相关论文: The characteristic polynomial of the next-nearest-…
We calculate the radiative properties for a linear dipole-coupled chain of qubits. Using the explicit energy eigenstates of the system, we find the radiation patterns for spontaneous transitions from the one-photon eigenstates to the ground…
The characteristic polynomial of the effective Hamiltonian for a general model has been discussed. It is found that, compared with the associated energy eigenvalues, this characteristic polynomial generally has better analytical properties…
We calculate the energy eigenvalues and eigenstates corresponding to coherent single and multiple excitations of an array of N identical qubits or two-level atoms (TLA's) arranged on the vertices of a regular polygon. We assume only that…
We present a technique to identify exact analytic expressions for the multi-quantum eigenstates of a linear chain of coupled qubits. A choice of Hilbert subspaces is described which allows an exact solution of the stationary Schr\"{o}dinger…
We explore some interesting features of the characteristic polynomial of the Cartan matrix of a simple Lie algebra. The characteristic polynomial is closely related with the Chebyshev polynomials of first and second kind. In addition, we…
The electronic properties of one-dimensional clusters of N atoms or molecules have been studied. The model used is similar to the Kronig-Penney model with the potential offered by each ion being approximated by an attractive delta function.…
A self-consistent-field theory is given for the electronic collective modes of a chain containing a finite number, $N$, of Coulomb-coupled spherical two-dimensional electron gases (S2DE's) arranged with their centers along a straight line,…
We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the…
We present analysis of a system of three two-level atoms interacting with each other through the dipole-dipole interaction. The interaction manifests between excited state of one of the atoms and the ground state of its nearest neighbour.…
Modifications of photoionization arising from resonant electron-electron correlations between neighbouring atoms in an atomic sample are studied. The sample contains atomic species A and B, with the ionization potential of A being smaller…
In this paper, we investigate characteristic polynomials of matrices in min-plus algebra. Eigenvalues of min-plus matrices are known to be the minimum roots of the characteristic polynomials based on tropical determinants which are designed…
We develop a theory for the interaction of classical light fields with an a chain of coupled quantum dots (QDs), in the strong-coupling regime, taking into account the local-field effects. The QD chain is modeled by a one-dimensional (1D)…
Entanglement between two electrons belonging to an auto-ionization system and a neighbor two-level atom produced by the dipole-dipole interaction is studied. The entanglement is quantified using the quadratic negativity of a bipartite…
Polynomial ensembles are a sub-class of probability measures within determinantal point processes. Examples include products of independent random matrices, with applications to Lyapunov exponents, and random matrices with an external…
The discrete Fourier analysis on the $30^{\degree}$-$60^{\degree}$-$90^{\degree}$ triangle is deduced from the corresponding results on the regular hexagon by considering functions invariant under the group $G_2$, which leads to the…
The problem of one pair of identical nucleons sitting in ${\cal N}$ single particle levels of a potential well and interacting through the pairing force is treated introducing, in the Hamiltonian formalism, even Grassmann variables. The…
Fibonacci chains are special diatomic, harmonic chains with uniform nearest neighbour interaction and two kinds of atoms (mass-ratio $r$) arranged according to the self-similar binary Fibonacci sequence $ABAABABA...$, which is obtained by…
Resonant dipole-dipole interaction modifies the energy and decay rate of electronic excitations for finite one dimensional chains of ultracold atoms in an optical lattice. We show that collective excited states of the atomic chain can be…
For a family of near banded Toeplitz matrices, generalized characteristic polynomials are shown to be orthogonal polynomials of two variables, which include the Chebyshev polynomials of the second kind on the deltoid as a special case.…
Non-separable $D-$dimensional partial differential Schr\"{o}dinger equations are considered at $D=2$ and $D=3$, with the even-parity local potentials $V(x,y,\ldots)$ which are polynomials of degree four (cusp catastrophe resembling case)…