Related papers: Conservation laws in the continuum $1/r^2$ systems
It is shown that the traditional conservation laws for total charge, energy, linear and angular momentum, hold jointly in classical electron theory if and only if classical electron spin is included as dynamical degree of freedom.
The equations of fluid motions are considered in the case of internal energy depending on mass density, volume entropy and their spatial derivatives. The model corresponds to domains with large density gradients in which the temperature is…
We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion…
An interesting observation was reported by Corrigan-Sasaki that all the frequencies of small oscillations around equilibrium are " quantised" for Calogero and Sutherland (C-S) systems, typical integrable multi-particle dynamics. We present…
Within a strong coupling expansion, we construct local quasi-conserved operators for a class of Hamiltonians that includes both integrable and non-integrable models. We explicitly show that at the lowest orders of perturbation theory the…
We explore the relationship between mechanical systems describing the motion of a particle with the mechanical systems describing a continuous medium. More specifically, we will study how the so-called intermediate integrals or fields of…
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…
We give a direct proof of the relation between vacuum singular vectors and conservation laws for the quantum KdV equation or equivalently for $\Phi_{(1,3)}$-perturbed conformal field theories. For each degree at which a classical…
Whether gravity must be quantized remains one of the biggest open problems in fundamental physics. Classical-quantum hybrid theories have recently attracted attention as a possible framework in which gravity is treated classically yet…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
Generalising a result of classical mechanics an infinite set of conserved quantities can be found for the bare equations of motion describing the evolution of a scalar field in out of equilibrium quantum field theory, in the large N…
We study the stability of quantum motion of classically regular systems in presence of small perturbations. Onthe base of a uniform semiclassical theory we derive the fidelity decay which displays a quite complexbehaviour, from Gaussian to…
In classical continuum mechanics, quasi-linear systems of conservation laws can be symmetrized if they admit an additional convex conservation law. In particular, this implies the hyperbolicity of governing equations. For capillary fluids,…
We study conservation laws of a general class of quantum many-body systems subjected to an external time dependent quasi-periodic driving. {When the frequency of the driving is large enough or the strength of the driving is small enough, we…
The aim of this paper is to describe a class of conservative systems on $S^2$ possessing an integral cubic in momenta. We prove that this class of systems consists off the case of Goryachev-Chaplygin, the one-parameter family of systems…
It's well known that Noether symmetries lead to the conservation laws. Conserved quantities are constructed out of generator of the symmetry - invariant Hamiltonian vector field. Considering more general class of vector fields -…
The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical applications the latter is either the…
The appearance of a geometric flow in the conservation law of particle number in classical particle diffusion and in the conservation law of probability in quantum mechanics is discussed in the geometrical environment of a two-dimensional…
Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…
Examples are worked out using a new equation proposed in the previous paper to show that it has new physical predictions for mesoscopic systems.