Related papers: The characteristic polynomial of the next-nearest-…
In this overview paper a direct approach to q-Chebyshev polynomials and their elementary properties is given. Special emphasis is placed on analogies with the classical case. There are also some connections with q-tangent and q-Genocchi…
The Julia set of the Chebyshev's method applied to polynomials with exactly two distinct roots is shown to be connected, and its Fatou set is proved to be the union of attracting basins corresponding to the two roots. Further, if the two…
We primarily investigate the properties of characteristic polynomials of semimatroids. In particular, we provide a combinatorial interpretation of their coefficients, generalizing the Whitney's Broken Circuit Theorem. We also prove that the…
We analyze Su-Schrieffer-Heeger (SSH) models using the doubling method for orthogonal polynomial sequences. This approach yields the analytical spectrum and exact eigenstates of the models. We demonstrate that the standard SSH model is…
We use complete enumeration and Monte Carlo techniques to study two-dimensional self-avoiding polymer chains with quenched ``charges'' $\pm 1$. The interaction of charges at neighboring lattice sites is described by $q_i q_j$. We find that…
We theoretically investigate the dynamical phase diagram of a one-dimensional chain of laser-excited two-species Rydberg atoms. The existence of a variety of unique dynamical phases in the experimentally-achievable parameter region is…
In this contribution we give an explicit formula for the eigenvectors of Hamiltonians of open Bazhanov-Stroganov quantum chain. The Hamiltonians of this quantum chain is defined by the generation polynomial $A_n(\lambda)$ which is…
An effective Hamiltonian and equations of motion for treating both the resonant dipole-dipole interaction between two-level atoms and the resonant atom-field interaction are derived, which can suitably be used for studying the influence of…
We calculate the values of observables in chiral eigenstates of the XX quantum spin chain that were introduced in previous work and compare the form of the result with the respective expressions obtained in the more familiar eigenbasis of…
The polynomials that arise as coefficients when a power series is raised to the power $x$ include many important special cases, which have surprising properties that are not widely known. This paper explains how to recognize and use such…
Double ionization of an atom by single-photon absorption in the presence of a neighbouring atom is studied. The latter is, first, resonantly photoexcited and, afterwards, transfers the excitation energy radiationlessly to the other atom,…
We investigate the entire family of multi-center point interaction Hamiltonians. We show that a large sub-family of these operators do not become either singular or trivial when the positions of two or more scattering centers tend to…
The single-particle spectral properties near the Mott transition in the two-dimensional Hubbard model with next-nearest-neighbor hopping are investigated by using cluster perturbation theory. Complicated spectral features of this model are…
The low-energy eigenstates of two interacting electrons in a square quantum dot in a magnetic field are determined by numerical diagonalization. In the strong correlation regime, the low-energy eigenstates show Aharonov-Bohm type…
We study polynomials with complex coefficients which are nondegenerate in two senses, one of Kouchnirenko and the other with respect to its Newton polyhedron, through data on contact loci and motivic nearby cycles. Introducing an explicit…
Photoionization of an atom via interatomic correlations to N neighboring atoms may be strongly enhanced due to constructive interference of quantum pathways. The ionization proceeds via resonant photoexcitation of a neighbor atom and…
The study of sequences of polynomials satisfying high order recurrence relations is connected with the asymptotic behavior of multiple orthogonal polynomials, the convergence properties of type II Hermite-Pad\'e approximation, and…
Quantum correlations between two neighbor atoms are studied. It is assumed that one atomic system comprises a single auto-ionizing level and the other atom does not contain any auto-ionizing level. The excitation of both atoms is achieved…
We obtain the following characterization of $Q$-polynomial distance-regular graphs. Let $\G$ denote a distance-regular graph with diameter $d\ge 3$. Let $E$ denote a minimal idempotent of $\G$ which is not the trivial idempotent $E_0$. Let…
By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and then we obtain an explicit expression for the generic term of the coefficient sequence, which yields the trace…