A Monte Carlo method for propagating multi‐dimensional wave packets

Abstract

A method for propagating multi-dimensional wave packets in time using a product ansatz for the wave function is presented. Other than in the time-dependent Hartree approach which is based on a variational scheme, the current method is based on the stochastic Ito calculus. The correlations between the different one-dimensional wave functions are taken into account via stochastic processes such that on average the original Schraedinger equation is reproduced. Numerical tests of the proposed scheme have been performed in two and four dimensions.

Theoretical Insights into Photoinduced Charge Transfer and Catalysis at Oxide Interfaces

“…Prezhdo pointed out that decoherence constitutes the physical mechanism for stochastic quantum transitions and nuclear trajectory branching that surface hopping was designed to achieve. A number of approaches to nonadiabatic molecular dynamics were followed based on the decoherence ideas. ,,− These techniques are closely related to stochastic Schrödinger equations. ,, …”

“…145,200,235−240 These techniques are closely related to stochastic Schrodinger equations. 200,241,242 Decoherence-induced surface hopping (DISH) is a particularly simple algorithm of the above type. 243 In DISH, decoherence events are stochastically identified, and trajectory surface hops occur during these events.…”