Non-Hermitian flat-band generator in one dimension

Energy band correction due to one dimension tension in phosphorene

Among graphene-like family, phosphorene is a typical semiconducting layered material, which can also be a superconductor in low temperature. Applying pressure or tension on phosphorene lattice results in changing the hopping terms, which change the energy bands of the material. In this research we use the tight-binding Hamiltonian, including relevant hopping terms, to calculate energy bands of ...

A QES Band-Structure Problem in One Dimension

I show that the potential V (x,m) = [b 4 −m(1−m)a(a+ 1) ] sn(x,m) dn(x,m) − b(a+ 1 2 ) cn(x,m) dn(x,m) constitutes a QES band-structure problem in one dimension. In particular, I show that for any positive integral or half-integral a, 2a+ 1 band edge eigenvalues and eigenfunctions can be obtained analytically. In the limit of m going to 0 or 1, I recover the well known results for the QES doubl...

An Unusual QES Band-Structure Problem in One Dimension

I show that the potential V (x,m) = [b 4 −m(1−m)a(a+ 1) ] sn(x,m) dn(x,m) − b(a+ 1 2 ) cn(x,m) dn(x,m) constitutes an unusual QES band-structure problem in one dimension. In particular, I show that for any positive integral or half-integral a, 2a+ 1 band edge eigenvalues and eigenfunctions can be obtained analytically. However, the associated orthogonal polynomials satisfy fourterm (rather than...

Simulations of transport in one dimension

Advection-dispersion equation is solved in numerically by using combinations of differential quadrature method (DQM) and various time integration techniques covering some explicit or implicit single and multi step methods. Two different initial boundary value problems modeling conservative and nonconservative transports of some substance represented by initial data are chosen as test problems. ...

Non-rectifiable Limit Sets of Dimension One