Related papers: Conservative Integrators for Many-body Problems
In this work, we consider the error estimates and the long-time conservation or near-conservation of geometric structures, including energy, mass shell and phase-space volume, for four two-step symmetric methods applied to relativistic…
Many interesting applications of hyperbolic systems of equations are stiff, and require the time step to satisfy restrictive stability conditions. One way to avoid small time steps is to use implicit time integration. Implicit integration…
$N$-body integrations are used to model a wide range of astrophysical dynamics, but they suffer from errors which make their orbits diverge exponentially in time from the correct orbits. Over long time-scales, their reliability needs to be…
`Dual composition', a new method of constructing energy-preserving discretizations of conservative PDEs, is introduced. It extends the summation-by-parts approach to arbitrary differential operators and conserved quantities. Links to…
We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the energy integral and exact preservation of the trajectories…
High-order accurate, $\textit{entropy stable}$ numerical methods for hyperbolic conservation laws have attracted much interest over the last decade, but only a few rigorous convergence results are available, particularly in multiple space…
This paper develops a structure-preserving numerical integration scheme for a class of higher-order mechanical systems. The dynamics of these systems are governed by invariant variational principles defined on higher-order tangent bundles…
Recently, it has been suggested that the Many-Body Localized phase can be characterized by local integrals of motion. Here we introduce a Hilbert space preserving renormalization scheme that iteratively finds such integrals of motion…
Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are PT symmetric. The standard and well-known real solutions to such dynamical systems constitute an…
This paper deals with the numerical solution of conservation laws in the two dimensional case using a novel compact implicit time discretization that enables applications of fast algebraic solvers. We present details for the second order…
In this paper, we develop a provably energy stable and conservative discontinuous spectral element method for the shifted wave equation in second order form. The proposed method combines the advantages and central ideas of very successful…
We study quantum many-body systems with a global U(1) conservation law, focusing on a theory of $N$ interacting fermions with charge conservation, or $N$ interacting spins with one conserved component of total spin. We define an effective…
Recent work shows that highly excited many-body localized eigenstates can exhibit broken symmetries and topological order, including in dimensions where such order would be forbidden in equilibrium. In this paper we extend this analysis to…
We review our results for the dynamics of isolated many-body quantum systems described by one-dimensional spin-1/2 models. We explain how the evolution of these systems depends on the initial state and the strength of the perturbation that…
Invariant finite-difference schemes are considered for one-dimensional magnetohydrodynamics (MHD) equations in mass Lagrangian coordinates for the cases of finite and infinite conductivity. For construction these schemes previously obtained…
We propose a high resolution finite volume scheme for a (m+1)x(m+1) system of non strictly hyperbolic conservation laws which models multicomponent polymer flooding in enhanced oil-recovery process in two dimensions. In the presence of…
In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the…
The nonlinear Schr\"{o}dinger (NLS) equation possesses an infinite hierarchy of conserved densities and the numerical preservation of some of these quantities is critical for accurate long-time simulations, particularly for multi-soliton…
First-order energy dissipative schemes in time are available in literature for the Poisson-Nernst-Planck (PNP) equations, but second-order ones are still in lack. This work proposes novel second-order discretization in time and finite…
We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general…