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 ...

For a regular chain R in dimension one, we propose an algorithm which computes the (non-trivial) limit points of the quasi-component of R, that is, the set W (R) \W (R). Our procedure relies on Puiseux series expansions and does not require to compute a system of generators of the saturated ideal of R. We provide experimental results illustrating the benefits of our algorithms.

With modern microelectronics moving towards smaller and smaller length scales on the (sub-) nm scale, quantum effects (apart from band structure and band gaps) have begun to play an increasingly important role. This especially concerns dimensional confinement to 2D (high electron mobility transistors and integer/fractional quantum Hall effect physics, graphene and topological insulators) and 1D...

Due to progress in nanotechnology high-quality quantum wires can nowadays be fabricated. The behavior of particles in one dimension differs significantly from that in three-dimensional (3D) systems, yet the physics of such lowdimensional systems is generally not very well represented in standard undergraduate or graduate curricula. For instance, the Fermi liquid paradigm, working well for elect...

Magnetic impurities coupled antiferromagnetically to a one-dimensional Heisenberg model are studied by numerical diagonalization of chains of finite clusters. By calculating the binding energy and the correlation function, it is shown that a local singlet develops around each impurity. This holds true for systems with a single impurity, with two impurities, and for impurities forming a lattice....

We show how to use variational methods to prove two diierent results: Existence of periodic solutions with irrational periods of some hyperbolic equations in one dimension and existence of spatially quasi-periodic solutions of some elliptic equations .

It is shown that the quasi-one-dimensional Bose-Einstein condensate is experimentally accessible and rich in intriguing phenomena. We demonstrate numerically and analytically the existence, stability, and perturbation-induced dynamics of all types of stationary states of the quasi-one-dimensional nonlinear Schrödinger equation for both repulsive and attractive cases. Among our results are: the ...