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We introduce the notion of asymptotic integrability into the theory of nonlinear wave equations. It means that the Hamiltonian structure of equations describing propagation of high-frequency wave packets is preserved by hydrodynamic evolution of the large-scale background wave so that these equations have an additional integral of motion. This condition is expressed mathematically as a system of equations for the carrier wave number as a function of the background variables.
View Article and Find Full Text PDFQuasiclassical approaches to the generalized quantum master equation.
J Chem Phys
December 2022
Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland.
The formalism of the generalized quantum master equation (GQME) is an effective tool to simultaneously increase the accuracy and the efficiency of quasiclassical trajectory methods in the simulation of nonadiabatic quantum dynamics. The GQME expresses correlation functions in terms of a non-Markovian equation of motion, involving memory kernels that are typically fast-decaying and can therefore be computed by short-time quasiclassical trajectories. In this paper, we study the approximate solution of the GQME, obtained by calculating the kernels with two methods: Ehrenfest mean-field theory and spin-mapping.
View Article and Find Full Text PDFCombining Machine Learning and Spectroscopy to Model Reactive Atom + Diatom Collisions.
J Phys Chem A
November 2022
Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056Basel, Switzerland.
The prediction of product translational, vibrational, and rotational energy distributions for arbitrary initial conditions for reactive atom + diatom collisions is of considerable practical interest in atmospheric re-entry. Because of the large number of accessible states, determination of the necessary information from explicit (quasi-classical or quantum) dynamics studies is impractical. Here, a machine-learned (ML) model based on translational energy and product vibrational states assigned from a spectroscopic, ro-vibrational coupled energy expression based on the Dunham expansion is developed and tested quantitatively.
View Article and Find Full Text PDFThe processes leading to the N lasing are rather complex and even the population distribution after the pump laser excitation is unknown. In this paper, we study the population distribution at electronic and vibrational levels in N driven by ultra-short laser pulse at the wavelengths of 800 nm and 400 nm by using the quantum-mechanical time-domain incoherent superposition model based on the time-dependent Schrödinger equation and the quasi-classical model assuming instantaneous ionization injection described by density matrix. It is shown that while both models provide qualitatively similar results, the quasi-classical instantaneous ionization injection model underestimates the population inversions corresponding to the optical transitions at 391 nm, 423 nm and 428 nm due to the assumption of quantum mixed states at the ionization time.
View Article and Find Full Text PDFTemporally stable rotational coherent states for molecular simulations. II. Symmetric rotor case.
J Chem Phys
June 2022
Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, USA.
Following our preceding work on spherical and linear rotors [C. Stopera and J. A.
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