A time-dependent multi-reference unified cluster cumulant formulation to study the subdynamics of quantum system coupled both to thermal and stochastic bath

Department of Chemistry, Rishi Bankim Chandra College, Naihati, North 24-Parganas-743 165, West Bengal, India

E-mail: hanrkm1@yahoo.co.in

Manuscript received online 05 March 2019, accepted 25 April 2019

This is to introduce a time-local effective hamiltonian unified cluster cumulant method based on the time-dependent multireference cluster cumulant (TDMRCC) and thermal cluster cumulant (TCC) strategy developed by Mukherjee and his coworkers. A factorized ansatz for U_IP = [U_I] _ex [U_I ]_MP with P = |j _i > Ä  |0_b> Ä|0_f>, where |j_i >,|0_b  > and |0_f > denote the purely quantum mechanical vacuum state, the thermal vacuum state, the base state for the solvent degrees of freedom respectively, and [U_I]_ex consists of operators admixing the thermally as well as the stochastically projected model space functions with that of the virtual space outside the model space whose functions govern the time-evolution of [UI ]M via the time-local effective operator, V_eff [b,x,t ](=<< v_l[u_l]_ex>b>f ), where < ... >_b and < ... >_f denote thermal and stochastic averaging respectively. The exponential ansatz is introduced both for [U_I]_ex and [U_I ]_M and these ansatze are normal ordered with respect to