Related papers: Drift-Free Conservative Dynamics from Quantized In…
Experiments on bird flocks and midge swarms reveal that these natural systems are well described by an active theory in which conservation laws play a crucial role. By building a symplectic structure that couples the particles' velocities…
A temporally varying discretization often features in discrete gravitational systems and appears in lattice field theory models subject to a coarse graining or refining dynamics. To better understand such discretization changing dynamics in…
Burgers equation is a classic model, which arises in numerous applications. At its very core it is a simple conservation law, which serves as a toy model for various dynamics phenomena. In particular, it supports explicit heteroclinic…
We focus on entropy admissible solutions of scalar conservation laws in one space dimension and establish new regularity results with respect to time. First, we assume that the flux function $f$ is strictly convex and show that, for every $…
Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In…
Control over spin dynamics has been obtained in NMR via coherent averaging, which is implemented through a sequence of RF pulses, and via quantum codes which can protect against incoherent evolution. Here, we discuss the design and…
A generic data-assisted control architecture within the port-Hamiltonian framework is proposed, introducing a physically meaningful observable that links conservative dynamics to all actuation, dissipation, and disturbance channels. A…
We address here the topological equivalence of knots through the so-called Reidemeister moves. These topology-conserving manipulations are recast into dynamical rules on the crossings of knot diagrams. This is presented in terms of a simple…
The quantization scheme by noncommutative geometry developed in string theory is applied to establish the conservation law of twisted spin and spin current densities in the spin-orbit coupled systems. Starting from the pedagogical…
We study diffusion processes driven by a Brownian motion with regular drift in a finite dimension setting. The drift has two components on different time scales, a fast conservative component and a slow dissipative component. Using the…
The motion of a radiating point particle can be represented by a series of geodesics whose "constants" of motion evolve slowly with time. The evolution of these constants of motion can be determined directly from the self-force equations of…
Preservation of linear and quadratic invariants by numerical integrators has been well studied. However, many systems have linear or quadratic observables that are not invariant, but which satisfy evolution equations expressing important…
We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be…
This research note documents new developments regarding finite-element discretizations of the relativistic Beliaev-Budker Coulomb collision operator and the nonrelativistic Landau operator. Where energy conservation in a finite-element…
Conservation laws can constrain entanglement dynamics in isolated quantum systems, manifest in a slowdown of higher R\'enyi entropies. Here, we explore this phenomenon in a class of long-range random Clifford circuits with U$(1)$ symmetry…
In this work we complete the spin-dependent conservative dynamics of inspiralling compact binaries at the fourth post-Newtonian order, and in particular the derivation of the next-to-next-to-leading order spin-squared interaction potential.…
This paper studies the problem of stabilizing target formations specified by inter-neighbor bearings with relative position measurements. While the undirected case has been studied in the existing works, this paper focuses on the case where…
We extend beyond the Euler scales the hydrodynamic theory for quantum and classical integrable models developed in recent years, accounting for diffusive dynamics and local entropy production. We review how the diffusive scale can be…
We develop an interacting extension of the Double Covariance Model (DCM), a stochastic subquantum framework in which macroscopic quantum dynamics emerge through coarse-graining of correlated microscopic fluctuations. Starting from local…
Entropic Dynamics is an information-based framework that seeks to derive the laws of physics as an application of the methods of entropic inference. The dynamics is derived by maximizing an entropy subject to constraints that represent the…