Related papers: Asymptotic structure of electrodynamics revisited
We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include…
The asymptotic structure of space-time is studied by imposing conditions on the asymptotics of the metric. These conditions are weak enough to include large classes of physically relevant isolated space-times, but have a rich enough…
The role played by non-extensive thermodynamics in physical systems has been under intense debate for the last decades. Some possible mechanisms that could give rise to non-extensive statistics have been formulated along the last few years,…
Asymptotic properties of classical field electrodynamics are considered. Special attention is paid to the long-range structure of the electromagnetic field. It is shown that conserved Poincare quantities may be expressed in terms of the…
The irreversibility of the dynamics of the conservative systems on example of hard disks and potentially of interacting elements is investigated in terms of laws of classical mechanics. The equation of the motion of interacting systems and…
Quantifying irreversibility of a system using finite information constitutes a major challenge in stochastic thermodynamics. We introduce an observable that measures the time-reversal asymmetry between two states after a given time lag. Our…
We will look for an implementation of new symmetries in the space-time structure and their cosmological implications. This search will allow us to find a unified vision for electrodynamics and gravitation. We will attempt to develop a…
The aims of this letter are three-fold: First is to show that nonlinear generalizations of electrodynamics support various types of knotted solutions in vacuum. The solutions are universal in the sense that they do not depend on the…
This is my dissertation. Its research object is a symmetric group of permutations acting on a finite set. The density of permutations with a given cycle structure pattern is explored when the group order tends to infinity. New and sharper…
This text is written based on the author's publications during the period from 1991 to 2001. The work is devoted to the theory of Markov intertwining operators and joinings of measure-preserving group actions, as well as to their…
We introduce a framework for probing the spacetime structure of vacuum entanglement that exhibits infinite range correlations between the future and the past, as well as spatially separated regions. Our results are non-perturbative and…
The main focus of these notes is recent work on linear systems in which line arrangements play a role, including problems such as semi-effectivity, containment problems of symbolic powers of homogeneous ideals in their powers, bounded…
Discontinuous changes in the electronic structure upon infinitesimal changes to the Hamiltonian are demonstrated. Remarkably, these are revealed in one and two electron molecular systems if the realm of the nuclear charge is extended to be…
The nature of the behaviour of an isolated many-body quantum system periodically driven in time has been an open question since the beginning of quantum mechanics. After an initial transient, such a system is known to synchronize with the…
We propose a new notion of Partial Inertial Manifold to study the long-time asymptotic behavior of dissipative differential equations. As shown on an example, such manifolds may exist in the cases when the classical Inertial manifold does…
Some pedagogical aspects of the formulation of electrodynamics independently of the system of units are commented. Only electrodynamics in vacuum is considered. It is pointed out the efficiency of using a notation system close to SI.
We consider a certain ultrahyperbolic equation in a Euclidean space being a generalization of Klein-Gordon-Fock equation. The behavior of solutions at points tending to infinity along timelike directions is studied. We examine the issue of…
We review recent developments in the field of string cosmology with particular emphasis on open problems having to do mainly with geometric asymptotics and singularities. We discuss outstanding issues in a variety of currently popular…
It is well known that the spacetime $\text{AdS}_2\times S^2$ arises as the `near horizon' geometry of the extremal Reisser-Nordstrom solution, and for that reason it has been studied in connection with the AdS/CFT correspondence. Motivated…
We discuss how asymptotic quantities, originally introduced on null infinity in terms of Bondi-type gauge conditions, can be calculated near space-like infinity to any desired precision.