Non-equilibrium Dynamics of Renyi Entropy for Bosonic Many-Particle Systems

We propose a new field theoretic method for calculating Renyi entropy of a sub-system of many interacting Bosons without using replica methods. This method is applicable to dynamics of both open and closed quantum systems starting from arbitrary initial conditions. Our method identifies the Wigner characteristic of a reduced density matrix with the partition function of the whole system with a set of linear sources turned on only in the subsystem and uses this to calculate the subsystem's Renyi entropy. We use this method to study evolution of Renyi entropy in a non-interacting open quantum system starting from an initial Fock state. We find a relation between the initial state and final density matrix which determines whether the entropy shows non-monotonic behaviour in time. For non-Markovian dynamics, we show that the entropy approaches its steady state value as a power law with exponents governed by non-analyticities of the bath. We illustrate that this field-theoretic method can be used to study large bosonic open quantum systems.