Evaluation of specific heat for superfluid helium between 0 - 2.1 K based on nonlinear theory

The specific heat of liquid helium was calculated theoretically in the Landau theory. The results deviate from experimental data in the temperature region of 1.3 - 2.1 K. Many theorists subsequently improved the results of the Landau theory by applying temperature dependence of the elementary excitation energy. As well known, many-body system has a total energy of Galilean covariant form. Therefore, the total energy of liquid helium has a nonlinear form for the number distribution function. The function form can be determined using the excitation energy at zero temperature and the latent heat per helium atom at zero temperature. The nonlinear form produces new temperature dependence for the excitation energy from Bose condensate. We evaluate the specific heat using iteration method. The calculation results of the second iteration show good agreement with the experimental data in the temperature region of 0 - 2.1 K, where we have only used the elementary excitation energy at 1.1 K.Comment: 6 pages, 3 figures, submitted to Journal of Physics: Conference Serie

The alphaalphas2alpha alpha_s^2 corrections to the first moment of the polarized virtual photon structure function g1gamma(x,Q2,P2)g_1^gamma(x,Q^2,P^2)

We present the next-to-next-to-leading order ($alpha alpha_s^2$) corrections to the first moment of the polarized virtual photon structure function $g_1^gamma(x,Q^2,P^2)$ in the kinematical region $Lambda^2 ll P^2 ll Q^2$, where $-Q^2(-P^2)$ is the mass squared of the probe (target) photon and $Lambda$ is the QCD scale parameter. In order to evaluate the three-loop-level photon matrix element of the flavor singlet axial current, we resort to the Adler-Bardeen theorem for the axial anomaly and we calculate in effect the two-loop diagrams for the photon matrix element of the gluon operator. The $alpha alpha_s^2$ corrections are found to be about 3% of the sum of the leading order ($alpha$) andthe next-to-leading order ($alpha alpha_s$) contributions, when $Q^2=30 sim 100 {rm GeV}^2$and $P^2=3{rm GeV}^2$, and the number of active quark flavors $n_f$ is three to five.Comment: 21 page

A Calculation of Baryon Diffusion Constant in Hot and Dense Hadronic Matter Based on an Event Generator URASiMA

We evaluate thermodynamical quantities and transport coefficients of a dense and hot hadronic matter based on an event generator URASiMA (Ultra-Relativistic AA collision Simulator based on Multiple Scattering Algorithm). The statistical ensembles in equilibrium with fixed temperature and chemical potential are generated by imposing periodic boundary condition to the simulation of URASiMA, where energy density and baryon number density is conserved. Achievement of the thermal equilibrium and the chemical equilibrium are confirmed by the common value of slope parameter in the energy distributions and the saturation of the numbers of contained particles, respectively. By using the generated ensembles, we investigate the temperature dependence and the chemical potential dependence of the baryon diffusion constant of a dense and hot hadronic matter.Comment: 15 pages, 5 figures, LaTeX2

Chaos in temperature in the Sherrington-Kirkpatrick model

We prove the existence of chaos in temperature in the Sherringhton-Kirkpatrick model. The effect is exceedingly small, namely of the ninth order in perturbation theory. The equations describing two systems at different temperatures constrained to have a fixed overlap are studied analytically and numerically, yielding information about the behaviour of the overlap distribution function $P_{T_1,T_2}(q)$ in finite-size systems.Comment: REVTEX, 6 pages, 2 figure

Calculating the mass fraction of primordial black holes

We reinspect the calculation for the mass fraction of primordial black holes (PBHs) which are formed from primordial perturbations, finding that performing the calculation using the comoving curvature perturbation c in the standard way vastly overestimates the number of PBHs, by many orders of magnitude. This is because PBHs form shortly after horizon entry, meaning modes significantly larger than the PBH are unobservable and should not affect whether a PBH forms or not - this important effect is not taken into account by smoothing the distribution in the standard fashion. We discuss alternative methods and argue that the density contrast, Δ, should be used instead as super-horizon modes are damped by a factor k2. We make a comparison between using a Press-Schechter approach and peaks theory, finding that the two are in close agreement in the region of interest. We also investigate the effect of varying the spectral index, and the running of the spectral index, on the abundance of primordial black holes

Target Mass Corrections for the Virtual Photon Structure Functions to the Next-to-next-to-leading Order in QCD

We investigate target mass effects in the unpolarized virtual photon structure functions $F_2^\gamma(x,Q^2,P^2)$ and $F_L^\gamma(x,Q^2,P^2)$ in perturbative QCD for the kinematical region $\Lambda^2 \ll P^2 \ll Q^2$, where $-Q^2(-P^2)$ is the mass squared of the probe (target) photon and $\Lambda$ is the QCD scale parameter. We obtain the Nachtmann moments for the structure functions and then, by inverting the moments, we get the expressions in closed form for $F_2^\gamma(x,Q^2,P^2)$ up to the next-to-next-to-leading order and for $F_L^\gamma(x,Q^2,P^2)$ up to the next-to-leading order, both of which include the target mass corrections. Numerical analysis exhibits that target mass effects appear at large $x$ and become sizable near $x_{\rm max}(=1/(1+\frac{P^2}{Q^2}))$, the maximal value of $x$, as the ratio $P^2/Q^2$ increases.Comment: 24 pages, LaTeX, 7 eps figures, REVTeX