We consider unitary analogs of d−dimensional Anderson models on l2(Zd) defined by the product Uω = DωS where S is a deterministic unitary and Dω is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on parameters controlling the size of its off-diagonal elements. We adapt the method of Aizenman-Molchanov to get exponential estimates o...

Smallest and greatest 1-Lipschitz aggregation operators with given diagonal section, opposite diagonal section, and with graphs passing through a single point of the unit cube, respectively, are determined. These results are used to find smallest and greatest copulas and quasi-copulas with these properties (provided they exist).

We analyze the peculiarities of the motional narrowing effect in disordered one-dimensional Frenkel chains with off-diagonal disorder, induced by uncorrelated Gaussian fluctuations in the positions of the host units. A clear difference in the scaling laws with respect to the magnitude of the positional disorder and the chain size is found, as compared to those for uncorrelated diagonal disorder...

A general fusion method to find solutions to the reflection equation in higher spin representations starting from the fundamental one is shown. The method is illustrated by applying it to obtaining the K diagonal boundary matrices in an alternating spin 1/2 and spin 1 chain. The hamiltonian is also given. The applicability of the method to higher rank algebras is shown by obtaining the K diagon...

In this paper, the off-diagonal geometric phase of thermal state in hydrogen atom under the effects of external magnetic field is considered. Increasing temperature tends to suppress the off-diagonal geometric phase, including 1-order and 2-order cases. On the other hand, the relationship between the geometric phase and external magnetic field is discussed.

In this article, we introduce a family of weighted lattice paths, whose step set is {H = (1, 0), V = (0, 1), D1 = (1, 1), . . . , Dm−1 = (1,m − 1)}. Using these lattice paths, we define a family of Riordan arrays whose sum on the rising diagonal is the k-bonacci sequence. This construction generalizes the Pascal and Delannoy Riordan arrays, whose sum on the rising diagonal is the Fibonacci and ...

We derive a general expression for the multipole expansion of the electromagnetic interaction in relativistic heavy-ion collisions, which can be employed in higher-order dynamical calculations of Coulomb excitation. The interaction has diagonal as well as off-diagonal multipole components, associated with the intrinsic and relative coordinates of projectile and target. A simple truncation in th...

Our goal is to find an asymptotic behavior as n ? ? of the orthogonal polynomials P ( z ) defined by Jacobi recurrence coefficients a (off-diagonal terms) and b (diagonal terms). We consider case , in such way that ? ? 1 < (that is, Carleman condition violated) ? : = 2 ? . In | ? formulas for are known; they depend crucially on sign study critical The obtained qualitatively different cases 0 + ...

Let A = [Uii] be a non-negative matrix. A diagonal of A is a set of positions D,,={(U(I). I). . . . . (O(H), II)) of A where u is a permutation of { !, . . . , n). A position of A is called positive if the entry of A from that position is positive. The diagonal D,, is called a positive diagonal provided all its positions are positive. Since the notion of a positive diagonal depends only on the ...