Generalized CC-TDSCF and LCSA: The system-energy representation

Abstract

Typical (sub)system-bath quantum dynamical problems are often investigated by means of (approximate) reduced equations of motion. Wavepacket approaches to the dynamics of the whole system have gained momentum in recent years and there is hope that properly designed approximations to the wavefunction will allow one to correctly describe the subsystem evolution. The continuous-configuration time-dependent self-consistent field (CC-TDSCF) and local coherent-state approximation (LCSA) methods, for instance, use a simple Hartree product of bath single-particle-functions for each discrete variable representation (DVR) state introduced in the Hilbert space of the subsystem. Here we focus on the above two methods and replace the DVR states with the eigenstates of the subsystem Hamiltonian, i.e., we adopt an energy-local representation for the subsystem. We find that stable and semiquantitative results are obtained for a number of dissipative problems, at the same (small) computational cost of the original methods. Furthermore, we find that both methods give very similar results, thus suggesting that coherent-states are well suited to describe (local) bath states. As a whole, present results highlight the importance of the system basis-set in the selected-multiconfiguration expansion of the wavefunction. They suggest that accurate and yet computationally cheap methods may be simply obtained from CC-TDSCF/LCSA by letting the subsystem states be variationally optimized.

Unitary Approaches to Dissipative Quantum Dynamics

“…This concludes the description of the original LCSA method. Several variants are possible (e.g., replacing the DVR states with energy eigenstates or fully flexible system states) and can be found in the original literature [35,36]. Also, the closely related CC-TDSCF method [49] in which the CSs are replaced by fully flexible functions has been shown to provide essentially the same results as LCSA [36], thereby showing the soundness of the CS approximation for the (local) bath dynamics.…”

“…(1) is appropriate to cases where only the near equilibrium configurations of the system are explored (s ≈ 0), but is clearly limited because it describes a coupling which steadily increases when moving the system out of its equilibrium position. Thus, for instance, in previous scattering calculations using a model Morse potential, a coupling function with a finite limit for s → + ∞ [27,36], (6) (but yet such that f(s) ≈ s for s ≈ 0 was used to correctly describe the asymptotically free system.…”

“…Here, we present some numerical applications of the IO model, starting from simple simulations of a Brownian anharmonic oscillator-used as a testing ground for new dynamical methodologies [34,[36][37][38] and/or for different representation of the Hamiltonian [27]. The last part of the contribution will be devoted to a "real-world" application, namely the hydrogen atom dynamics on the graphene surface [40,41].…”

“…We describe the now standard and numerically exact multi-configurational time-dependent Hartree (MCTDH) approach [16,32,33], as well as related approximate approaches which better suit to the description of a bath in the IO form. In particular, we discuss in some detail the local coherent-state approximation (LCSA), where the bath evolution is described by a number of Hartree products of pseudo-classically evolving coherent states [34][35][36]. All these approaches are variational and, as such, they share a number of highly desirable features which will be described in some detail.…”

“…Finally, we present the results of some numerical investigations on both model and realistic systems. Issues, such as vibrational relaxation, decoherence, and scattering, have been extensively investigated in model systems (a harmonic or a Morse oscillator coupled to an oscillator bath) [27,29,[34][35][36][37][38][39] and will be summarized in the following. Work on "real-world" problems is still at its infancy, but already offers some notable examples.…”