The plethora application of classical random walks which in recent years have been elevated to a quantum version has found its significance in various areas of applied sciences. In this talk, I present a new family of quantum walks which interpolates between the two types of quantum walks known till now (i.e. unitary quantum walks and open quantum walks). In particular, this new family is an extension of the open type by blocks where we allow interference to occur inside the blocks. By changing the size of the blocks as well as moving at the scale of blocks one can see different limit distributions appearing via simulations. This unitary-dissipative quantum walks can also be used to simulate a nice model of an out of equilibrium quantum system which shows behaviours like a quantum Fourier law.
