We review recent progresses in the study of flat band systems, especially focusing on fundamental physics related to singularity band’s Bloch wave functions. first explain that bands can be classified into two classes: singular and non-singular bands, based presence or absence The is generated by crossing with another dispersive band. In band, one find a special kind eigenmodes, called non-cont...

Abstract Bootstrap methods, initially developed for solving statistical and quantum field theories, have recently been shown to capture the discrete spectrum of mechanical problems, such as single particle Schrödinger equation with an anharmonic potential. The core bootstrap methods builds on exact recursion relations arbitrary moments some operator use adequate set positivity criteria. We exte...

oligoclonal bands (ocb) can be detected in a significant percentage (90%) of patients with multiple sclerosis (ms), however, a much lower percentage has been reported in some studies, mainly from oriental countries. on the other hand, ocb have been detected in other neurological disorders (ond), even in diseases without any definite evidence for inflammation in csf such as myasthenia gravis. th...

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...