Related papers: High-order geometric integrators for representatio…
We propose a numerical method which embeds the variational non-Gaussian wavefunction approach within exact diagonalization, allowing for efficient treatment of correlated systems with both electron-electron and electron-phonon interactions.…
The paper presents a new method of geometric solution of a Schrodinger equation by a construction of an equivalent first-order partial differential equation with a bigger number of variables. The equivalent equation shall be restricted to a…
We propose a trajectory-based method for simulating nonadiabatic dynamics in molecular systems with two coupled electronic states. Employing a quantum-mechanically exact mapping of the two-level problem to a spin-1/2 coherent state, we…
This article considers non-relativistic charged particle dynamics in both static and non-static electromagnetic fields, which are governed by nonseparable, possibly time-dependent Hamiltonians. For the first time, explicit symplectic…
We extend the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), a semiclassical method for computing real-time correlation functions, to electronically nonadiabatic systems using the Meyer-Miller-Stock-Thoss (MMST) Hamiltonian…
Coupled nonlinear Schr\"odinger equations model various physical phenomena, such as wave propagation in nonlinear optics, multi-component Bose-Einstein condensates, and shallow water waves. Despite their extensive applications, analytical…
We review the implementation of individual particle time-stepping for N-body dynamics. We present a class of integrators derived from second order Hamiltonian splitting. In contrast to the usual implementation of individual time-stepping,…
A semiclassical approximation is derived by using a family of wavepackets to map arbitrary wavefunctions into phase space. If the Hamiltonian can be approximated as linear over each individual wavepacket, as often done when presenting…
Quantum geometrical molecular dynamics provides a quantum geometric picture for understanding reactive dynamics, especially excited-state conical intersection dynamics, and also a numerically exact method for strongly correlated…
This article explains and illustrates the use of a set of coupled dynamical equations, second order in a fictitious time, which converges to solutions of stationary Schr\"{o}dinger equations with additional constraints. We include three…
A small deformation controlled by four free parameters to the Schwarzschild metric could be referred to a nonspinning black hole solution in alternative theories of gravity. Because such a non-Schwarzschild metric can be changed into a…
The recently developed exact factorization approach condenses all electronic effects on the nuclear subsystem into scalar and vector potentials that appear in an effective time dependent Schr\"{o}dinger equation. Starting from this…
A mixed quantum-classical approach to simulate the coupled dynamics of electrons and nuclei in nanoscale molecular systems is presented. The method relies on a second order expansion of the Lagrangian in time-dependent density functional…
Quantum computation is an attractive front for many problems that are intractable for computers today. One such problem is nonadiabatic quantum molecular dynamics, where quantized internal states coupling to parameterized modes result in a…
Mixed quantum-classical dynamics is a set of methods often used to understand systems too complex to treat fully quantum mechanically. Many techniques exist for full quantum mechanical evolution on quantum computers, but mixed…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
There is a growing interest in the conservation of invariants when numerically solving a system of ordinary differential equations. Methods that exactly preserve these quantities in time are known as geometric integrators. In this paper we…
Ab initio modeling of conical intersection dynamics is crucial for various photochemical, photophysical, and biological processes. However, adiabatic electronic states obtained from electronic structure computations involve random phases,…
We apply a numerical method based on multi-configurational Ehrenfest tra jectories, and demonstrate converged results for the Choi fidelity of an entangling quantum gate between two two-level systems interacting through a set of bosonic…
We propose a hybrid quantum-classical eigensolver to address the computational challenges of simulating strongly correlated quantum many-body systems, where the exponential growth of the Hilbert space and extensive entanglement render…