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.

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 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.

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.

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.

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.

Background and Objectives:-similarity problem defined as measuring the similarity among objects and finding a group of objects from a dataset that have the most similarity to each other. This problem has been become an important issue in information retrieval and data mining. Theory of this concept is mathematically proven, but it practically has high memory complexity and is so time consuming. Besides, the solutions found by metaheuristics are not Exact. Methods: This paper is conducted to propose an Exact Method to solve similarity problem reducing the memory complexity and decreasing the execution time by parallelism using Open-MP. The experiments are performed on the application of text document resemblance. Results: It has been shown that the memory complexity of the proposed Method is decreased to , and the experimental results show that this Method accelerates the speed of the computations about 5 times. Conclusion: The simulated results of the proposed Method display a good improvement in speed, the used memory space, and scalability compared with the previous Exact Method.