We compute using a microscopic mean-field theory the structure and the quasiparticle excitation spectrum of a dilute, trapped Bose–Einstein condensate penetrated by an axisymmetric vortex line. The Gross–Pitaevskii equation for the condensate and the coupled Hartree–Fock–Bogoliubov–Popov equations describing the elementary excitations are solved self-consistently using finite-difference methods...

In this paper we consider the asymptotic behavior of the GinzburgLandau model for superconductivity in 3-d, in various energy regimes. We rigorously derive, through an analysis via Γ-convergence, a reduced model for the vortex density, and deduce a curvature equation for the vortex lines. In the companion paper [2] we describe further applications to superconductivity and superfluidity, such as...

We determine the structure of the hydrodynamics with conserved current, using the gauge/ gravity duality of charged black-hole background. It turns out that even in the presence of the external electromagnetic field at the boundary, bulk Einstein equation is equivalent to the boundary conservation of energy momentum tensor and that of current. As a consequence, the thermal conductivity and elec...

We consider the ground state of a trapped Bose-Einstein condensate in two dimensions. In the mean-field approximation, the ground state density profile satisfies the Gross-Pitaevskii equation. We compute the leading quantum corrections to the density profile to second order in an expansion around the Thomas-Fermi limit. By summing the ladder diagrams,we are generalizing Schick’s result for the ...

Geometric analysis can be said to originate in the 19’th century work of Weierstrass, Riemann, Schwarz and others on minimal surfaces, a problem whose history can be traced at least as far back as the work of Meusnier and Lagrange in the 18’th century. The experiments performed by Plateau in the mid-19’th century, on soap films spanning wire contours, served as an important inspiration for this...

Magnetic curvature effects in Einstein general relativistic (GR) open Friedmann universe , has been investigated by Barrow and Tsagas (BT) [Phys Rev D 77,(2008)]. They demonstrated that this mechanism induces a magnetic field decay. In this report, one shows that by using the GR-(3+1)-space-time magnetohydrodynamic (MHD) induction equation derived by Marklund and Clarkson (CM) [MNRAS (2004)], t...

We considered an extension of the standard functional for the Einstein-Dirac equation where the Dirac operator is replaced by the square of the Dirac operator and a real parameter controlling the length of spinors is introduced. For one distinguished value of the parameter, the resulting Euler-Lagrange equations provide a new type of EinsteinDirac coupling. We establish a special method for con...

Temperature-dependent rotational diffusion of tetraethylene glycol dimethyl ether (TEGDE) is measured by optical heterodyne-detected optical Kerr effect (OHD-OKE) spectroscopy and compared to previous measurements of rotational diffusion as a function of water content. Both types of data, temperature-dependent and hydration-dependent, follow the Debye-Stokes-Einstein (DSE) equation and agree qu...

The conformal space M was introduced by Dirac in 1936. It is an algebraic manifold with a spin structure and possesses naturally an invariant Lorentz metric. By carefully studying the birational transformations of M, we obtain explicitly the transition functions of the spin bundle over M. Since the transition functions are closely related to the propagation in physics, we get a kind of solution...