Adiabatic and Nonadiabatic Dynamics with Interacting Quantum Trajectories

Abstract

We present a quantum dynamics method based on the propagation of interacting quantum trajectories to describe both adiabatic and nonadiabatic processes within the same formalism. The idea originates from the work of Poirier [Chem. Phys. 2010, 370, 4–14] and Schiff and Poirier [J. Chem. Phys. 2012, 136, 031102] on quantum dynamics without wavefunctions. It consists of determining the quantum force arising in the Bohmian hydrodynamic formulation of quantum dynamics using only information about quantum trajectories. The particular time-dependent propagation scheme proposed here results in very stable dynamics. Its performance is discussed by applying the method to analytical potentials in the adiabatic regime, and by combining it with the exact factorization method in the nonadiabatic regime.

Towards a mathematical theory of the Madelung equations: Takabayasi’s quantization condition, quantum quasi-irrotationality, weak formulations, and the Wallstrom phenomenon

“…We refer to [101-104, 108, 114, 140, 173]. Similarly, one should note that there exist approaches in the 'Lagrangian picture' 58 [51,87,138,155,166] and approaches based on the calculus of variations [64,72,108,183,184].…”

“…Though Berry's example [19] is particularly illustrative, it is a well-known fact that not all L 2 -functions are weakly differentiable. Moreover, as neither dom Ĥ, H 1 0 (Ω, C), or even H 1 (Ω, C) are closed 51 We refer, for instance, to the beginning of section 8.4 in Brezis' book [35] for an example of how homogeneous Dirichlet boundary conditions are treated within the mathematical theory of PDEs. 52 Note that in [30] the authors considered the case dom Ĥ = H 2 0 (Ω, C) instead.…”

Quantum molecular dynamics simulations of the effect of secondary modes on the photoisomerization of a retinal chromophore model

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“…Furthermore, the D λ coefficients are (−1) L−|λ| C L−|λ| n−1 and C j i are binomial coefficients. However, in the present study, we have used constraints adapted to a system-bath separation [55] with three Smolyak parameters: (i) L b , a parameter associated to the bath modes (i…”

Consistent Construction of the Density Matrix from Surface Hopping Trajectories

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