremath{\sigma}M

Phases of a polar spin-1 Bose gas in a magnetic field

). A novel zero temperature parametrization is proposed for the mass dependence of the couplings away from the physical point based on the three-flavor chiral perturbation theory (U(3) ChPT). One-loop thermodynamics is constructed by applying optimized perturbation theory. The unknown dependence of the scalar spectra on the pseudoscalar masses limits the accuracy of the predictions. Results are compared to lattice data and similar investigations with other variants of effective chiral models. The critical value of the pion mass is below 65 MeV for all