In this paper energy bands and Berry curvature of graphene was studied. Desired Hamiltonian regarding the next-nearest neighbors obtained by tight binding model. By using the second quantization approach, the transformation matrix is calculated and the Hamiltonian of system is diagonalized. With this Hamiltonian, the band structure and wave function can be calculated. By using calculated wave f...

‎In this paper Lie point symmetries‎, ‎Hamiltonian equations and conservation‎ ‎laws of general three-dimensional anisotropic non-linear sourceless heat transfer‎ ‎equation are investigated‎. ‎First of all Lie symmetries are obtained by using the general method‎ based on invariance condition of a system of differential equations under a pro‎longed vector field‎. ‎Then the structure of symmetry ...

An L×∞ system of odd number of coupled Heisenberg spin chains is studied using a degenerate perturbation theory, where L is the number of coupled chains. An effective chain Hamiltonian is derived explicitly in terms of two spin half degrees of freedom of a closed chain of L sites, valid in the regime the inter-chain coupling is stronger than the intra-chain coupling. The spin gap has been calcu...

The Bose-Hubbard hamiltonian will be introduced and justified as an effective description of some relevant physical systems (dilute alkali gases in optical lattices, arrays of Josephson junctions). I will also show a mean field theory solution and the resulting phase diagram. Finally, I will describe in detail one of the more important experiments with an optical lattice of Rb atoms. 1. The Bos...

A perturbative renormalization group (RG) scheme for light-front Hamiltonian is formulated on the basis of the Bloch-Horowitz effective Hamiltonian, and applied to the simplest φ4 model with spontaneous breaking of the Z2 symmetry. RG equations are derived at one-loop order for both symmetric and broken phases. The equations are consistent with those calculated in the covariant perturbation the...