Quantitative rigidity of almost maximal volume entropy for both RCD spaces and integral Ricci curvature bound

The volume entropy of a compact metric measure space is known to be the exponential growth rate of the measure lifted to its universal cover at infinity. For a compact Riemannian $n$-manifold with a negative lower Ricci curvature bound and a upper diameter bound, it was known that it admits an almost maximal volume entropy if and only if it is diffeomorphic and Gromov-Hausdorff close to a hyperbolic space form. We prove the quantitative rigidity of almost maximal volume entropy for $\operatorname{RCD}$-spaces with a negative lower Ricci curvature bound and Riemannian manifolds with a negative $L^p$-integral Ricci curvature lower bound.Comment: 21 page

Topological susceptibility in full QCD: lattice results versus the prediction from the QCD partition function with granularity

Recent lattice data from CP-PACS, UKQCD, SESAM/TXL and the Pisa group regarding the quark mass dependence of the topological susceptibility in 2-flavour QCD are compared to each other and to theoretical expectations. The latter get specified by referring to the QCD finite-volume partition function with ``granularity'' which accounts for the entropy brought by instantons and anti-instantons. The chiral condensate in $N_f=2$ QCD, if determined by this method, turns out surprisingly large.Comment: 24 pages, 9 figures containing 21 graphs; v2: modifications to account for the changes in the SESAM/TXL data, otherwise minor alterations, except for 4 new references added; to appear in Nucl. Phys.

Coupling techniques for nonlinear hyperbolic equations. III. The well-balanced approximation of thick interfaces

We continue our analysis of the coupling between nonlinear hyperbolic problems across possibly resonant interfaces. In the first two parts of this series, we introduced a new framework for coupling problems which is based on the so-called thin interface model and uses an augmented formulation and an additional unknown for the interface location; this framework has the advantage of avoiding any explicit modeling of the interface structure. In the present paper, we pursue our investigation of the augmented formulation and we introduce a new coupling framework which is now based on the so-called thick interface model. For scalar nonlinear hyperbolic equations in one space variable, we observe that the Cauchy problem is well-posed. Then, our main achievement in the present paper is the design of a new well-balanced finite volume scheme which is adapted to the thick interface model, together with a proof of its convergence toward the unique entropy solution (for a broad class of nonlinear hyperbolic equations). Due to the presence of a possibly resonant interface, the standard technique based on a total variation estimate does not apply, and DiPerna's uniqueness theorem must be used. Following a method proposed by Coquel and LeFloch, our proof relies on discrete entropy inequalities for the coupling problem and an estimate of the discrete entropy dissipation in the proposed scheme.Comment: 21 page

Path Integral Monte Carlo study of phonons in the bcc phase of 4^4He

Using Path Integral Monte Carlo and the Maximum Entropy method, we calculate the dynamic structure factor of solid $^4$He in the bcc phase at a finite temperature of T = 1.6 K and a molar volume of 21 cm$^3$. Both the single-phonon contribution to the dynamic structure factor and the total dynamic structure factor are evaluated. From the dynamic structure factor, we obtain the phonon dispersion relations along the main crystalline directions, [001], [011] and [111]. We calculate both the longitudinal and transverse phonon branches. For the latter, no previous simulations exist. We discuss the differences between dispersion relations resulting from the single-phonon part vs. the total dynamic structure factor. In addition, we evaluate the formation energy of a vacancy.Comment: 10 figure

Spherical Shell Cosmological Model and Uniformity of Cosmic Microwave Background Radiation

Considered is spherical shell as a model for visible universe and parameters that such model must have to comply with the observable data. The topology of the model requires that motion of all galaxies and light must be confined inside a spherical shell. Consequently the observable universe cannot be defined as a sphere centered on the observer, rather it is an arc length within the volume of the spherical shell. The radius of the shell is 4.46 $\pm$ 0.06 Gpc, which is for factor $\pi$ smaller than radius of a corresponding 3-sphere. However the event horizon, defined as the arc length inside the shell, has the size of 14.0 $\pm$ 0.2 Gpc, which is in agreement with the observable data. The model predicts, without inflation theory, the isotropy and uniformity of the CMB. It predicts the correct value for the Hubble constant $H_0$ = 67.26 $\pm$ 0.90 km/s/Mpc, the cosmic expansion rate $H(z)$, and the speed of the event horizon in agreement with observations. The theoretical suport for shell model comes from general relativity, curvature of space by mass, and from holographic principle. The model explains the reason for the established discrepancy between the non-covariant version of the holographic principle and the calculated dimensionless entropy $(S/k)$ for the visible universe, which exceeds the entropy of a black hole. The model is in accordance with the distribution of radio sources in space, type Ia data, and data from the Hubble Ultra Deep Field optical and near-infrared survey.Comment: 7 pages 2 figures, Conference: Low Dimensional Physics and Gauge Principles, Yerevan, Armenaia, September 21-26, 201