Sub-threshold resonances in few-neutron systems

Three- and four-neutron systems are studied within the framework of the hyperspherical approach with a local S-wave nn-potential. Possible bound and resonant states of these systems are sought as zeros of three- and four-body Jost functions in the complex momentum plane. It is found that zeros closest to the origin correspond to sub-threshold (nnn) (1/2-) and (nnnn) (0+) resonant states. The positions of these zeros turned out to be sensitive to the choice of the $nn$--potential. For the Malfliet- Tjon potential they are E(nnn)=-4.9-i6.9 (MeV) and E(nnnn)=-2.6-i9.0 (MeV). Movement of the zeros with an artificial increase of the potential strength also shows an extreme sensitivity to the choice of potential. Thus, to generate ^3n and ^4n bound states, the Yukawa potential needs to be multiplied by 2.67 and 2.32 respectively, while for the Malfliet-Tjon potential the required multiplicative factors are 4.04 and 3.59.Comment: Latex, 22 pages, no PS-figures, submitted to J.Phys.

On a Poisson structure on the space of Stokes matrices

In this paper we study the map associating to a linear differential operator with rational coefficients its monodromy data. The operator has one regular and one irregular singularity of Poincare' rank 1. We compute the Poisson structure of the corresponding Monodromy Preserving Deformation Equations on the space of the monodromy data.Comment: 16 pages,Tex,to be published in IMR

Stability Properties of the Riemann Ellipsoids

We study the ellipticity and the ``Nekhoroshev stability'' (stability properties for finite, but very long, time scales) of the Riemann ellipsoids. We provide numerical evidence that the regions of ellipticity of the ellipsoids of types II and III are larger than those found by Chandrasekhar in the 60's and that all Riemann ellipsoids, except a finite number of codimension one subfamilies, are Nekhoroshev--stable. We base our analysis on a Hamiltonian formulation of the problem on a covering space, using recent results from Hamiltonian perturbation theory.Comment: 29 pages, 6 figure

Existence and uniqueness of solutions for singular fourth-order boundary value problems

AbstractBy mixed monotone method, the existence and uniqueness are established for singular fourth-order boundary value problems. The theorems obtained are very general and complement previous known results

Nonlinear Differential Equations on Bounded and Unbounded Domains

Differential equations represent one of the strongest connections between Mathematics and real life. This is due to the fact that almost all the physical phenomena, as well as many other in economy, biology or chemistry, are modelled by differential equations. This Thesis includes a detailed study of nonlinear differential equations, both on bounded and unbounded domains. In particular, we analyze the qualitative properties of the solutions of nonlinear differential equations, focusing on the study of constant sign solutions on the whole domain of definition or, at least, on some subset of it. The main technique is based on the construction of an abstract formulation included into functional analysis, in which the solutions of the differential equations coincide with the fixed points of certain operators

Existence and multiplicity of solutions for a periodic hill’s equation with parametric dependence and singularities

We deal with the existence and multiplicity of solutions for the periodic boundary value problem positive parameter. The function f : is allowed to be singular, and the related Green’s function is nonnegative and can vanish at some points.This work was partially supported by FEDER and Ministerio de Educacion y Ciencia, Spain, project no. MTM2010-15314S

Multi-Scale Jacobi Method for Anderson Localization

A new KAM-style proof of Anderson localization is obtained. A sequence of local rotations is defined, such that off-diagonal matrix elements of the Hamiltonian are driven rapidly to zero. This leads to the first proof via multi-scale analysis of exponential decay of the eigenfunction correlator (this implies strong dynamical localization). The method has been used in recent work on many-body localization [arXiv:1403.7837].Comment: 34 pages, 8 figures, clarifications and corrections for published version; more detail in Section 4.

Attitude stability of a spinning passive orbiting satellite

Attitude stability of spinning passive orbiting satellit