Non-equilibrium field theory

A widely used approach to study non-equilibrium dynamics of quantum systems is to solve the equation of motion (EOM) of the density matrix, which is given by Heisenberg equation in closed systems and quantum Master equations in open quantum systems under various approximations. But this direct method runs into difficulty to deal with many body systems as the Hilbert space grows exponentially with the system size. Moreover, in presence of long range memory kernel in the dynamics, solving the EOM of the density matrix becomes extremely challenging, even for a few body system. The problem of exponentially growing Hilbert space can be avoided by using field theoretic methods which allow us to obtain useful approximate answers for correlation functions for large systems. Field theoretic techniques have also been recently used to calculate entanglement entropy of the system. Our group is interested in developing non-equilibrium field theoretic formalism applicable to various open quantum systems, specially to systems initialized in non-thermal initial density matrices.