Effect of realistic interatomic interactions and two-body correlation on the heat capacity of a trapped BEC

An approximate many-body theory has been used to calculate the heat capacity and the condensate fraction of a BEC with effective repulsive interaction. The effect of interactions has been analyzed and compared with the non-interacting case. It has been found that the repulsive interaction lowers the critical temperature from the value found in the non-interacting case. The difference between the critical temperatures increases with the increase in the total number of atoms in the trap.Comment: 15 pages, 5 figure

Quantum Gravity Equation In Schroedinger Form In Minisuperspace Description

We start from classical Hamiltonian constraint of general relativity to obtain the Einstein-Hamiltonian-Jacobi equation. We obtain a time parameter prescription demanding that geometry itself determines the time, not the matter field, such that the time so defined being equivalent to the time that enters into the Schroedinger equation. Without any reference to the Wheeler-DeWitt equation and without invoking the expansion of exponent in WKB wavefunction in powers of Planck mass, we obtain an equation for quantum gravity in Schroedinger form containing time. We restrict ourselves to a minisuperspace description. Unlike matter field equation our equation is equivalent to the Wheeler-DeWitt equation in the sense that our solutions reproduce also the wavefunction of the Wheeler-DeWitt equation provided one evaluates the normalization constant according to the wormhole dominance proposal recently proposed by us.Comment: 11 Pages, ReVTeX, no figur

Self-Gravitational Corrections to the Cardy-Verlinde Formula and the FRW Brane Cosmology in SdS_5 Bulk

The semiclassical corrections to the Cardy-Verlinde entropy of a five-dimensional Schwarzschild de-Sitter black hole (SdS_5) are explicitly evaluated. These corrections are considered within the context of KKW analysis and arise as a result of the self-gravitation effect. In addition, a four-dimensional spacelike brane is considered as the boundary of the SdS_5 bulk background. It is already known that the induced geometry of the brane is exactly given by that of a radiation-dominated FRW universe. By exploiting the CFT/FRW-cosmology relation, we derive the self-gravitational corrections to the first Friedmann-like equation which is the equation of the brane motion. The additional term that arises due to the semiclassical analysis can be viewed as stiff matter where the self-gravitational corrections act as the source for it. This result is contrary to standard analysis that regards the charge of SdS_5 bulk black hole as the source for stiff matter. Furthermore, we rewrite the Friedmann-like equation in a such way that it represents the conservation equation of energy of a point particle moving in a one-dimensional effective potential. The self-gravitational corrections to the effective potential and, consequently, to the point particle's motion are obtained. A short analysis on the asymptotic behavior of the 4-dimensional brane is presented.Comment: 16 pages, LaTeX; (v2) references added and correcte

Time in Quantum Gravity

The Wheeler-DeWitt equation in quantum gravity is timeless in character. In order to discuss quantum to classical transition of the universe, one uses a time prescription in quantum gravity to obtain a time contained description starting from Wheeler-DeWitt equation and WKB ansatz for the WD wavefunction. The approach has some drawbacks. In this work, we obtain the time-contained Schroedinger-Wheeler-DeWitt equation without using the WD equation and the WKB ansatz for the wavefunction. We further show that a Gaussian ansatz for SWD wavefunction is consistent with the Hartle-Hawking or wormhole dominance proposal boundary condition. We thus find an answer to the small scale boundary conditions.Comment: 12 Pages, LaTeX, no figur

Collapse of the charge ordering gap of Nd_{0.5}Sr_{0.5}MnO_{3} in an applied magnetic field

We report results of tunneling studies on the charge ordering compound Nd_{0.5}Sr_{0.5}MnO_{3} in a magnetic field up to 6T and for temperature down to 25K.We show that a gap (2\Delta_{CO} \approx 0.5eV opens up in the density of state (DOS) at the Fermilevel (E_F) on charge ordering (T_{CO}=150K) which collapses in an applied magnetic field when the charge ordered state melts. There is a clear correspondence between the behavior of the resistivity and the gap formation and its collapse in an applied magnetic field. We conclude that a gap in the DOS at E_F is necessary for the stability of the charge ordered state.Comment: 4 pages REVTeX, 5 postscript figures included, submitted to Phys. Rev. Let

The Topology of Parabolic Character Varieties of Free Groups

Let G be a complex affine algebraic reductive group, and let K be a maximal compact subgroup of G. Fix elements h_1,...,h_m in K. For n greater than or equal to 0, let X (respectively, Y) be the space of equivalence classes of representations of the free group of m+n generators in G (respectively, K) such that for each i between 1 and m, the image of the i-th free generator is conjugate to h_i. These spaces are parabolic analogues of character varieties of free groups. We prove that Y is a strong deformation retraction of X. In particular, X and Y are homotopy equivalent. We also describe explicit examples relating X to relative character varieties.Comment: 16 pages, version 2 includes minor revisions and some modified proofs, accepted for publication in Geometriae Dedicat

Periodic Orbits in Polygonal Billiards

We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed new light on the proliferation law and its variation with the genus of the invariant surface. Finally, we deal with correlations in the length spectrum and find that long orbits display Poisson fluctuations.Comment: 30 pages (Latex) including 11 figure

Coupled Inflation and Brane Gases

We study an effective four-dimensional theory with an action with two scalar fields minimally coupled to gravity, and with a matter action which couples to the two scalar fields via an overall field-dependent coefficient in the action. Such a theory could arise from a dimensional reduction of supergravity coupled to a gas of branes winding the compactified dimensions. We show the existence of solutions corresponding to power-law inflation. The graceful exit from inflation can be obtained by postulating the decay of the branes, as would occur if the branes are unstable in the vacuum and stabilized at high densities by plasma effects. This construction provides an avenue for connecting string gas cosmology and the late-time universe.Comment: 11 page

Kinetic exchange opinion model: solution in the single parameter map limit

We study a recently proposed kinetic exchange opinion model (Lallouache et. al., Phys. Rev E 82:056112, 2010) in the limit of a single parameter map. Although it does not include the essentially complex behavior of the multiagent version, it provides us with the insight regarding the choice of order parameter for the system as well as some of its other dynamical properties. We also study the generalized two- parameter version of the model, and provide the exact phase diagram. The universal behavior along this phase boundary in terms of the suitably defined order parameter is seen.Comment: 14 pages, 9 figure