Supersymmetric Hamiltonian and Vortex Formation Model in a Quantum Nonlinear System in an Inhomogeneous Electromagnetic Field. Issue 5 (18th March 2019) - Manzetti, Sergio; Trounev, Alexander
Abstract: Vortices and quasiparticles in 2D systems are studied for the last decades in relation to the development of technologies in quantum electromagnetics, optics, and quantum computation. Hamiltonians are a fundamental part for studying quasiparticles and vortices, and provide models to calculate the eigenvalues and eigenfunctions that describe a real physical state. By devising supersymmetry, a Hamiltonian for the description of vortices is developed forming in an 2D electron gas and study the numerical solutions under the effects of an alternating electromagnetic field. The numerical analysis shows that vorticity is formed spontaneously without symmetry‐breaking and vortices arise from the boundaries and converge toward the center of the system in a similar fashion to natural hydrodynamic phenomena in water or plasma. Additionally, the equation under damping conditions is studied, a homogenous magnetic field and under the absence of an electromagnetic field. The results and the study of the parameters indicate that the supersymmetic wave equation (SWE) may be a good model equation to describe vorticity for quantum electromagnetics, hydrodynamics, and other physical phenomena in the realm of physical and quantum physical sciences. Abstract : A supersymmetric wave‐equation (SWE) is developed for the analysis of vortex dynamics in 2D quantum systems. The supersymmetry‐derived wave‐equation describes vortex formation without symmetry breaking. Numerical analysis of the vortex formation is carried out under damped conditions and under a variating electromagnetic field and an electric field. Results show that the SWE describes quantized vortex systems, and can be applied to large‐ and small‐ scale vorticity phenomena.