Abstract
In this paper, a two-layer scheme is outlined for the coupled coherent states (CCS) method, dubbed two-layer CCS (2L-CCS). The theoretical framework is motivated by that of the multiconfigurational Ehrenfest method, where different dynamical descriptions are used for different subsystems of a quantum mechanical system. This leads to a flexible representation of the wavefunction, making the method particularly suited to the study of composite systems. It was tested on a 20-dimensional asymmetric system-bath tunnelling problem, with results compared to a benchmark calculation, as well as existing CCS, matching-pursuit/split-operator Fourier transform, and configuration interaction expansion methods. The two-layer method was found to lead to improved short and long term propagation over standard CCS, alongside improved numerical efficiency and parallel scalability. These promising results provide impetus for future development of the method for on-the-fly direct dynamics calculations.
Highlights
Multilayer variants of existing numerical methods in multidimensional quantum mechanics offer an increase in flexibility and give better scalability for the description of complex quantum systems
A two-layer scheme is outlined for the coupled coherent states (CCS) method, dubbed two-layer CCS (2L-CCS)
The theoretical framework is motivated by that of the multiconfigurational Ehrenfest method, where different dynamical descriptions are used for different subsystems of a quantum mechanical system
Summary
Multilayer variants of existing numerical methods in multidimensional quantum mechanics offer an increase in flexibility and give better scalability for the description of complex quantum systems. Motivated by the extension of multiconfigurational time-dependent Hartree (MCTDH) to its multilayer formalism (ML-MCTDH), Gaussian based methods have already been extended in this direction, and a two-layer approach for the Gaussian-based MCTDH (G-MCTDH) has been proposed in Ref. 6. Numerous Gaussian based techniques exist for both semiclassical and quantum propagations. Following the seminal work by Heller, many of those methods represent the wavefunction as a superposition of trajectory guided Gaussian coherent states, N. In the z-notation representation of coherent states, an M-. Dimensional coherent state (CS) is a product of M onedimensional.
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