Topological entropy for some isotropic cosmological models

The chaotical dynamics is studied in different Friedmann-Robertson- Walker cosmological models with scalar (inflaton) field and hydrodynamical matter. The topological entropy is calculated for some particular cases. Suggested scheme can be easily generalized for wide class of models. Different methods of calculation of topological entropy are compared.Comment: Final version to appear in Phys. Rev D. Minor changes, typos corrected; 29 pages with 2 eps figure

A generalisation of the Heckmann - Schucking cosmological solution

An exact solution of the Einstein equations for a Bianchi -I universe in the presence of dust, stiff matter and cosmological constant, generalising the well-known Heckmann-Schucking solution is presented. PACS: 04.20-q; 04.20.Dw Keywords: Exact cosmological solutionsComment: LaTeX file, 10 pages. Physics Letters B, to appea

The Equation of State for Cool Relativistic Two-Constituent Superfluid Dynamics

The natural relativistic generalisation of Landau's two constituent superfluid theory can be formulated in terms of a Lagrangian $L$ that is given as a function of the entropy current 4-vector $s^\rho$ and the gradient $\nabla\varphi$ of the superfluid phase scalar. It is shown that in the ``cool" regime, for which the entropy is attributable just to phonons (not rotons), the Lagrangian function $L(\vec s, \nabla\varphi)$ is given by an expression of the form $L=P-3\psi$ where $P$ represents the pressure as a function just of $\nabla\varphi$ in the (isotropic) cold limit. The entropy current dependent contribution $\psi$ represents the generalised pressure of the (non-isotropic) phonon gas, which is obtained as the negative of the corresponding grand potential energy per unit volume, whose explicit form has a simple algebraic dependence on the sound or ``phonon" speed $c_P$ that is determined by the cold pressure function $P$.Comment: 26 pages, RevTeX, no figures, published in Phys. Rev. D. 15 May 199

On Sound Reflection in Superfluid

We consider reflection of the first and the second sound waves by a rigid flat wall in superfluid. Nontrivial dependence of the reflection coefficients on the angle of incidence is obtained. Sound conversion is predicted at slanted incidence.Comment: 9 pages, 4 figure

Astronomical bounds on future big freeze singularity

Recently it was found that dark energy in the form of phantom generalized Chaplygin gas may lead to a new form of the cosmic doomsday, the big freeze singularity. Like the big rip singularity, the big freeze singularity would also take place at a finite future cosmic time, but unlike the big rip singularity it happens for a finite scale factor.Our goal is to test if a universe filled with phantom generalized Chaplygin gas can conform to the data of astronomical observations. We shall see that if the universe is only filled with generalized phantom Chaplygin gas with equation of state $p=-c^2s^2/\rho^{\alpha}$ with $\alpha<-1$, then such a model cannot be matched to the data of astronomical observations. To construct matched models one actually need to add dark matter. This procedure results in cosmological scenarios which do not contradict the data of astronomical observations and allows one to estimate how long we are now from the future big freeze doomsday.Comment: 8 page

Polarization Effects in Superfluid 4^4He

A theory of thermoelectric phenomena in superfluid $^4He$ is developed. It is found an estimation of the dipole moment of helium atom arising due to electron shell deformation caused by pushing forces from the side of its surrounding atoms. The corresponding electric signal generated in a liquid consisting of electrically neutral atoms by the ordinary sound waves is found extremely small. The second sound waves in superfluid $^4He$ generate the polarization of liquid induced by the relative accelerated motion of the superfluid and the normal component. The derived ratio of the amplitudes of temperature and electric polarization potential was proved to be practically temperature independent. Its magnitude is in reasonable correspondence with the experimental observations. The polarity of electric signal is determined by the sign of temperature gradient in accordance with the measurements. The problem of the roton excitations dipole moment is also discussed.Comment: 8 pages, no figure

Longitudinal Scaling of Elliptic Flow in Landau Hydrodynamics

This study presents generalization of the Landau hydrodynamic solution for multiparticle production applied to non-central relativistic heavy ion collisions. Obtained results shows longitudinal scaling of elliptic flow $v_2$ as a function of rapidity shifted by beam rapidity ($y-y_{beam}$) for different energies ($\sqrt{s_{NN}}=62.4$ GeV and 200 GeV) and for different systems (Au-Au and Cu-Cu). It is argued, that the elliptic flow and its longitudinal scaling is due to the initial transverse energy density distribution and initial longitudinal thickness effect.Comment: 7 pages 1 figur

Two-dimensional dilute Bose gas in the normal phase

We consider a two-dimensional dilute Bose gas above its superfluid transition temperature. We show that the t-matrix approximation corresponds to the leading set of diagrams in the dilute limit, provided the temperature is sufficiently larger than the superfluid transition temperature. Within this approximation, we give an explicit expression for the wave vector and frequency dependence of the self-energy, and calculate the corrections to the chemical potential and the effective mass arising from the interaction. We also argue that the breakdown of the t-matrix approximation, which occurs upon lowering the temperature, provides a simple criterion to estimate the superfluid critical temperature for the two-dimensional dilute Bose gas. The critical temperature identified by this criterion coincides with earlier results obtained by Popov and by Fisher and Hohenberg using different methods. Extension of this procedure to the three-dimensional case gives good agreement with recent Monte Carlo data.Comment: 9 pages, 3 Figure

Relativistic Kinetics of Phonon Gas in Superfluids

The relativistic kinetic theory of the phonon gas in superfluids is developed. The technique of the derivation of macroscopic balance equations from microscopic equations of motion for individual particles is applied to an ensemble of quasi-particles. The necessary expressions are constructed in terms of a Hamilton function of a (quasi-)particle. A phonon contribution into superfluid dynamic parameters is obtained from energy-momentum balance equations for the phonon gas together with the conservation law for superfluids as a whole. Relations between dynamic flows being in agreement with results of relativistic hydrodynamic consideration are found. Based on the kinetic approach a problem of relativistic variation of the speed of sound under phonon influence at low temperature is solved.Comment: 23 pages, Revtex fil

Equation of state and initial temperature of quark gluon plasma at RHIC

In gold-gold collisions of the Relativistic Heavy Ion Collider (RHIC) a perfect fluid of quarks, sometimes called the strongly interacting quark gluon plasma (sQGP) is created for an extremely short time. The time evolution of this fluid can be described by hydrodynamical models. After expansion and cooling, the freeze-out happens and hadrons are created. Their distribution reveals information about the final state of the fluid. To investigate the time evolution one needs to analyze penetrating probes, such as direct photon observables. Transverse momentum distributions of low energy direct photons were mesured in 2010 by PHENIX, while azimuthal asymmetry in 2011. These measurements can be compared to hydrodynamics to determine the equation of state and the initial temperature of sQGP. In this paper we analyze an 1+3 dimensional solution of relativistic hydrodynamics. We calculate momentum distribution, azimuthal asymmetry and momentum correlations of direct photons. Based on earlier fits to hadronic spectra, we compare photon calculations to measurements to determine the equation of state and the initial temperature of sQGP. We find that the initial temperature in the center of the fireball is 507+-12 MeV, while for the sound speed we get a speed of sound of 0.36+-0.02. We also estimate a systematic error of these results. We find that the measured azimuthal asymmetry is also not incompatible with this model, and predict a photon source that is significantly larger in the out direction than in the side direction.Comment: 12 pages, 4 figures. This work was supported by the OTKA grant NK-73143 and NK-101438 and M. Csanad's Bolyai scholarshi