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Pramana

Hermite-distributed approximating functional-based formulation of multiconfiguration time-dependent Hartree method: A case study of quantum tunnelling in a coupled double-well system

Kaushik Maji

Published Jul 29, 2016• 1 citation
Publisher
DOI
10.1007/s12043-016-1243-5

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Comment on: A multiconfiguration time-dependent Hartree approximation based on natural single particle states

Uwe Manthe

•Jan 1, 1994•0 citations
A variational approach for the quantum dynamics of statistical mixtures is developed, which is based upon the representation of the natural states of the mixture in terms of hybrid Gaussian-based Multiconfiguration Time-Dependent Hartree (G-MCTDH) wavefunctions. The method, termed ρG-MCTDH, is combined with a treatment of dissipation and decoherence based on the nonstochastic open-system Schrödinger equations. The performance and the convergence properties of the approach are illustrated for a two-dimensional tunneling system, where the primary tunneling coordinate, represented by flexible single-particle functions, is resonantly coupled to a second harmonic mode, represented by Gaussian wave packets. The harmonic coordinate is coupled to the environment and two different processes are studied: (i) vibrational relaxation at zero temperature described by a master equation in the Lindblad form and (ii) thermalization induced by the Caldeira-Leggett master equation. In the second case, the evolution from a quantum tunneling regime to a quasistationary classical-limit distribution, driven by the heat bath, is visualized using a flux analysis.
Absorbing boundary conditions in the form of a complex absorbing potential are routinely introduced in the Schr\"odinger equation to limit the computational domain or to study reactive scattering events using the multiconfigurational time-dependent Hartree (MCTDH) method. However, it is known that a pure wave-function description does not allow the modeling and propagation of the remnants of a system of which some parts are removed by the absorbing boundary. It was recently shown [S. Selst\o{} and S. Kvaal, J. Phys. B: At. Mol. Opt. Phys. 43, 065004 (2010)] that a master equation of Lindblad form was necessary for such a description. We formulate a MCTDH method for this master equation, usable for any quantum system composed of any mixture of species. The formulation is a strict generalization of pure-state propagation using standard MCTDH for identical particles and mixtures. We demonstrate the formulation with a numerical experiment.