Abstract
Previously, we introduced two versions of the Multiconfigurational Ehrenfest (MCE) approach to high dimensional quantum dynamics. It has been shown that the first version, MCEv1, converges well to the existing benchmarks for high dimensional model systems. At the same time, it was found that the second version, MCEv2, had more difficulty converging in some regimes. As MCEv2 is particularly suited for direct dynamics, it is important to facilitate its convergence. This paper investigates an efficient method of basis set sampling, called Quantum Superposition Sampling (QSS), which dramatically improves the performance of the MCEv2 approach. QSS is tested on the spin-boson model, often used for modeling of open quantum systems. It is also shown that the quantum subsystem in the spin-boson model can be conveniently treated with the help of two level system coherent states. Generalized coherent states, which combine two level system coherent states for the description of the system and Gaussian coherent states for description of the bath, are introduced. Various forms of quantum equations of motion in the basis of generalized coherent states can be developed by analogy with known quantum dynamics equations in the basis of Gaussian coherent states; in particular, the multiconfigurational Ehrenfest method becomes a version of coupled generalized coherent states, and QSS can then be viewed as a generalization of a sampling method known for the existing coupled coherent states method which uses Gaussian coherent states.
Highlights
The most straightforward way of simulating open systems would be to model them by a small quantum subsystem coupled with a large number of bath modes describing the environment and to solve the time dependent Schrödinger equation for all degrees of freedom, both those of the main system and the bath
In Multiconfigurational time dependent Hartree (MCTDH), the bath is discretized and a large number of bath modes are combined in groups so that a small number of very flexible time dependent scitation.org/journal/jcp basis functions per group are sufficient for adequate description of the dynamics
We show how this technique arises naturally if the quantum subsystem is treated with a basis of so called SU(2) coherent states so that MCEv2 can be viewed as a version of the recently introduced Coupled Generalized Coherent States (CGCS) approach
Summary
The most straightforward way of simulating open systems would be to model them by a small quantum subsystem coupled with a large number of bath modes describing the environment and to solve the time dependent Schrödinger equation for all degrees of freedom, both those of the main system and the bath. We have developed the Multiconfigurational Ehrenfest (MCE) approach, which uses trajectory guided basis sets of Gaussian coherent states to perform formally exact multidimensional quantum simulations. Several other techniques have been developed, all using basis sets of Gaussian coherent states which follow the quantum wave function, economizing the basis set size, with these methods only differing in the way they guide the trajectories of the CS basis set. Two versions of MCE, referred to as MCEv1 and MCEv2, have been developed Both methods represent the propagating wave function as a superposition of Ehrenfest configurations guided by Ehrenfest trajectories, but MCEv1 and MCEv2 differ in the way quantum coupling between the configurations works. We show how this technique arises naturally if the quantum subsystem is treated with a basis of so called SU(2) coherent states so that MCEv2 can be viewed as a version of the recently introduced Coupled Generalized Coherent States (CGCS) approach. In the supplementary material, we derive various forms of equations for treating quantum system-bath models with CGCS
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