Related papers: Fast spin dynamics algorithms for classical spin s…
The concept of effective order is a popular methodology in the deterministic literature for the construction of efficient and accurate integrators for differential equations over long times. The idea is to enhance the accuracy of a…
Two-dimensional superintegrable systems with one third order and one lower order integral of motion are reviewed. The fact that Hamiltonian systems with higher order integrals of motion are not the same in classical and quantum mechanics is…
Symplectic integration methods based on operator splitting are well established in many branches of science. For Hamiltonian systems which split in more than two parts, symplectic methods of higher order have been studied in detail only for…
In recent work, we initiated a research program aimed at the systematic investigation of quantum superintegrable systems describing the interaction of two non-relativistic spin-$1/2$ particles in three-dimensional Euclidean space. In that…
Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and…
A wide range of implicit time integration methods, including multi-step, implicit Runge-Kutta, and Galerkin finite-time element schemes, is evaluated in the context of chaotic dynamical systems. The schemes are applied to solve the Lorenz…
Symplectic integration algorithms have become popular in recent years in long-term orbital integrations because these algorithms enforce certain conservation laws that are intrinsic to Hamiltonian systems. For problems with large variations…
Two specialized algorithms for the numerical integration of the equations of motion of a Brownian walker obeying detailed balance are introduced. The algorithms become symplectic in the appropriate limits, and reproduce the equilibrium…
We propose a hybrid approach to simulate quantum many body dynamics by combining Trotter based quantum algorithm with classical dynamic mode decomposition. The interest often lies in estimating observables rather than explicitly obtaining…
In this paper a formalism for studying the dynamics of quantum systems coupled to classical spin environments is reviewed. The theory is based on generalized antisymmetric brackets and naturally predicts open-path off-diagonal geometric…
The optimization of physical parameters serves various purposes, such as system identification and efficiency in developing devices. Spin-torque oscillators have been applied to neuromorphic computing experimentally and theoretically, but…
A method for time-reversible numerical integration of the deterministic Landau-Lifshitz Gilbert equation by means of a second order Suzuki-Trotter decomposition is presented and tested against commonly used second order predictor-corrector…
The two-dimensional n-body problem of classical mechanics is a non-integrable Hamiltonian system for n > 2. Traditional numerical integration algorithms, which are polynomials in the time step, typically lead to systematic drifts in the…
Lie-Trotter-Suzuki decompositions are an efficient way to approximate operator exponentials $\exp(t H)$ when $H$ is a sum of $n$ (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution…
Simulation of many-particle system evolution by molecular dynamics takes to decrease integration step to provide numerical scheme stability on the sufficiently large time interval. It leads to a significant increase of the volume of…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider a model for spin-orbital motion: orbital…
A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…
A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then…
This work introduces the high-order Boris-SDC method for integrating the equations of motion for electrically charged particles in an electric and magnetic field. Boris-SDC relies on a combination of the Boris-integrator with spectral…
A new scheme for numerical integration of motion for classical systems composed of rigid polyatomic molecules is proposed. The scheme is based on a matrix representation of the rotational degrees of freedom. The equations of motion are…