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 ...

Predicting and controlling quantum mechanical phenomena require knowledge of the system Hamiltonian. A detailed understanding of the quantum pathways used to construct the Hamiltonian is essential for deterministic control and improved performance of coherent control schemes. In complex systems, parameters characterizing the pathways, especially those associated with inter-particle interactions...

We revisit the HD molecular ion by starting from a definition of the nonrelativistic adiabatic Hamiltonian that recovers the isotopic splitting. The Hamiltonian is written in prolate spheroidal coordinates with the origin at the nuclear center of mass. This prescription for the adiabatic Hamiltonian implicitly contains the symmetrybreaking effects arising from the mass difference between the pr...

Interaction of alkali atoms with external magnetic field induced a splitting and a shift of their energy levels. We have study this interaction for external field from 0 to 5000 Gauss when the alkali vapor is confined in submicron thin vapor cell with thickness L = λ/2. Rubidium and Sodium vapors have been studied. The Hamiltonian can be expressed as the sum of the unperturbated atomic Hamilton...

published in Advance ACS Absrracrs, February 1 , 1994. 0022-365419412098-2158$04.50/0 exists in larger quantum dots (11000 atoms) for which such methods appear impractical. Three classes of electronic structure approaches exist for such large sizes: ( i ) The Effective Mass Approximation (EMA).lo Here one replaces the microscopic quasi-periodic potential V(r) (which exists inside the material) ...

This is the continuation of a previous article in which the Bjorken and Voloshin sum rules were interpreted as statements of conservation of probability and energy. Here the formalism is extended to higher moments of the Hamiltonian operator. From the conservation of the second moment of the Hamiltonian operator one can derive a sum rule which, in the small velocity limit, reduces to the Bigi-G...

We investigate the celebrated analogy [1] between Anderson localization phenomena in condensed matter physics [2] and related effects in the ionization process of driven Rydberg atoms, and put them on a quantitative footing. The atomic system we consider for a comprehensive numerical analysis of its ionization properties is a highly excited hydrogen atom exposed to a monochromatic electromagnet...

Electroweak radiative corrections to the matrix elements 〈ns1/2|ĤPNC|n′p1/2〉 are calculated for highly charged hydrogenlike ions. These matrix elements constitute the basis for the description of the most parity nonconserving (PNC) processes in atomic physics. The operator ĤPNC represents the parity nonconserving relativistic effective atomic Hamiltonian at the tree level. The deviation of thes...

We illuminate the importance of a self-consistent many-body treatment in calculations of vacuum polarization corrections to the energies of atomic orbitals in many-electron atoms. Including vacuum polarization in the atomic Hamiltonian causes a readjustment (relaxation) of the electrostatic self-consistent field. The induced change in the electrostatic energies is substantial for states with th...