Related papers: Irrational Numbers of Constant Type --- A New Char…
In the context of quantum field theory, an anomaly exists when a theory has a classical symmetry which is not a symmetry of the quantum theory. This short exposition aims at introducing a new point of view, which is that the proper setting…
We prove that for a large and important class of $C^1$ twist maps of the torus periodic and quasi-periodic orbits of a new type exist, provided that there are no rotational invariant circles (R.I.C's). These orbits have a non-zero…
Motivated by intuitive properties of physical quantities, the notion of a non-anomalous semigroup is formulated. These are totally ordered semigroups where there are no `infinitesimally close' elements. The real numbers are then defined as…
We show that a recently proposed numerical technique for the calculation of unstable periodic orbits in chaotic attractors is capable of finding the least unstable periodic orbits of any given order. This is achieved by introducing a…
We show that quasiparticle excitations with irrational charge and irrational exchange statistics exist in tight-biding systems described, in the continuum approximation, by the Dirac equation in (2+1)-dimensional space and time. These…
In this paper, we will first summarize known results concerning continued fractions. Then we will limit our consideration to continued fractions of quadratic numbers. The second author described periods and sometimes precise form of…
The possibility of variations of the values of fundamental constants is a phenomenon predicted by a number of scenarios beyond General Relativity. This can happen if ``our'' fundamental constants are not the actual constants of the…
We define a new unstable state in the Friedrichs model of a two-level atom. This unstable state is a complex eigenstate of the time evolution operator $\exp(-iHt)$ with a restricted test function space, which is obtained from causality…
The theory of continued fractions has been generalized to l-adic numbers by several authors and presents many differences with respect to the real case. In the present paper we investigate the expansion of rationals and quadratic…
The concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms…
A new measure to characterize stability of complex dynamical systems against large perturbation is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable to disrupt the system and switch it…
Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…
Recently, sub-indices and sub-factors of groups with connections to number theory, additive combinatorics, and factorization of groups have been introduced and studied. Since all group subsets are considered in the theory and there are many…
Some fundamental aspects related with the construction of Robertson-Schr\"odinger like uncertainty principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum…
We shall show that the rotation of some irrational rotation number on the circle admits suspensions which are kinematic expansive.
In this article, we give an account of some recent irreducibility testing criteria for polynomials having integer coefficients over the field of rational numbers.
The multi-valued quantum $j$-invariant in positive characteristic is studied at quadratic elements. For every quadratic $f$, an explicit expression for each of the values of $j^{\rm qt}(f)$ is given as a limit of rational functions of $f$.…
The non-relativistic version of the multi-temporal quantization scheme of relativistic particles in a family of non-inertial frames (see hep-th/0502194) is defined. At the classical level the description of a family of non-rigid…
The theory of integral quadratic constraints (IQCs) allows verification of stability and gain-bound properties of systems containing nonlinear or uncertain elements. Gain bounds often imply exponential stability, but it can be challenging…
We establish stability criterion for a two-class retrial system with Poisson inputs, general class-dependent service times and class-dependent constant retrial rates. We also characterise an interesting phenomenon of partial stability when…