Spinodal decomposition: An alternate mechanism of phase conversion

The scenario of homogeneous nucleation is investigated for a first order quark-hadron phase transition in a rapidly expanding background of quark gluon plasma. It is found that significant supercooling is possible before hadronization begins. This study also suggests that spinodal decomposition competes with nucleation and may provide an alternative mechanism for phase conversion.Comment: LaTeX, 4 pages with 3 Postscript figures. Talk given at International Conference on Physics and Astrophysics of Quark Gluon Plasma (ICPAQGP 2001), Nov. 26-30, 2001, Jaipur, Indi

Simulation study of the filamentation of counter-streaming beams of the electrons and positrons in plasmas

The filamentation instability driven by two spatially uniform and counter-streaming beams of charged particles in plasmas is modelled by a particle-in-cell (PIC) simulation. Each beam consists of the electrons and positrons. The four species are equally dense and they have the same temperature. The one-dimensional simulation direction is orthogonal to the beam velocity vector. The magnetic field grows spontaneously and rearranges the particles in space, such that the distributions of the electrons of one beam and the positrons of the second beam match. The simulation demonstrates that as a result no electrostatic field is generated by the magnetic field through its magnetic pressure gradient prior to its saturation. This electrostatic field would be repulsive at the centres of the filaments and limit the maximum charge and current density. The filaments of electrons and positrons in this simulation reach higher charge and current densities than in one with no positrons. The oscillations of the magnetic field strength induced by the magnetically trapped particles result in an oscillatory magnetic pressure gradient force. The latter interplays with the statistical fluctuations in the particle density and it probably enforces a charge separation, by which electrostatic waves grow after the filamentation instability has saturated.Comment: 13 pages, 8 figure

Random Matrices with Correlated Elements: A Model for Disorder with Interactions

The complicated interactions in presence of disorder lead to a correlated randomization of states. The Hamiltonian as a result behaves like a multi-parametric random matrix with correlated elements. We show that the eigenvalue correlations of these matrices can be described by the single parametric Brownian ensembles. The analogy helps us to reveal many important features of the level-statistics in interacting systems e.g. a critical point behavior different from that of non-interacting systems, the possibility of extended states even in one dimension and a universal formulation of level correlations.Comment: 19 Pages, No Figures, Major Changes to Explain the Mathematical Detail

Gauge transformation through an accelerated frame of reference

The Schr\"{o}dinger equation of a charged particle in a uniform electric field can be specified in either a time-independent or a time-dependent gauge. The wave-function solutions in these two gauges are related by a phase-factor reflecting the gauge symmetry of the problem. In this article we show that the effect of such a gauge transformation connecting the two wave-functions can be mimicked by the effect of two successive extended Galilean transformations connecting the two wave-function. An extended Galilean transformation connects two reference frames out of which one is accelerating with respect to the other.Comment: 7 Pages, Latex fil

Metal-insulator transitions in tetrahedral semiconductors under lattice change

Although most insulators are expected to undergo insulator to metal transition on lattice compression, tetrahedral semiconductors Si, GaAs and InSb can become metallic on compression as well as by expansion. We focus on the transition by expansion which is rather peculiar; in all cases the direct gap at $\Gamma$ point closes on expansion and thereafter a zero-gap state persists over a wide range of lattice constant. The solids become metallic at an expansion of 13 % to 15 % when an electron fermi surface around L-point and a hole fermi surface at $\Gamma$-point develop. We provide an understanding of this behavior in terms of arguments based on symmetry and simple tight-binding considerations. We also report results on the critical behavior of conductivity in the metal phase and the static dielectric constant in the insulating phase and find common behaviour. We consider the possibility of excitonic phases and distortions which might intervene between insulating and metallic phases.Comment: 12 pages, 8 figure