Related papers: Controlling energy conservation in quantum dynamic…
The goal of this paper is to develop energy-preserving variational integrators for time-dependent mechanical systems with forcing. We first present the Lagrange-d'Alembert principle in the extended Lagrangian mechanics framework and derive…
We derive the fundamental equations of an optimal control theory for systems containing both quantum electrons and classical ions. The system is modeled with Ehrenfest dynamics, a non-adiabatic variant of molecular dynamics. The general…
Mixed quantum-classical mechanics descriptions are critical to modeling coupled electron-nuclear dynamics, i.e. non-adiabatic molecular dynamics, relevant to photochemical and photophysical processes. We argue that, for polyatomic…
A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities…
We review techniques for simulating fully quantum nonadiabatic dynamics using the frozen-width moving Gaussian basis functions to represent the nuclear wavefunction. A choice of these basis functions is primarily motivated by the idea of…
We have derived equations for nonadiabatic Ehrenfest molecular dynamics which conserve the total energy in the case of time-dependent discretization for electrons. A discretization is time-dependent in all cases where it or part of it…
Energetic particle effects in magnetic confinement fusion devices are commonly studied by hybrid kinetic-fluid simulation codes whose underlying continuum evolution equations often lack the correct energy balance. While two different…
We present a Lagrangian-based implementation of Ehrenfest dynamics with nuclear-electronic orbital (NEO) theory and real-time time-dependent density functional theory (RT-TDDFT) for extended periodic systems. In addition to a quantum…
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…
Nonlinear energy-conserving drift-fluid equations that are suitable to describe self-consistent finite-beta low-frequency electromagnetic (drift-Alfven) turbulent fluctuations in a nonuniform, anisotropic, magnetized plasma are derived from…
Methods of quantum nuclear wave-function dynamics have become very efficient in simulating large isolated systems using the time-dependent variational principle (TDVP). However, a straightforward extension of the TDVP to the density matrix…
Considering the emblematic Hartree-Fock (HF) energy expression with single Slater determinant and the ortho-normal molecular orbits (MO) in it, expressed as a linear combination (LC) of atomic orbits (LCAO) basis set functions, the HF…
We present an alternative field theoretical approach to the definition of conserved quantities, based directly on the field equations content of a Lagrangian theory (in the standard framework of the Calculus of Variations in jet bundles).…
In this paper, we introduce a Lagrange multiplier approach to construct linearly implicit energy-preserving schemes of arbitrary order for general Hamiltonian PDEs. Unlike the widely used auxiliary variable methods, this novel approach does…
Density functional theory with linear combination of atomic orbitals (LCAO) basis sets is useful for studying large atomic systems, especially when it comes to computationally highly demanding time-dependent dynamics. We have implemented…
Ehrenfest dynamics is a useful approximation for ab initio mixed quantum-classical molecular dynamics that can treat electronically nonadiabatic effects. Although a severe approximation to the exact solution of the molecular time-dependent…
Determining low-energy eigenstates in electronic many-body quantum systems is a key challenge in computational chemistry and condensed-matter physics. Hybrid quantum-classical approaches, such as the Variational Quantum Eigensolver and…
A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…
A new formalism for the optimal control of quantum mechanical physical observables is presented. This approach is based on an analogous classical control technique reported previously[J. Botina, H. Rabitz and N. Rahman, J. chem. Phys. Vol.…
We consider the dynamics of interacting quantum and classical systems in the Heisenberg representation. Unlike the usual construction in standard quantum mechanics, mixed quantum-classical systems involve the interplay of unitary operators…