Related papers: A slow-down time-transformed symplectic integrator…
Hamiltonian systems such as the gravitational N-body problem have time-reversal symmetry. However, all numerical N-body integration schemes, including symplectic ones, respect this property only approximately. In this paper, we present the…
We introduce a numerically exact real-time evolution scheme for quantum impurities in a macroscopically large bath. The algorithm is few-body revealing, namely it identifies the electronic orbitals that can be made inactive (in a trivial…
In this work, we present a symplectic integration scheme to numerically compute space debris motion. Such an integrator is particularly suitable to obtain reliable trajectories of objects lying on high orbits, especially geostationary ones.…
Spherically symmetric equal mass star clusters containing a large amount of primordial binaries are studied using a hybrid method, consisting of a gas dynamical model for single stars and a Monte Carlo treatment for relaxation of binaries…
When fitting N-body models to astronomical data - including transit times, radial velocity, and astrometric positions at observed times - the derivatives of the model outputs with respect to the initial conditions can help with model…
This paper focuses on the numerical approximation of the linearized shallow water equations using hybridizable discontinuous Galerkin (HDG) methods, leveraging the Hamiltonian structure of the evolution system. First, we propose an…
We present a new method for computing the lowest few eigenvalues and the corresponding eigenvectors of a nuclear many-body Hamiltonian represented in a truncated configuration interaction subspace, i.e., the no-core shell model (NCSM). The…
The N-representability problem consists in determining whether, for a given p-body matrix, there exists at least one N-body density matrix from which the p-body matrix can be obtained by contraction, that is, if the given matrix is a p-body…
We extend coupled-cluster theory performed on top of a Slater determinant breaking rotational symmetry to allow for the exact restoration of the angular momentum at any truncation order. The main objective relates to the description of…
We developed a Keplerian-based Hamiltonian splitting for solving the gravitational $N$-body problem. This splitting allows us to approximate the solution of a general $N$-body problem by a composition of multiple, independently evolved…
This paper deals with an implicit Newton-like inertial dynamical system governed by a maximally comonotone inclusion problem in a Hilbert space. Under suitable conditions, we establish not only pointwise estimates and integral estimates for…
We construct symplectic blenders for two classical Hamiltonian systems: the 3-body problem and its restricted version. We use these objects to show that both models exhibit a robust, strong form of topological instability. We do not assume…
Symplectic integrators are the preferred method of solving conservative $N$-body problems in cosmological, stellar cluster, and planetary system simulations because of their superior error properties and ability to compute orbital…
Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. The existing algorithms generally approximate the time evolution operators, which may need a deep…
The symplectic Wisdom-Holman map revolutionized long-term integrations of planetary systems. There is freedom in such methods of how to split the Hamiltonian and which coordinate system to employ, and several options have been proposed in…
We develop a new analytical method for solving real time evolution problems of quantum many-body systems. Our approach is a direct generalization of the well-known canonical perturbation theory for classical systems. Similar to canonical…
The complexity of quantum many-body problems scales exponentially with the size of the system, rendering any finite size scaling analysis a formidable challenge. This is particularly true for methods based on the full representation of the…
The paper considers a coupled system of linear Boltzmann transport equations (BTE), and its Continuous Slowing Down Approximation (CSDA). This system can be used to model the relevant transport of particles used e.g. in dose calculation in…
We discuss a new analytical approach to real-time evolution in quantum many-body systems. Our approach extends the framework of continuous unitary transformations such that it amounts to a novel solution method for the Heisenberg equations…
$N$-body simulations study the dynamics of $N$ particles under the influence of mutual long-distant forces such as gravity. In practice, $N$-body codes will violate Newton's third law if they use either an approximate Poisson solver or…