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We construct the linear and quadratic polynomial dynamical invariants for the classical and quantum time-dependent harmonic oscillator driven by a time-dependent force. To obtain them, we use exclusively the associated equations of motion…

Generation of Wigner functions of Landau levels and determination of their symmetries and generic properties are achieved in the autonomous framework of deformation quantization. Transformation properties of diagonal Wigner functions under…

Numerical simulations of the time-dependent Swift-Hohenberg equation are used to test predictions of Cross [Phys. Rev. A 25:1065-1076 (1982)] that Rayleigh-Benard convection in the form of straight rolls or of an array of dislocations may…

This paper presents a method for learning Hamiltonian dynamics from a limited set of data points. The Hamiltonian vector field is found by regularized optimization over a reproducing kernel Hilbert space of vector fields that are inherently…

The paper suggests a Hamiltonian formulation for delay ordinary differential equations (DODEs). Such equations are related to DODEs with a Lagrangian formulation via a delay analog of the Legendre transformation. The Hamiltonian delay…

We expose some selected topics concerning the instability of the action variables in a priori unstable Hamiltonian systems, and outline a new strategy that may allow to apply these methods to a priori stable systems.

In this paper, a method to construct topological template in terms of symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm the topological template, rotation numbers of invariant manifolds around unstable periodic…

The Hamiltonian of an isolated quantum mechanical system determines its dynamics and physical behaviour. This study investigates the possibility of learning and utilising a system's Hamiltonian and its variational thermal state estimation…

This is a general description of a probabilistic formalism of mechanics, i.e., an extension of the Newtonian mechanics principles to the systems undergoing random motion. From an analysis of the induction procedure from experimental data to…

There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine…

We apply methods of the so-called `inverse problem of the calculus of variations' to the stabilization of an equilibrium of a class of two-dimensional controlled mechanical systems. The class is general enough to include, among others, the…

This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…

We employ variational autoencoders to extract physical insight from a dataset of one-particle Anderson impurity model spectral functions. Autoencoders are trained to find a low-dimensional, latent space representation that faithfully…

This paper explores a mathematical technique for deriving dynamical invariants (i.e. constants of motion) in time-dependent gravitational potentials. The method relies on the construction of a canonical transformation that removes the…

A proposal for a calculational program in fluid turbulence is presented. It is proposed that the fluid probability density functional has an attractor for its time-evolution, just as the dynamical system itself has. The evolution of the…

It is commonplace to encounter nonstationary data, of which the underlying generating process may change over time or across domains. The nonstationarity presents both challenges and opportunities for causal discovery. In this paper we…

We study the circumstances under which one can reconstruct a stack from its associated functor of isomorphism classes. This is possible surprisingly often: we show that many of the standard examples of moduli stacks are determined by their…

We discuss the evaluation of certain d dimensional angular integrals which arise in perturbative field theory calculations. We find that the angular integral with n denominators can be computed in terms of a certain special function, the…

A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…

We describe a computational method for constructing a coarse combinatorial model of some dynamical system in which the macroscopic states are given by elementary cycling motions of the system. Our method is in particular applicable to time…