In this talk we will describe an interesting relation between zero temperature Feynman graphs and their finite temperature counterparts. In this process we will discover the notion of a radiative renormalization of the chemical potential.

The volatility of an Indian stock market is examined in terms of aspects like participation, synchronization of stocks and quantification of volatility using the random matrix approach. Volatility pattern of the market is found using the Bombay Stock Index for the three-year period 00-2002$. Random matrix analysis is carried out using daily returns of $ stocks for several time windows of $ days in 01$ to (i) do a brief comparative analysis with statistics of eigenvalues and eigenvectors of the matrix C of correlations between price fluctuations, in time regimes of different volatilities. While a bulk of eigenvalues falls within Random Matrix Theory bounds in all the time periods, we see that the largest (deviating) eigenvalue correlates well with the volatility of the index (ii) observe the corresponding eigenvector clearly shows a shift in the distribution of its components from volatile to less volatile periods and verifies the qualitative association between participation and volatility (iii) set up a variability index, V whose temporal evolution is found to be significantly correlated with the volatility of the overall market index.

Non-equilibrium systems are less understood compared to their equilibriumcounter-parts. I will introduce a simple non equilibrium model which isexactly solvable and explain it’s application to Celebrity Markets(crickets performance), Biological systems, Generic rules fornon-equilibrium transitions, Anomalous diffusion etc.

We discuss a Polyakov loop enhanced NJL model to describe the QCD phase transition. Linear and nonlinear susceptibilities, specific heat, speed of sound etc. have been obtained and compared to those obtained through Lattice regularization.