[en] A reply to the comment on the paper by Ansaripour (2010 Phys. Scr. 82 045008). (reply to comment)

[en] We study L²-solutions of (-Δ+V-E)ψ = 0 in Rⁿ, n ≥ 2 and derive a sharp upper bound to l_x0(ψ) in terms of x₀, E and V under rather restrictive assumptions on V. We show for V smooth that an upper bound to l_x0(ψ) implies an upper bound to the dimension of the eigenspace associated to E. 16 refs. (Authors)

[en] The power iteration method is the standard Monte Carlo approach for obtaining the eigenfunctions of a nuclear system, but the power method sometimes converges very slowly. Most discussions give a mathematical reason for the slow convergence of the Monte Carlo power method using the same concepts and terminology as when the power method is applied to a deterministic problem. This note first looks at why the convergence is slow from an intuitive Monte Carlo neutron perspective. Second, this note proposes building an eigenfunction intuitively in a cumulative (and noniterative) neutron by neutron manner that tends to better direct neutrons to where the neutrons need to be. Third, a very similar method for building the second eigenfunction is speculatively proposed.

[en] Yangian symmetric correlators are defined as eigenfunctions of monodromy operators. Examples and relations are given and an evaluation method of the symmetry condition is described

[en] A holographic description of scalar mesons is presented, in which two- and three-point functions are hieroglyphically reconstructed. Mass spectrum, decay constants, eigenfunctions and the coupling of the scalar states with two pseudoscalars are found. A comparison of the results with current phenomenology is discussed.

[en] The quantum SL(3,ℂ)-invariant spin magnet with infinite-dimensional principal series representation in local spaces is considered. We construct eigenfunctions of the Sklyanin B-operator which define the representation of separated variables of the model.

[en] A higher rank generalization of the (rank one) Racah algebra is obtained as the symmetry algebra of the Laplace–Dunkl operator associated to the ${\mathbb{Z}}_2^n$ root system. This algebra is also the invariance algebra of the generic superintegrable model on the n-sphere. Bases of Dunkl harmonics are constructed explicitly using a Cauchy–Kovalevskaia theorem. These bases consist of joint eigenfunctions of labelling Abelian subalgebras of the higher rank Racah algebra. A method to obtain expressions for both the connection coefficients between these bases and the action of the symmetries on these bases is presented. (paper)

[en] A study is made of the iso-energetic spectral problem for two classes of multidimensional periodic difference operators. The first class of operators is defined on a regular simplicial lattice. The second class is defined on a standard rectangular lattice and is the difference analogue of a multidimensional Schroedinger operator. The varieties arising in the direct spectral problem are described, along with the divisor of an eigenfunction, defined on the spectral variety, of the corresponding operator. Multidimensional analogues are given for the Veselov-Novikov correspondences connecting the divisors of the eigenfunction with the canonical divisor of the spectral variety. Also, a method is proposed for solving the inverse spectral problem in terms of θ-functions of curves lying 'at infinity' on the spectral variety

[en] We consider some special reductions of generic Darboux-Crum dressing formulae and of their difference versions. As a matter of fact, we obtain some new formulae for Darboux-Poeschl-Teller (DPT) potentials by means of Wronskian determinants. For their difference deformations (called DDPT-I and DDPT-II potentials) and the related eigenfunctions, we obtain new formulae described by the ratios of Casorati determinants given by the functional difference generalization of the Darboux-Crum dressing formula.

[en] A new method is applied for calculating the escape rate from chaotic repellers or semi-attractors, based on the eigenvalue problem of the master equation of discrete dynamical systems. The corresponding eigenfunction is found to be smooth along unstable directions and to be, in general, a fractal measure. Examples of one and two dimensional maps are investigated. (author)