Related papers: A slow-down time-transformed symplectic integrator…
In this letter we give a systematic derivation and justification of the semiclassical model for the slow degrees of freedom in adiabatic slow-fast systems first found by Littlejohn and Flynn [5]. The classical Hamiltonian obtains a…
In previous papers, explicit symplectic integrators were designed for nonrotating black holes, such as a Schwarzschild black hole. However, they fail to work in the Kerr spacetime because not all variables can be separable, or not all…
This article reviews some integrators particularly suitable for the numerical resolution of differential equations on a large time interval. Symplectic integrators are presented. Their stability on exponentially large time is shown through…
We present a statistical approximate solution of the bound, non-hierarchical three-body problem, and extend it to a general analysis of encounters between hard binary systems and single stars. Any such encounter terminates when one of the…
We present a fast iterative solver for scattering problems in 2D, where a penetrable object with compact support is considered. By representing the scattered field as a volume potential in terms of the Green's function, we arrive at the…
This work introduces advanced computational techniques for modeling the time evolution of compact binary systems using machine learning. The dynamics of compact binary systems, such as black holes and neutron stars, present significant…
We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e. integrals of motion. The core idea of the…
Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as…
Reliable studies of the long-term dynamics of planetary systems require numerical integrators that are accurate and fast. The challenge is often formidable because the chaotic nature of many systems requires relative numerical error bounds…
We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). We use observed data to locate a low-dimensional, attracting slow SSM and compute a…
In this paper, explicit stable integrators based on symplectic and contact geometries are proposed for a non-autonomous ordinarily differential equation (ODE) found in improving convergence rate of Nesterov's accelerated gradient method.…
We show that symplectic Runge-Kutta methods provide effective symplectic integrators for Hamiltonian systems with index one constraints. These include the Hamiltonian description of variational problems subject to position and velocity…
This work is focused on the application of functional-type a posteriori error estimates and corresponding indicators to a class of time-dependent problems. We consider the algorithmic part of their derivation and implementation and also…
Symplectic integrators separate a problem into parts that can be solved in isolation, alternately advancing these sub-problems to approximate the evolution of the complete system. Problems with a single, dominant mass can use mixed-variable…
The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one and two-body reduced density matrices (RDM) instead of many-electron…
Over short time intervals planetary ephemerides have been traditionally represented in analytical form as finite sums of periodic terms or sums of Poisson terms that are periodic terms with polynomial amplitudes. Nevertheless, this…
Transcorrelated methods provide an efficient way of partially transferring the description of electronic correlations from the ground state wavefunction directly into the underlying Hamiltonian. In particular, Dobrautz et al. [Phys. Rev. B,…
By combining a standard symmetric, symplectic integrator with a new step size controller, we provide an integration scheme that is symmetric, reversible and conserves the values of the constants of motion. This new scheme is appropriate for…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Microscopically conserving reduced models of many-body systems have a long, highly successful history. Established theories of this type are the random-phase approximation for Coulomb fluids and the particle-particle ladder model for…