Related papers: A Short Comparison of Classical Complex Dynamics a…

This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…

It is shown that the vacuum state of weakly interacting quantum field theories can be described, in the Heisenberg picture, as a linear combination of randomly distributed incoherent paths that obey classical equations of motion with…

This paper extends the classical theory of joinings of measurable dynamical systems to the noncommutative setting from several interconnected points of view. Among these is a particularly fruitful identification of joinings with equivariant…

We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…

The aim of this paper is to study the semi-classical behaviour of Schr\"odinger's dynamics for an one-dimesional quantum Hamiltonian with a classical hyperbolic trajectory. As in the regular case (elliptic trajectory), we prove, that for an…

The theory of polynomial-like maps is of fundamental importance in holomorphic dynamics. We study dynamical properties of a larger class of maps. Our main result is that, under some natural conditions, a map of this class has a completely…

We address the decay in open chaotic quantum systems and calculate semiclassical corrections to the classical exponential decay. We confirm random matrix predictions and, going beyond, calculate Ehrenfest time effects. To support our…

We consider the quantum kinetic-theory description for interacting massive spin-half fermions using the Wigner function formalism. We derive a general kinetic theory description assuming that the spin effects appear at the classical and…

An integrable Hamiltonian system presents monodromy if the action-angle variables cannot be defined globally. As a prototype of classical monodromy with azimuthal symmetry, we consider a linear molecule interacting with external fields and…

We study the Moyal evolution of the canonical position and momentum variables. We compare it with the classical evolution and show that, contrary to what is commonly found in the literature, the two dynamics do not coincide. We prove that…

Let F be a totally real field and p a rational prime unramified in F. We prove a partial classicality theorem for overconvergent Hilbert modular forms: when the slope is small compared to certain but not all weights, an overconvergent form…

Given two quasi-definite moment functionals, the corresponding orthogonal polynomial systems satisfy an algebraic differential relation(called an extended coherent pair). We study generalizing extended coherent pairs that unify extended…

The probabilistic description of finite classical systems often leads to linear kinetic equations. A set of physically motivated mathematical requirements is accordingly formulated. We show that it necessarily implies that solutions of such…

We consider complex manifolds that admit actions by holomorphic transformations of classical simple real Lie groups and classify all such manifolds in a natural situation. Under our assumptions, which require the group at hand to be…

We are interested in finding a dense part of the space of $C^1$-diffeomorphisms which decomposes into open subsets corresponding to different dynamical behaviors: we discuss results and questions in this direction. In particular we present…

Conformable derivatives involve a fractional parameter while preserving locality: on smooth functions they reduce to a classical derivative multiplied by an explicit weight. Exploiting this structural feature, we show that conformable time…

The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…

In this article we give a panoramic view on semi-classical analysis.

In these four lectures I describe basic ideas and methods applicable to both classical and quantum systems displaying slow relaxation and non-equilibrium dynamics. The first half of these notes considers classical systems, and the second…

We study the dynamics of an arbitrary semigroup of transcendental entire functions using Fatou-Julia theory. Several results of the dynamics associated with iteration of a transcendental entire function have been extended to transcendental…