Related papers: Learning Hamiltonians of constrained mechanical sy…

We develop a computational method to learn a molecular Hamiltonian matrix from matrix-valued time series of the electron density. As we demonstrate for three small molecules, the resulting Hamiltonians can be used for electron density…

Efficiently characterising quantum systems, verifying operations of quantum devices and validating underpinning physical models, are central challenges for the development of quantum technologies and for our continued understanding of…

Data driven models of dynamical systems help planners and controllers to provide more precise and accurate motions. Most model learning algorithms will try to minimize a loss function between the observed data and the model's predictions.…

A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward…

We explore a particular approach to the analysis of dynamical and geometrical properties of autonomous, Pfaffian non-holonomic systems in classical mechanics. The method is based on the construction of a certain auxiliary constrained…

The most common physical formalisms are the Lagrangian formalism and the Hamiltonian formalism. From the superficial point of view, they are one and the same, but rewritten in other terms. However, it seems that the Hamiltonian formalism…

We consider a relativistic extended object described by a reparametrization invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the…

We propose new symplectic networks (SympNets) for identifying Hamiltonian systems from data based on a composition of linear, activation and gradient modules. In particular, we define two classes of SympNets: the LA-SympNets composed of…

The Hamiltonian Monte Carlo method generates samples by introducing a mechanical system that explores the target density. For distributions on manifolds it is not always simple to perform the mechanics as a result of the lack of global…

This paper develops a new approach to small time local attainability of smooth manifolds of any dimension, possibly with boundary and to prove H\"older continuity of the minimum time function. We give explicit pointwise conditions of any…

This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…

This paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomically constrained system, and characterize regularity…

This paper shows that various relevant dynamical systems can be described as vector fields associated to smooth functions via a bracket that defines what we call a Leibniz structure. We show that gradient flows, some dissipative systems,…

The singularity structure of solutions of a class of Hamiltonian systems of ordinary differential equations in two dependent variables is studied. It is shown that for any solution, all movable singularities, obtained by analytic…

The reasons which restrict opportunities of classical mechanics at the description of nonequilibrium systems are discussed. The way of overcoming of the key restrictions is offered. This way is based on an opportunity of representation of…

The problem of proper symmetry definition for constraint dynamical systems with Hamiltonians is considered. Finally, we choose a definition of symmetry which agrees with the analogous definition used for the non-constraint dynamical systems…

Near-integrability is usually associated with smooth small perturbations of smooth integrable systems. Studying integrable mechanical Hamiltonian flows with impacts that respect the symmetries of the integrable structure provides an…

Spinfoam models provide a covariant formulation of the dynamics of loop quantum gravity. They are non-perturbatively defined in the group field theory (GFT) framework: the GFT partition function defines the sum of spinfoam transition…

Transport in Hamiltonian systems with weak chaotic perturbations has been much studied in the past. In this paper, we introduce a new class of problems: transport in Hamiltonian systems with slowly changing phase space structure that are…

The relative equilibria of a symmetric Hamiltonian dynamical system are the critical points of the so-called augmented Hamiltonian. The underlying geometric structure of the system is used to decompose the critical point equations and…