Quantum mechanical phenomena have a ected our lives in numerous ways. Their impact on modern technology ranges from everyday applications such as transistors, lasers and solar cells to ground breaking equipment such as Scanning-Tunneling electron microscopes. However, in spite all results in fundamental quantum theory research, various aspects of the theory are still not fully understood. This ...

In the quantized two-dimensional non-linear supersymmetric σ-model, the supercurrent supermultiplet, which contains the energy-momentum tensor, is transformed by the nonlocal symmetry of the model into the isospin current supermultiplet. This effect incorporates supersymmetry into the known infinite-dimensional Yangian deformation symmetry of plain σ-models, leads to precisely the same nontrivi...

We present an existence theory based on minimization of the nonlocal energies appearing in peridynamics, which is a nonlocal continuum model in solid mechanics that avoids the use of deformation gradients. We employ the direct method of the calculus of variations in order to find minimizers of the energy of a deformation. Lower semicontinuity is proved under a weaker condition than convexity, w...

Magnetohydrodynamic turbulence affects both terrestrial and astrophysical plasmas. The properties of magnetized must be better understood to more accurately characterize these systems. This work presents ideal MHD simulations the compressible Taylor-Green vortex under a range initial sub-sonic Mach numbers magnetic field strengths. We find that regardless strength, energy becomes dominant over ...

Abstract In this paper, we present numerical studies of a recently proposed scalar nonlocal nonlinear conservation law in one space dimension. The nonlocal model accounts for nonlocal interactions over a finite horizon and enjoys maximum principle, monotonicity-preserving and entropy condition on the continuum level. Moreover, it has a well-defined local limit given by a conventional local cons...

Abstract Partial wave theory of a three dmensional scattering problem for an arbitray short range potential and a nonlocal Aharonov-Bohm magnetic flux is established. The scattering process of a “hard shere” like potential and the magnetic flux is examined. An anomalous total cross section is revealed at the specific quantized magnetic flux at low energy which helps explain the composite fermio...

The electromagnetic enhancement factor for surface enhanced Raman scattering is reexamined taking into account the nonlocal dielectric response of the substrate surface. Surface roughness is represented typically by a spherical island and nonlocal effect is introduced via a simple phenomenological model which makes possible a closer quantitative comparison with experiments. It is found that the...

We study the bound states of two-dimensional bright solitons in nonlocal nonlin-ear media. The general properties and stability of these multisolitary structures are investigated analytically and numerically. We have found that a steady bound state of coherent nonrotating and rotating solitary structures (azimuthons) can exist above some threshold power. A dipolar nonrotating multisoliton occur...