Position-dependent mass approach and quantization for a torus Lagrangian

Abstract

We have shown that a Lagrangian for a torus surface can yield second order nonlinear differential equations using the Euler-Lagrange formulation. It is seen that these second order nonlinear differential equations can be transformed into the nonlinear quadratic and Mathews-Lakshmanan equations using the position dependent mass approach developed by Mustafa [15] for the classical systems. Then, we have applied the quantization procedure to the nonlinear quadratic and MathewsLakshmanan equations and found their exact solutions.

The stabilizer group of honeycomb lattices and its application to deformed monolayers

“…We have shown here how to build a lattice that enjoys such property. Related work in photonic lattices can be found in [34], while the extended discrete symmetry C P T was studied in [35], with additional contributions to symmetry breaking in [36].…”