Related papers: On the single-Hessian Gaussian wavepacket dynamics
Gaussian wavepacket dynamics has proven to be a useful semiclassical approximation for quantum simulations of high-dimensional systems with low anharmonicity. Compared to Heller's original local harmonic method, the variational Gaussian…
The paper gives a symplectic-geometric account of semiclassical Gaussian wave packet dynamics. We employ geometric techniques to "strip away" the symplectic structure behind the time-dependent Schr\"odinger equation and incorporate it into…
Many approximate solutions of the time-dependent Schr\"odinger equation can be formulated as exact solutions of a nonlinear Schr\"odinger equation with an effective Hamiltonian operator depending on the state of the system. We show that…
Simulating vibrationally resolved electronic spectra of anharmonic systems, especially those involving double-well potential energy surfaces, often requires expensive quantum dynamics methods. Here, we explore the applicability and…
Hagedorn functions are carefully constructed generalizations of Hermite functions to the setting of many-dimensional squeezed and coupled harmonic systems. Wavepackets formed by superpositions of Hagedorn functions have been successfully…
One-dimensional integrable and quasi-integrable systems display, on macroscopic scales, a universal form of transport known as Generalized Hydrodynamics (GHD). In its standard Euler-scale formulation, GHD mirrors the equations of a…
A method for performing variable-width (thawed) Gaussian wavepacket (GWP) variational dynamics on machine-learned potentials is presented. Instead of fitting the potential energy surface (PES), the anharmonic correction to the global…
Among the single-trajectory Gaussian-based methods for solving the time-dependent Schr\"{o}dinger equation, the variational Gaussian approximation is the most accurate one. In contrast to Heller's original thawed Gaussian approximation, it…
Hagedorn wavepackets have been used to compute single vibronic level (SVL) spectra efficiently in model harmonic potentials. To make the Hagedorn approach practical for realistic polyatomic molecules with anharmonicity, here we combine…
In this article, we develop and analyse a new spectral method to solve the semi-classical Schr\"odinger equation based on the Gaussian wave-packet transform (GWPT) and Hagedorn's semi-classical wave-packets (HWP). The GWPT equivalently…
We develop structure-preserving time integration schemes for Gaussian wave packet dynamics associated with the magnetic Schr\"odinger equation. The variational Dirac--Frenkel formulation yields a finite-dimensional Hamiltonian system for…
We find a relationship between the dynamics of the Gaussian wave packet and the dynamics of the corresponding Gaussian Wigner function from the Hamiltonian/symplectic point of view. The main result states that the momentum map corresponding…
To alleviate the computational cost associated with on-the-fly ab initio semiclassical calculations of molecular spectra, we propose the single-Hessian thawed Gaussian approximation, in which the Hessian of the potential energy at all…
We present a novel method of magnetohydrodynamics (MHD) within the smoothed particle hydrodynamics scheme using the Geometric Density average force expression (GDSPH). GDSPH has recently been shown to reduce the leading order errors and…
Hagedorn wavepacket dynamics yields exact single vibronic level (SVL) fluorescence spectra in global harmonic models. To partially describe the effects of anharmonicity, important in the spectra of real molecules, we describe a combination…
Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…
A model of localized electron wave packets (EWPs), floating and breathing Gaussians with non-orthogonal valence-bond spin-coupling, is applied to compute the high-harmonic generation (HHG) spectrum from a LiH molecule induced by an intense…
In single vibronic level (SVL) fluorescence experiments, the electronically excited initial state is also excited in one or several vibrational modes. Whereas computing all contributing Franck-Condon factors individually becomes impractical…
"Generalized Hydrodynamics" (GHD) stands for a model that describes one-dimensional \textit{integrable} systems in quantum physics, such as ultra-cold atoms or spin chains. Mathematically, GHD corresponds to nonlinear equations of kinetic…
We present a practical, ab initio time-dependent method using Hagedorn wavepackets to efficiently simulate single vibronic level (SVL) fluorescence spectra of polyatomic molecules from arbitrary initial vibrational levels. We apply the…