Wavepacket revivals via complex trajectory propagation

Koch, Werner; Tannor, David J.

doi:10.1016/j.cplett.2017.02.020

Cited by 16 publications

(7 citation statements)

References 34 publications

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“…Note that for the Morse, Coulomb and Eckart systems, imaginary time contour propagation is required to obtain all relevant contributions [14,20,24]. A separate publication will give more details of the implementation and the phase space geometry of the caustics in the four prototypical potentials.…”

Section: Application To Wavepacket Reconstructionmentioning

confidence: 99%

“…14,20,24 A separate publication will give more details of the implementation and the phase space geometry of the caustics in the four prototypical potentials.…”

Section: Application To Wavepacket Reconstructionmentioning

confidence: 99%

“…4,5 However, simply removing trajectories with σ(ξ) > 0 leads to inaccurate numerical results, due to the rapidly fluctuating phase e i σ(ξ) at the boundary σ(ξ) = 0. A number of criteria have been proposed to remove divergences based on the value of σ(ξ) or components thereof, 11,12,15,20 but these are empirical at best and do not lead to satisfactory results for long time propagation.…”

Section: Stokes Divergencesmentioning

confidence: 99%

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Communication: Systematic elimination of Stokes divergences emanating from complex phase space caustics

Koch

Tannor

2018

The Journal of Chemical Physics

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Perspective: Ab initio force field methods derived from quantum mechanics The Journal of Chemical Physics 148, 090901 (2018) Stokes phenomenon refers to the fact that an asymptotic expansion of complex functions can differ in different regions of the complex plane, and that beyond the so-called Stokes lines the expansion has an unphysical divergence. An important special case is when the Stokes lines emanate from phase space caustics of a complex trajectory manifold. In this case, symmetry determines that to second order there is a double coverage of the space, one portion of which is unphysical. Building on the seminal but laconic findings of Adachi, we show that the deviation from second order can be used to rigorously determine the Stokes lines and therefore the region of the space that should be removed. The method has applications to wavepacket reconstruction from complex valued classical trajectories. With a rigorous method in hand for removing unphysical divergences, we demonstrate excellent wavepacket reconstruction for the Morse, Quartic, Coulomb, and Eckart systems. Published by AIP Publishing.

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Section: Application To Wavepacket Reconstructionmentioning

confidence: 99%

“…14,20,24 A separate publication will give more details of the implementation and the phase space geometry of the caustics in the four prototypical potentials.…”

Section: Application To Wavepacket Reconstructionmentioning

confidence: 99%

Section: Stokes Divergencesmentioning

confidence: 99%

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Communication: Systematic elimination of Stokes divergences emanating from complex phase space caustics

Koch

Tannor

2018

The Journal of Chemical Physics

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“…In recent years, the discussion of the quantum trajectory has been extended to the complex space [ 31 , 32 , 33 , 34 , 35 , 36 ]. Higher dimensions provide leverage in tackling unsolved quantum issues and explaining more quantum phenomena [ 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 ]. Underlying the framework of complex trajectory interpretation, tunneling dynamics have been provided and studied.…”

Section: Introductionmentioning

confidence: 99%

Tunneling Quantum Dynamics in Ammonia

Yang

Han

2021

IJMS

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Ammonia is a well-known example of a two-state system and must be described in quantum-mechanical terms. In this article, we will explain the tunneling phenomenon that occurs in ammonia molecules from the perspective of trajectory-based quantum dynamics, rather than the usual quantum probability perspective. The tunneling of the nitrogen atom through the potential barrier in ammonia is not merely a probability problem; there are underlying reasons and mechanisms explaining why and how the tunneling in ammonia can happen. Under the framework of quantum Hamilton mechanics, the tunneling motion of the nitrogen atom in ammonia can be described deterministically in terms of the quantum trajectories of the nitrogen atom and the quantum forces applied. The vibrations of the nitrogen atom about its two equilibrium positions are analyzed in terms of its quantum trajectories, which are solved from the Hamilton equations of motion. The vibration periods are then computed by the quantum trajectories and compared with the experimental measurements.

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“…because some consider it not to have the measurement problem. [25][26][27] For practical applications, Bohmian mechanics can be viewed as trajectory-based quantum hydrodynamics, and in the last years a number of studies have appeared that aim at using these quantum trajectories to develop simulation methods, in particular for molecular dynamics [28][29][30][31][32][33], also by extending it to complex-valued trajectories [34][35][36][37] or by using the "conditional wavefunction" approach [38][39][40][41].…”

mentioning

confidence: 99%

Time in quantum mechanics: A fresh look on quantum hydrodynamics and quantum trajectories

Schild

2019

Preprint

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Quantum hydrodynamics is a formulation of quantum mechanics based on the probability density and flux (current) density of a quantum system. It can be used to define trajectories which allow for a particle-based interpretation of quantum mechanics, commonly known as Bohmian mechanics. However, quantum hydrodynamics rests on the usual time-dependent formulation of quantum mechanics where time appears as a parameter. This parameter describes the correlation of the state of the quantum system with an external system -a clock -which behaves according to classical mechanics. With the Exact Factorization of a quantum system into a marginal and a conditional system, quantum mechanics and hence quantum hydrodynamics can be generalized for quantum clocks. In this article, the theory is developed and it is shown that trajectories for the quantum system can still be defined, and that these trajectories depend conditionally on the trajectory of the clock. Such trajectories are not only interesting from a fundamental point of view, but they can also find practical applications whenever a dynamics relative to an external time parameter is composed of "fast" and "slow" degrees of freedom and the interest is in the fast ones, while quantum effects of the slow ones (like a branching of the wavepacket) cannot be neglected. As an illustration, time-and clock-dependent trajectories are calculated for a model system of a non-adiabatic dynamics, where an electron is the quantum system, a nucleus is the quantum clock, and an external time parameter is provided, e.g. via an interaction with a laser field that is not treated explicitly.

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Wavepacket revivals via complex trajectory propagation

Cited by 16 publications

References 34 publications

Communication: Systematic elimination of Stokes divergences emanating from complex phase space caustics

Communication: Systematic elimination of Stokes divergences emanating from complex phase space caustics

Tunneling Quantum Dynamics in Ammonia

Time in quantum mechanics: A fresh look on quantum hydrodynamics and quantum trajectories

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