Quantum quench in fermionic systems with extended d+id pairing*

We consider the problem of non-adiabatic dynamics of 2-D fermions with extended d+id pairing following a sudden quantum quench of coupling constant. Our approach is based on Lax vector and integrability of underlying classical model. Depending upon number of complex roots of Lax equation, we identify three regions in our phase diagram defining behavior of extended d+id order paramete △(t) at long times following quantum quench. Region 1 is characterized by vanishing order parameter, in region 2 order parameter asymptotes to a constant and periodically oscillates in region 3 at long times. We also perform numerical integration of extended d+id many-body Green's functions E.O.M. following a quantum quench and found it in exact agreement with the result obtained by Lax root method. Dynamics of order parameter for non-integrable case i.e. d+id, following quantum quenches, will also be presented and compared against extended d+id results .