Related papers: A variational symplectic scheme based on Simpson's…
Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. It is often multi-scale and requires accurate long-term numerical simulations using…
We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis…
In this paper, we develop a novel, linearly implicit and local energy-preserving scheme for the sine-Gordon equation. The basic idea is from the invariant energy quadratization approach to construct energy stable schemes for gradient…
A variational framework for accelerated optimization was recently introduced on normed vector spaces and Riemannian manifolds in Wibisono et al. (2016) and Duruisseaux and Leok (2021). It was observed that a careful combination of…
In this work, we have applied the integrals of motion method in a nonunitary approach and so obtained the time-dependent displacement and squeezed parameters of the coherent squeezed states (CSS). On its turn, CSS for one-dimensional…
Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term…
We study the stability of a vector field associated to a nearly-integrable Hamiltonian dynamical system to which a dissipation is added. Such a system is governed by two parameters, named the perturbing and dissipative parameters, and it…
Many applications in computational physics that use numerical integrators based on splitting and composition can benefit from the development of optimized algorithms and from choosing the best ordering of terms. The cost in programming and…
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…
This work investigates variational compilation methods for simulating quantum systems with internal SU(2) symmetry. The central component of the research is the application of the Dynamic Mode Decomposition (DMD) method to extrapolate…
Taking advantage of the flexibility of the variational method with coordinate transformations, we derive a self-consistent set of equations of motion from a discretized Lagrangian to study kinetic plasmas using a Fourier decomposed…
Most material properties of great physical interest are directly related to nuclear dynamics, e.g. the ionic thermal conductivity, Raman/IR vibrational spectra, inelastic X-ray, and Neutron scattering. A theory able to compute from first…
We report a few sumerical tests comparing some newly defined energy-preserving integrators and symplectic methods, using either constant and variable stepsize.
Using a variational approach based on a Lagrangian formulation and Gaussian trial functions, we derive a simple dynamical system that captures the main features of the time-dependent Schr\"odinger-Newton equations. With little analytical or…
We describe a simple quantum algorithm to simulate time-dependent Hamiltonian, extending the methodology of quantum signal processing. The framework achieves optimal scaling up to some factor with respect to other parameters, and nearly…
Using operator ordering techniques based on BCH-like relations of the su(1,1) Lie algebra and a time-splitting approach,we present an alternative method of solving the dynamics of a time-dependent quantum harmonic oscillator for any initial…
Theory of the quantum quartic oscillator is developed with close attention to the energy cutoff one needs to impose on the system in order to approximate the smallest eigenvalues and corresponding eigenstates of its Hamiltonian by…
We propose three new discrete variational schemes that capture the conservative-dissipative structure of a generalized Kramers equation. The first two schemes are single-step minimization schemes while the third one combines a streaming and…
We demonstrate how to derive the exponential decrease of amplitude and an excellent approximation of the energy decay of a weakly damped harmonic oscillator without solving the associated equation of motion and without insight into the…
We introduce a new approach to the the asymptotic iteration method (AIM) by means of which we establish the standard AIM connection with the continued fractions technique and we develop a novel termination condition in terms of the…