Related papers: Polynomial propagators for classical molecular dyn…
We present a new molecular-dynamics algorithm for integrating the equations of motion for a system of particles interacting with mixed continuous/impulsive forces. This method, which we call Impulsive Verlet, is constructed using operator…
We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev…
Classical molecular dynamics simulations are based on solving Newton's equations of motion. Using a small timestep, numerical integrators such as Verlet generate trajectories of particles as solutions to Newton's equations. We introduce…
We propose and develop a general method of numerical calculation of the wave function time evolution in a quantum system which is described by Hamiltonian of an arbitrary dimensionality and with arbitrary interactions. For this, we obtain a…
In ab initio molecular dynamics simulations of real-world problems, the simple Verlet method is still widely used for integrating the equations of motion, while more efficient algorithms are routinely used in classical molecular dynamics.…
We extend the recently proposed Time-Dependent Multi-Determinant approach (ref.[1]) to the description of fermionic propagators. The method hinges on equations of motions obtained using variational principles of Dirac type. In particular we…
New explicit velocity- and position-Verlet-like algorithms of the second order are proposed to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an extended decomposition scheme at the…
The Minkowski operators (addition and substraction of sets in vectorial spaces) has been extensively used for Computer Graphics and Image Processing to represent complex shapes. Here we propose to apply those mathematical concepts to extend…
A vector field splitting approach is discussed for the systematic derivation of numerical propagators for deterministic dynamics. Based on the formalism, a class of numerical integrators for Langevin dynamics are presented for single and…
We present a super-polynomial improvement in the precision scaling of quantum simulations for coupled classical-quantum systems in this paper. Such systems are found, for example, in molecular dynamics simulations within the…
In the setting of polynomial jump-diffusion dynamics, we provide an explicit formula for computing correlators, namely, cross-moments of the process at different time points along its path. The formula appears as a linear combination of…
Although driven Brownian particles are ubiquitous in stochastic dynamics and often serve as paradigmatic model systems for many aspects of stochastic thermodynamics, fully analytically solvable models are few and far between. In this paper,…
A recent article in J. Chem. Phys. argues that the two algorithms, the velocity-Verlet, and position-Verlet integrators, commonly used in Molecular Dynamics (MD) simulations, are different \cite{Ni2024}. But not only are the two algorithms…
Simulations of objects with classical dynamics are in fact a particular version of discrete dynamics since almost all the classical dynamics simulations in natural science are performed with the use of the simple ''Leapfrog" or ''Verlet"…
We propose a computationally efficient and systematically convergent approach for elastodynamics simulations. We recast the second-order dynamical equation of elastodynamics into an equivalent first-order system of coupled equations, so as…
A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…
Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in…
We propose and simulate a protocol to evolve a quantum particle forward in time such that its trajectory closely matches that of the particle's Newtonian counterpart. Using short bursts of Schr\"odinger time-evolution interleaved with…
Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this…
With growing demand for time-domain simulations of correlated many-body systems, the development of efficient and stable integration schemes for the time-dependent Schr\"odinger equation is of keen interest in modern electronic structure…