Related papers: Switching integrators reversibly in the astrophysi…
Most numerical methods for time integration use real time steps. Complex time steps provide an additional degree of freedom, as we can select the magnitude of the step in both the real and imaginary directions. By time stepping along…
Many exoplanetary systems are multiplanet configurations whose long-term dynamics are governed by N-body gravitational interactions. Consequently, their detection signatures cannot be adequately described by Keplerian orbits. Accurately…
A numerical integrator is presented that computes a symmetric or skew-symmetric low-rank approximation to large symmetric or skew-symmetric time-dependent matrices that are either given explicitly or are the unknown solution to a matrix…
This is the first in a series of papers devoted to fully general-relativistic $N$-body simulations applied to late-time cosmology. The purpose of this paper is to present the combination of a numerical relativity scheme, discretization…
The gravitational three-body problem is a fundamental problem in physics and has significant applications to astronomy. Three-body configurations are often considered stable as long the system is hierarchical; that is, the two orbital…
We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an…
Access to the time-reverse $U^{-1}$ of an unknown quantum unitary process $U$ is widely assumed in quantum learning, metrology, and many-body physics. The fundamental task of unitary time-reversal dictates implementing $U^{-1}$ to within…
Time reversal symmetry is studied in a space with noncommutativity of coordinates and noncommutativity of momenta of canonical type. The circular motion is examined as an apparent example of time reversal symmetry breaking in the space. On…
Modern N-body techniques for planetary dynamics are generally based on symplectic algorithms specially adapted to the Kepler problem. These methods have proven very useful in studying planet formation, but typically require the timestep for…
A common problem in physics and engineering is determination of the orientation of an object given its angular velocity. When the direction of the angular velocity changes in time, this is a nontrivial problem involving coupled differential…
We explore the applicability of splitting methods involving complex coefficients to solve numerically the time-dependent Schr\"odinger equation. We prove that a particular class of integrators are conjugate to unitary methods for…
We consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backprojector pair; i.e., the backprojector is not the exact…
In this paper we introduce an alternative approach to studying the evolution of a quantum harmonic oscillator subject to an arbitrary time dependent force. With the purpose of finding the evolution operator, certain unitary transformations…
This work considers the {\em gravitational} $N$-body problem and introduces global time-renormalization {\em functions} that allow the efficient numerical integration with fixed time-steps. First, a lower bound of the radius of convergence…
In this work, we introduce a quadratically convergent and dynamically consistent integrator specifically designed for the replicator dynamics. The proposed scheme combines a two-stage rational approximation with a normalization step to…
We propose Poisson integrators for the numerical integration of separable Poisson systems. We analyze three situations in which the Poisson systems are separated in three ways and the Poisson integrators can be constructed by using the…
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…
Even though the evolution of an isolated quantum system is unitary, the complexity of interacting many-body systems prevents the observation of recurrences of quantum states for all but the smallest systems. For large systems one can not…
In this paper we study a one-parameter family of attractive reversible nearest particle system on a finite interval. As the length of the interval increases, the time that the nearest particle system first hits the empty set increases in…
The transition from rotational to discontinuous behavior of the return map of the perturbed oscillators-step system, a paradigm model for a perturbation of a pseudo-integrable Hamiltonian impact system, is studied. The form of the return…