In this paper, the problem of diagonalization of the autocovariance matrices of stationary processes is discussed. Basically, there is no explicit form for the diagonal matrices. An analytic solution has been provided for stationary ARMA models based on Band matrices. The results have been compared with Dargahi-Noubary and Fuller in a numerical study. It has been demonstrated that the results are more accurate compared to Dargahi-Noubary and Fuller approaches.

Hubbard model is an important model in the theory of strongly correlated electron systems. In this contribution we introduce this model and the concepts of electron correlation by building on a tight binding model. After enumerating various methods of tackling the Hubbard model, we introduce the numerical method of exact diagonalization in detail. The book keeping and practical implementation aspects are illustrated with analytically solvable example of two-site Hubbard model.

In this paper, first, we introduced a quantum system and how to create a quantum dot-paid and then with regard to the calculation of a quantum system uses quantum dots define a Hamiltonian for a Coulomb potential is caused by an electric dipole special functions particularly well as it could have obtained the relevant amounts. Finally, using a numerical method to compare the two discussed.

This manuscript is the collection of lectures given in the summer school on strongly correlated electron systems held at Isfahan University of technology, June 2007. A short overview on quantum magnetism and spin systems is presented. The numerical exact diagonalization (Lanczos) alghorithm is explained in a pedagogical ground. This is a method to get some ground state properties on finite cluster of lattice models. Two extensions of Lanczos method to get the excited states and also finite temperature properties of quantum models are also explained. The basic notions of quantum phase transition are discussed in term of Ising model in transverse field. Its phase diagram and critical properties are explained using the quantum renormalization group approach. Most of the topics are in tutorial level with hints to recent research activities.

In this paper, the electronic structure of a two-dimensional quantum ring under the influence of external electric and magnetic fields are studied in the presence of Rashba and Dresselhaus spin-orbit interactions. To do this, at first, the effective Hamiltonian of the system is demonstrated in the presence of applied electric and magnetic fields by considering the spin-orbit coupling. Afterwards, the Schrodinger equation is solved using the matrix diagonalization approach. Then, we investigate the effects of external fields and the size of the ring on the eigenvalues of the system. Our results indicate that spin-orbit interactions, external fields and the ring size have a great influence on the electronic structure of the system.

In the present work, the exact diagonalization method had been implemented to calculate the ground state energy of shallow donor impurity located at finite distance along the growth axis in GaAs/AlGaAs heterostructure in the presence of a magnetic field taken to be along z direction. The impurity binding energy of the ground state had been calculated as a function of confining frequency and magnetic field strength. We found that the ground state donor binding energy (BE) calculated at c ω =2R * and * 0 ω = 5. 421R, decreases from BE=7. 59822 R * to BE=2. 85165 R *, as we change the impurity position from d=0. 0 a* to d=0. 5 a*, respectively. In addition, the combined effects of pressure and temperature on the binding energy, as a function of magnetic field strength and impurity position, had been shown using the effective-mass approximation. The numerical results show that the donor impurity binding energy enhances with increasing the pressure while it decreases as the temperature decreases.

The ground state energies of two interacting electrons confined in a coupled double quantum dot (DQD) presented in a magnetic field has been calculated by solving the relative Hamiltonian using variational and exact diagonalization methods. The singlet-triplet transitions in the angular momentum and spin of the quantum dot ground state had been shown. We have studied the magnetic field versus confining frequency and magnetic field versus potential barrier height phase diagram of DQD. Furthermore, we have investigated the dependence of the exchange energy of two electron double quantum dot on the confining frequency, potential height barrier, barrier width and magnetic field strength. The comparisons show that our results are in very good agreement with reported works.

In this paper, a new method is proposed for DOA estimation of correlated acoustic signals, in the presence of unknown spatial correlation noise. By generating a matrix from the signal subspace with the Hankel-SVD method, the correlated resource information is extracted from each eigenvector. Then a joint-diagonalization structure is constructed of the signal subspace and basis it, independent linear component, related to sources are recovered. Simulation results and comparisons with other commonly presented methods show the capability of this algorithm in low signal-to-noise ratio and close sources.

In this paper, the crystal field parameters (CFPs) have been calculated in the framework of the density functional theory using a novel theoretical approach proposed by Pavel Nová k et al. and extracting the WANNIER functions from the Bloch eigenstates for the CeCl3 compound. Then, the calculated CFPs have been used in an effective atomic-like Hamiltonian, including the crystal field, 4f-4f correlation and spin-orbit coupling, and the splitted energy levels of Ce3+ ion by crystal field have been derived by diagonalization of the Hamiltonian. A hybridization parameter, , has been used to improve the results. The results are found to be in agreement with the experimental data.