Thermodynamics of soft wall model of AdS/QCD in Einstein-Maxwell-Gauss-Bonnet Gravity

We investigate the thermodynamics of confinement/deconfinement transition in soft wall model of QCD with Gauss-Bonnet corrections using AdS/CFT correspondence. In bulk AdS space-time the transition is geometric and is known as Hawking-Page transition. The Hawking-Page transition between two geometries, namely charged AdS black hole and thermally charged AdS have been studied with Gauss-Bonnet corrections up-to first order. The Gauss-Bonnet coupling modifies the transition temperature of the system, but qualitative features remain unchanged. We obtain the curves between chemical potential and transition temperature for different values of Gauss-Bonnet couplings. We find that there exist a point in μ-T plane where lines with different value of Gauss-Bonnet coupling cross each other. This point may be the onset of the transition from first order to cross over behavior. The results are compared with that of the hard wall model.

The Dynamics of Digits: Calculating Pi with Galperin’s Billiards

In Galperin billiards, two balls colliding with a hard wall form an analog calculator for the digits of the number π . This classical, one-dimensional three-body system (counting the hard wall) calculates the digits of π in a base determined by the ratio of the masses of the two particles. This base can be any integer, but it can also be an irrational number, or even the base can be π itself. This article reviews previous results for Galperin billiards and then pushes these results farther. We provide a complete explicit solution for the balls’ positions and velocities as a function of the collision number and time. We demonstrate that Galperin billiard can be mapped onto a two-particle Calogero-type model. We identify a second dynamical invariant for any mass ratio that provides integrability for the system, and for a sequence of specific mass ratios we identify a third dynamical invariant that establishes superintegrability. Integrability allows us to derive some new exact results for trajectories, and we apply these solutions to analyze the systematic errors that occur in calculating the digits of π with Galperin billiards, including curious cases with irrational number bases.

On the effects of rotation and violation of the Lorentz symmetry on the scalar field

We deal with the effects of rotation and violation of the Lorentz symmetry on the scalar field from a geometrical point of view. By choosing a fixed spacelike four-vector and a fixed timelike four-vector, we obtain two modified line elements for the Minkowski space–time. In addition, we consider a uniformly rotating frame. Then, we analyze how the effects of rotation and violation of the Lorentz symmetry determine the upper limit of the radial coordinate. Further, we analyze the effects of rotation and violation of the Lorentz symmetry on the confinement of the scalar field to a hard-wall confining potential.