Study of quantum effects in 2D driven dissipative systems with stochastic methods

The common description of the quantum many-body systems, such as Bose-Einstein condensates, is based on the mean-field analysis which, although being a useful tool to understand the collective phenomena, excludes the quantum effects from the considerations. To include quantum fluctuations and entanglement, beyond mean-field approaches are being developed. One class of such techniques is the phase space methods and in particular Truncated Wigner Approximations and exact Positive P method. For closed systems, although being exact, the positive P can lead to numerical instabilities during the simulations. For the open quantum system, Positive P has shown to be remarkably stable. In particular, the Positive P method, which provides the full quantum description of open quantum systems, has been recently shown to be successful in for example solving the driven-dissipative Bose-Hubbard model on a large lattice relevant to polariton lattices. The goal of the project is to study quantum systems with dissipations using the abovementioned stochastic methods, in collaboration with the experimental groups, to simulate the behaviour of the exciton polariton condensates and to extend the applicability of the methods beyond the bosonic systems, such as for example to spin-lattices.