A quantum mechanical description of the experiment on the observation of gravitationally bound states

Quantum states in the earth’s gravitational field have been observed, with ultra-cold neutrons falling under gravity. The experimental results can be described by the quantum mechanical scattering model presented here. We also discuss other geometries of the experimental setup, which correspond to the absence or the reversion of gravity. Since our quantum mechanical model quantitatively describes, particularly, the experimentally realized situation of reversed gravity, we can practically rule out alternative explanations of the quantum states, in terms of pure confinement effects. PACS  03.65.Ge; 03.65.Ta; 04.62.+v; 04.80.-y; 61.12.Ex     

Polytope Lyapunov Functions for Stable and for Stabilizable LSS

We present a new approach for constructing polytope Lyapunov functions for continuous-time linear switching systems (LSS). This allows us to decide the stability of LSS and to compute the Lyapunov exponent with a good precision in relatively high dimensions. The same technique is also extended for stabilizability of positive systems by evaluating a polytope concave Lyapunov function (“antinorm”) in the cone. The method is based on a suitable discretization of the underlying continuous system and provides both a lower and an upper bound for the Lyapunov exponent. The absolute error in the Lyapunov exponent computation is estimated from above and proved to be linear in the dwell time. The practical efficiency of the new method is demonstrated in several examples and in the list of numerical experiments with randomly generated matrices of dimensions up to 10 (for general linear systems) and up to 100 (for positive systems). The development of the method is based on several theoretical results proved in the paper: the existence of monotone invariant norms and antinorms for positively irreducible systems, the equivalence of all contractive norms for stable systems and the linear convergence theorem.     

Refinement equations with nonnegative coefficients

In this paper we analyze solutions of the n-scale functional equation Ф(x) = Σ_k∈ℤ ^Pk Ф(nx−k), where n≥2 is an integer, the coefficients {P_k} are nonnegative and Σpk = 1. We construct a sharp criterion for the existence of absolutely continuous solutions of bounded variation. This criterion implies several results concerning the problem of integrable solutions of n-scale refinement equations and the problem of absolutely continuity of distribution function of one random series. Further we obtain a complete classification of refinement equations with positive coefficients (in the case of finitely many terms) with respect to the existence of continuous or integrable compactly supported solutions.     

Anomalous Electrical Conductivity and Magnetization in Fe–Cr–Ni Austenite–Martensite Alloys

Technical Physics - We have measured the temperature dependence of the resistivity and magnetization of a special steel of the Fe–Cr–Ni austenite–martensite class in a wide...