Extended coupled-cluster method. II. Excited states and generalized random-phase approximation

Towards a Coupled Cluster Gauge-Field Approach to Quantum Hydrodynamics

“…We have shown 6 how the method m~be viewed as a biorthogonal formulation for a rather general quantal many-body problem. It is therefore best not to restrict ourselves from the start to Hamiltonians H or their relevant subsequent transforms that are necessarily manifestly hermitian.…”

“…The linked-cluster amplitudes pertaining to the operators S and SIt are now regarded as independent Tariables which~be determined variationally by demanding stationarity of the action functional, A = fdt <<I>leS"(t)e-SCt)Cia/at -H)e SCt ) 1<1» (6) The stationarity conditions then yield the eigenvalue. equations for the ground-state energy E in the time-independent case,…”

Quantum Fluid Dynamics: An Extended Coupled Cluster Treatment

“…The exact time-dependent states I~(t» and <~'(t)1 of our many-boson system obey the time-dependent Schrodinger equations, HI~(t» = i~tly(t» ; <~'(t)IH = -i~t <Y'(t)1 (3) in terms of the Hamiltonian H. We may also define an action functionaZ, A: = IAtn,y' ] = f dt <'I" (t)I(ia/at -H) Iy(t» (4) whose stationarity with respect to (independent) variations in the wavefunctions <y'(t)1 and I~(t» leads respectively to the Schrodinger equations (3). The exact states may be defined in terms of the model (vacuum) state in terms of the timedeveZopment operators U(t) and U(t) defined as, Iy(t» = U(t)I~> <y'(t)1 = <~IU(t) U(t) = e~(t)eS(t)e-E(t) U(t) = e-~(t)eE(t)e-S(t) (5) where~(t) and~(t) are c-number scale factors, and S(t) and E(t) are operators which contain only creation pieces and destruction pieces respectively with respect to the model state I~>, so that <~IS(t) = 0 = E(t)I~>.…”

“…4, where we show also that at the lowest level of truncation which puts to zero all amplitudes except 01 and ;1' the formalism simply degenerates to the mean field description of Gross and Pitaevskii [5-7J. The evolution of the one-body density matrix and its gauge-transformation properties are investigated in Sec.…”

Time evolution of the Rabi Hamiltonian from the unexcited vacuum

“…In order to investigate the evolution of the Rabi system from the state |0, ↓ we employ here one of the most versatile and most accurate semi-analytical formalisms of microscopic quantum many-body theory, namely the coupled cluster method (CCM) [23][24][25][26][27][28][29][30]. Coupled cluster techniques are widely regarded as being amongst the most powerful of all ab initio quantum many-body methods.…”