相关论文: Infinite dimensional symmetry groups of the Friedm…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
By a choice of new variables the pressure isotropy condition for spherically symmetric static perfect fluid spacetimes can be made a quadratic algebraic equation in one of the two functions appearing in it. Using the other variable as a…
We report a symmetry property of the Einstein-Friedmann equations for spatially flat Friedmann-Lema\^itre-Robertson-Walker universes filled with a perfect fluid with any constant equation of state. The symmetry transformations form a…
The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are…
We consider the relationship between symmetries of two-dimensional autonomous dynamical system in two common formulations; as a set of differential equations for the derivative of each state with respect to time, and a single differential…
Few equilibrium --even less so nonequilibrium-- statistical-mechanical models with continuous degrees of freedom can be solved exactly. Classical hard-spheres in infinitely many space dimensions are a notable exception. We show that even…
Given a quantum system consisting of many parts, we show that symmetry of the system's state, i.e., invariance under swappings of the subsystems, implies that almost all of its parts are virtually identical and independent of each other.…
In this paper, we show that a universe with a dynamical cosmological constant approaching pure de Sitter at timelike infinity, enjoys an infinite dimensional symmetry group at its horizon. This group is larger than the usual $SO(4,1)$ of…
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical…
Dependent symmetries, symmetries that depend on the situation of the subsystem in a larger closed system, are explored by looking at simple examples. This is a new kind of symmetry in the open quantum dynamics of a subsystem Each symmetry…
There are two very important subjects in physics: Symmetry of dynamical models and nonlinearity. All really fundamental models are invariant under some particular symmetry groups. There is also no true physics, no our Universe and life at…
The flow of the relativistic imperfect fluid in two dimensions is discussed. We calculate the symmetry group of the energy-momentum tensor conservation equation in the ultrarelativistic limit. Group-invariant solutions for the…
We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The…
A new approach for arbitrary dimension to the Friedmann cosmological models is presented. Taking suitable changes of the parameters of the spacetime the harmonic motion equations appear, where the curvature determines the angular frequency.…
We show that the Yang-Baxter equations for two dimensional models admit as a group of symmetry the infinite discrete group $A_2^{(1)}$. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the…
The symmetry group structures of two dimensional coupled nonlinear Shr\"{o}dinger equations are considered. We first show that the equations admit infinite dimensional symmetry algebra as well as the corresponding symmetry group depending…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
New boundary conditions for asymptotically flat spacetimes are given at spatial infinity. These boundary conditions are invariant under the BMS group, which acts non trivially. The boundary conditions fulfill all standard consistency…
We present a theory characterizing the phases emerging as a consequence of continuous symmetry-breaking in quantum and classical systems. In symmetry-breaking phases, dynamics is restricted due to the existence of a set of conserved charges…
Given the considerable theoretical challenges in understanding strongly coupled metals and non-Fermi liquids, it is valuable to have a framework to understand properties of metals that are universal, in the sense that they must hold in any…