Hidden vortices and Feynman rule in Bose-Einstein condensates with density-dependent gauge potential.

In this paper, we numerically investigate the vortex nucleation in a Bose-Einstein condensate (BEC) trapped in a double-well potential and subjected to a density-dependent gauge potential. A rotating Bose-Einstein condensate, when confined in a double-well potential, not only gives rise to visible vortices but also produces hidden vortices. We have empirically developed Feynman's rule for the number of vortices versus angular momentum in Bose-Einstein condensates in the presence of density-dependent gauge potentials.

Vortex nucleation in rotating Bose-Einstein condensates with density-dependent gauge potential.

We study numerically the vortex dynamics and vortex-lattice formation in a rotating density-dependent Bose-Einstein condensate (BEC), characterized by the presence of nonlinear rotation. By varying the strength of nonlinear rotation in density-dependent BECs, we calculate the critical frequency, Ω_{cr}, for vortex nucleation both in adiabatic and sudden external trap rotations. The nonlinear rotation modifies the extent of deformation experienced by the BEC due to the trap and shifts the Ω_{cr} values for vortex nucleation.

Vortex dynamics in cubic-quintic Bose-Einstein condensates.

We study vortex dynamics in a trapped Bose-Einstein condensate with tunable two- and three-body interactions. The dynamics is governed by two-dimensional cubic-quintic Gross-Pitaevskii equation. A time-dependent variational method has been used to obtain critical rotational frequency and surface mode frequency analytically and are compared with numerical simulation results.

Gap compactonlike solutions of coupled Kortweg-de Vries equations with linear and nonlinear dispersions.

We show the existence of a type of excitation, which we term as "gap compactonlike," within the gap of the linear spectrum of a system of coupled Kortweg-de Vries equations with linear and nonlinear dispersions. Since the solutions lie in the gap region of the spectra, they avoid resonance with the linear oscillatory wave and, therefore, do not decay into radiations. These types of solutions are important in energy localization and transport in polymers and biopolymers, optical systems, etc.

Effect of two length scales on the properties of MgB(2) for arbitrary applied magnetic field.

Experiments carried out on the intermetallic superconducting material MgB(2) have shown anomalous magnetic field dependence of upper critical field, small angle neutron scattering form factor, specific heat, critical current etc. Similarly, scanning tunnelling microscopy (STM) experiments on vortex structures have shown unusually large vortex core size and two different magnetic and spatial field scales. Also, whereas the specific heat measurements and isotope shift experiments have shown Bardeen-Cooper-Schrieffer-like (BCS-like) behaviour, the temperature dependences of the penetration depth experiments have shown non-BCS-like behaviour.

The effect of in-plane mass anisotropy on the properties of high temperature superconductors in states of mixed symmetry.

Experiments have suggested that the high- T(c) cuprate YBCO shows marked anisotropy in penetration depth and coherence length measurements. In order to take into account the presence of this anisotropy in the system and its corresponding effect on the various properties of the high- T(c) superconducting materials, we have developed an anisotropic two-order parameter Ginzburg-Landau (GL) theory involving a mixed symmetry state of the order parameter components. For this we have generalized a two-order parameter GL theory, recently developed for the isotropic high- T(c) superconductors involving a mixed symmetry state of the order parameter components (Karmakar and Dey 2008 J.

Dynamics of a curved Fermi-Pasta-Ulam chain: effects of geometry, long-range interaction, and nonlinear dispersion.

We study the dynamics of the bent Fermi-Pasta-Ulam (FPU) chain, incorporating the complicated effects of geometry, long-range interactions, as well as nonlinear dispersion. Within the rotating wave approximation, we obtain several exact discrete breather (DB) solutions, such as the odd-parity and even-parity discrete breathers, compactlike discrete breathers and moving discrete breathers for various geometries of the chain. In presence of long-range nonlinear dispersive interactions, we show that DBs exist in the discrete curved lattice for next-nearest-neighbor interactions as well.