
Observable Error Bounds of the Timesplitting Scheme for QuantumClassical Molecular Dynamics
Quantumclassical molecular dynamics, as a partial classical limit of th...
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A timedomain preconditioner for the Helmholtz equation
Timeharmonic solutions to the wave equation can be computed in the freq...
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Parallel transport dynamics for mixed quantum states with applications to timedependent density functional theory
Direct simulation of the von Neumann dynamics for a general (pure or mix...
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An efficient numerical scheme for a 3D spherical dynamo equation
We develop an efficient numerical scheme for the 3D meanfield spherical...
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Adaptive timestep control for a monolithic multirate scheme coupling the heat and wave equation
We consider the dynamics of a parabolic and a hyperbolic equation couple...
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A numerical damped oscillator approach to constrained Schrödinger equations
This article explains and illustrates the use of a set of coupled dynami...
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Mean Field Theory for the Quantum Rabi Model, Inconsistency to the Rotating Wave Approximation
Considering well localized atom, the mean field theory (MFT) was applied...
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Shadow Lagrangian dynamics for superfluidity
Motivated by a similar approach for BornOppenheimer molecular dynamics, this paper proposes an extended "shadow" Lagrangian density for quantum states of superfluids. The extended Lagrangian contains an additional field variable that is forced to follow the wave function of the quantum state through a rapidly oscillating extended harmonic oscillator. By considering the adiabatic limit for large frequencies of the harmonic oscillator, we can derive the two equations of motions, a Schrödingertype equation for the quantum state and a wave equation for the extended field variable. The equations are coupled in a nonlinear way, but each equation individually is linear with respect to the variable that it defines. The computational advantage of this new system is that it can be easily discretized using linear time stepping methods, where we propose to use a CrankNicolsontype approach for the Schrödinger equation and an extended leapfrog scheme for the wave equation. Furthermore, the difference between the quantum state and the extended field variable defines a consistency error that should go to zero if the frequency tends to infinity. By coupling the timestep size in our discretization to the frequency of the harmonic oscillator we can extract an easily computable consistency error indicator that can be used to estimate the numerical error without any additional costs. The findings are illustrated in numerical experiments.
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