Vortex Matter and its Phase Transitions

The mixed state of type II superconductors has magnetic flux penetrating the sample in the form of vortices, with each vortex carrying an identical quantum of flux. These vortices generally form a triangular lattice under weak mutually repulsive forces; the lattice spacing can be easily varied over many orders of magnitude by varying the external magnetic field. The elastic moduli of this lattice are small and this soft vortex matter can undergo phase transitions like normal matter, but with thermal fluctuations and underlying defects playing an important role. We discuss experimental studies on vortex matter phase transitions, with some emphasis on DC magnetisation measurements investigating the nature of the phase transition.Comment: 11 pages and 4 figure

Random growth lattice filling model of percolation: a crossover from continuous to discontinuous transition

A random growth lattice filling model of percolation with touch and stop growth rule is developed and studied numerically on a two dimensional square lattice. Nucleation centers are continuously added one at a time to the empty sites and the clusters are grown from these nucleation centers with a tunable growth probability g. As the growth probability g is varied from 0 to 1 two distinct regimes are found to occur. For g\le 0.5, the model exhibits continuous percolation transitions as ordinary percolation whereas for g\ge 0.8 the model exhibits discontinuous percolation transitions. The discontinuous transition is characterized by discontinuous jump in the order parameter, compact spanning cluster and absence of power law scaling of cluster size distribution. Instead of a sharp tricritical point, a tricritical region is found to occur for 0.5 < g < 0.8 within which the values of the critical exponents change continuously till the crossover from continuous to discontinuous transition is completed.Comment: 8 pages, 21 figure

Kinetic arrest of the first order ferromagnetic to antiferromagnetic transition in Ce(Fe0.96_{0.96}Ru0.04_{0.04})2_2 : formation of a magnetic-glass

We present results of dc magnetization and magnetic relaxation study showing the kinetic arrest of a first order ferromagnetic to antiferromagnetic transition in Ce(Fe$_{0.96}$Ru$_{0.04}$)$_2$. This leads to the formation of a non-ergodic glass-like magnetic state. The onset of the magnetic-glass transformation is tracked through the slowing down of the magnetization dynamics. This glassy state is formed with the assistance of an external magnetic field and this is distinctly different from the well known 'spin-glass' state.Comment: 10 pages of text and 4 figure

Bright solitons in asymmetrically trapped Bose-Einstein condensate

We study the dynamics of bright solitons in a Bose-Einstein condensate (BEC) confined in a highly asymmetric trap. While working within the f ramework of a variational approach we carry out the stability analysis o f BEC solitons against collapse. When the number of atoms in the soliton exceeds a critical number $N_c$, it undergoes the so called primary col lapse. We find an analytical expression for $N_c$ in terms of appropriat e experimental quantities that are used to produce and confine the conde nsate. We further demonstrate that, in the geometry of the problem consi dered, the width of the soliton varies inversely as the number of consti tuent atoms.Comment: 5 pages, 1 figure