The scalar-isoscalar spectral function of strong matter in a large N approximation

The enhancement of the scalar-isoscalar spectral function near the two-pion threshold is studied in the framework of an effective linear $\sigma$ model, using a large N approximation in the number of the Goldstone bosons. The effect is rather insensitive to the detailed T=0 characteristics of the $\sigma$ pole, it is accounted by a pole moving with increasing $T$ along the real axis of the second Riemann sheet towards the threshold location from below.Comment: 5 pages, poster presented at SEWM2002, Heidelberg, October 200

Finite temperature spectral function of the σ\sigma meson from large N expansion

The spectral function of the scalar-isoscalar channel of the O(N) symmetric linear $\sigma$ model is studied in the broken symmetry phase. The investigation is based on the leading order evaluation of the self-energy in the limit of large number of Goldstone bosons. We describe its temperature dependent variation in the whole low temperature phase. This variation closely reflects the trajectory of the scalar-isoscalar quasiparticle pole. In the model with no explicit chiral symmetry breaking we have studied near the critical point also the corresponding dynamical exponent.Comment: 9 pages, 3 figures. To be published in Proc. of Budapest'02 Workshop on Quark and Hadron Dynamics, Budapest, Hungary, March 3--7, 200

Analytic determination of the T-\mu phase diagram of the chiral quark model

Using a gap equation for the pion mass a nonperturbative method is given for solving the chiral quark-meson model in the chiral limit at the lowest order in the fermion contributions encountered in a large N_f approximation. The location of the tricritical point is analytically determined. A mean field potential is constructed from which critical exponents can be obtained.Comment: 8 pages, 2 figures. To be published in Proc.of Budapest'04 Workshop on Hot and Dense Matter in Relativistic Heavy Ion Physics, Budapest, Hungary, March 24-27, 200

Energies And Damping Rates of Elementary Excitations in Spin-1 Bose-einstein-condensed Gases

The finite temperature Green's function technique is used to calculate the energies and damping rates of the elementary excitations of homogeneous, dilute, spin-1 Bose gases below the Bose-Einstein condensation temperature in both the density and spin channels. For this purpose a self-consistent dynamical Hartree-Fock model is formulated, which takes into account the direct and exchange processes on equal footing by summing up certain classes of Feynman diagrams. The model is shown to satisfy the Goldstone theorem and to exhibit the hybridization of one-particle and collective excitations correctly. The results are applied to gases of Na-23 and Rb-87 atoms

Bursts in the Chaotic Trajectory Lifetimes Preceding the Controlled Periodic Motion

The average lifetime ($\tau(H)$) it takes for a randomly started trajectory to land in a small region ($H$) on a chaotic attractor is studied. $\tau(H)$ is an important issue for controlling chaos. We point out that if the region $H$ is visited by a short periodic orbit, the lifetime $\tau(H)$ strongly deviates from the inverse of the naturally invariant measure contained within that region ($\mu_N(H)^{-1}$). We introduce the formula that relates $\tau(H)/\mu_N(H)^{-1}$ to the expanding eigenvalue of the short periodic orbit visiting $H$.Comment: Accepted for publication in Phys. Rev. E, 3 PS figure

Damping of low-energy excitations of a trapped Bose condensate at finite temperatures

We present the theory of damping of low-energy excitations of a trapped Bose condensate at finite temperatures, where the damping is provided by the interaction of these excitations with the thermal excitations. We emphasize the key role of stochastization in the behavior of the thermal excitations for damping in non-spherical traps. The damping rates of the lowest excitations, following from our theory, are in fair agreement with the data of recent JILA and MIT experiments. The damping of quasiclassical excitations is determined by the condensate boundary region, and the result for the damping rate is drastically different from that in a spatially homogeneous gas.Comment: 10 pages RevTeX, correction of the misprints and addition of the sentence clarifying the result for quasiclassical excitationscorrection of the misprints and addition of the sentence clarifying the result for quasiclassical excitation

Finite Temperature Perturbation Theory for a Spatially Inhomogeneous Bose-condensed Gas

We develop a finite temperature perturbation theory (beyond the mean field) for a Bose-condensed gas and calculate temperature-dependent damping rates and energy shifts for Bogolyubov excitations of any energy. The theory is generalized for the case of excitations in a spatially inhomogeneous (trapped) Bose-condensed gas, where we emphasize the principal importance of inhomogeneouty of the condensate density profile and develop the method of calculating the self-energy functions. The use of the theory is demonstrated by calculating the damping rates and energy shifts of low-energy quasiclassical excitations, i.e. the quasiclassical excitations with energies much smaller than the mean field interaction between particles. In this case the boundary region of the condensate plays a crucial role, and the result for the damping rates and energy shifts is completely different from that in spatially homogeneous gases. We also analyze the frequency shifts and damping of sound waves in cylindrical Bose condensates and discuss the role of damping in the recent MIT experiment on the sound propagation.Comment: 16 pages, 3 figures, Revtex, uses epsfi

Complexity Characterization in a Probabilistic Approach to Dynamical Systems Through Information Geometry and Inductive Inference

Information geometric techniques and inductive inference methods hold great promise for solving computational problems of interest in classical and quantum physics, especially with regard to complexity characterization of dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this article, we investigate the possibility of describing the macroscopic behavior of complex systems in terms of the underlying statistical structure of their microscopic degrees of freedom by use of statistical inductive inference and information geometry. We review the Maximum Relative Entropy (MrE) formalism and the theoretical structure of the information geometrodynamical approach to chaos (IGAC) on statistical manifolds. Special focus is devoted to the description of the roles played by the sectional curvature, the Jacobi field intensity and the information geometrodynamical entropy (IGE). These quantities serve as powerful information geometric complexity measures of information-constrained dynamics associated with arbitrary chaotic and regular systems defined on the statistical manifold. Finally, the application of such information geometric techniques to several theoretical models are presented.Comment: 29 page

Chaotic Scattering Theory, Thermodynamic Formalism, and Transport Coefficients

The foundations of the chaotic scattering theory for transport and reaction-rate coefficients for classical many-body systems are considered here in some detail. The thermodynamic formalism of Sinai, Bowen, and Ruelle is employed to obtain an expression for the escape-rate for a phase space trajectory to leave a finite open region of phase space for the first time. This expression relates the escape rate to the difference between the sum of the positive Lyapunov exponents and the K-S entropy for the fractal set of trajectories which are trapped forever in the open region. This result is well known for systems of a few degrees of freedom and is here extended to systems of many degrees of freedom. The formalism is applied to smooth hyperbolic systems, to cellular-automata lattice gases, and to hard sphere sytems. In the latter case, the goemetric constructions of Sinai {\it et al} for billiard systems are used to describe the relevant chaotic scattering phenomena. Some applications of this formalism to non-hyperbolic systems are also discussed.Comment: 35 pages, compressed file, follow directions in header for ps file. Figures are available on request from [email protected]