Related papers: Non-Abelian evolution systems with conservation la…
We study in this paper some criterions to get polarized morphisms between abelian varieties. We deduce explicit dynamical systems with particular intersection properties.
We construct local zero curvature representations for non-linear sigma models on homogeneous spaces, defined on a space-time of any dimension, following a recently proposed approach to integrable theories in dimensions higher than two. We…
The conservation laws of nonrelativistic and relativistic systems are reviewed and some simple illustrations are provided for the restrictive nature of the relativistic conservation law involving the center of energy compared to the…
The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…
We apply a reduction to the Beauville systems to obtain a family of new algebraic completely integrable systems, related to curves with a cyclic automorphism.
We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting historically from the Heisenberg relations, we will explain…
A model of particle interacting with quantum field is considered. The model includes as particular cases the polaron model and non-relativistic quantum electrodynamics. We compute matrix elements of the evolution operator in the stochastic…
We study the Lax integrability of a nonlinear system of two coupled second-order evolution equations introduced by Ibragimov and Shabat. For this system we find a zero-curvature representation with an essential parameter, construct an…
The well posedness for a class of non local systems of conservation laws in a bounded domain is proved and various stability estimates are provided. This construction is motivated by the modelling of crowd dynamics, which also leads to…
Abelian and Non-Abelian evolution of a quantum system manifests differently in the geometric phase acquired by the system under such evolutions. In this work we develop and study, using dressed state techniques, an experimentally realizable…
We illustrate that a Hermitian nonlinear optical system consisting of hybridized parametric amplification and second harmonic generation mimics non-Hermitian evolution dynamics. Oscillation damping, evolution to a static steady state, and…
This paper presents recent work on connections between symmetries and conservation laws. After reviewing Noether's theorem and its limitations, we present the Direct Construction Method to show how to find directly the conservation laws for…
Building on the recent notion of non-uniform complete observability, and on the fact that this property ensures non-uniform exponential detectability, this paper establishes the converse implication under suitable additional assumptions.…
We prove the interior and boundary null-controllability of some parabolic evolutions with controls acting over measurable sets.
The Hofstadter model exemplifies a large class of physical systems characterized by particles hopping on a lattice immersed in a gauge field. Recent advancements on various synthetic platforms have enabled highly-controllable simulations of…
In this paper we study subalgebras of complex finite dimensional evolution algebras. We obtain the classification of nilpotent evolution algebras whose any subalgebra is an evolution subalgebra with a basis which can be extended to a…
The relativistic formulation of abstract evolution equations is introduced. The corresponding logarithmic representation is shown to exist without assuming the invertible property of evolution operators. Consequently, by means of the…
Genetic and evolution algebras arise naturally from applied probability and stochastic processes. Gibbs measures describe interacting systems commonly studied in thermodynamics and statistical mechanics with applications in several fields.…
We describe work on solutions of certain non-divergence type and therefore non-variational elliptic and parabolic systems on manifolds. These systems include Hermitian and affine harmonics which should become useful tools for studying…
We give the generalization of a recent variational formulation for nonconservative classical mechanics, for fermionic and sypersymmetric systems. Both cases require slightly modified boundary conditions. The supersymmetric version is given…