In this article we develop an effective medium model to characterize the electron wave propagation in graphene based nanostructures with electrostatic and magnetic vector potentials imposed on their surface. We use a numerical algorithm determine parameters of heterostructure calculate electronic band structure system. apply our formalism analyze superlattices solely potential reveal that respo...

Volume integral formulations for solving electromagnetic problems in the frequency domain are proposed. Firstly, it is based on a magnetic flux B and current density J facet interpolation for representing the electromagnetic problem through an equivalent circuit. Secondly, magnetic vector potentials A and electric vector potential T are considered thanks to discrete geometric approach. The form...

We theoretically investigate superradiance effects in quantum field theories curved space-times by proposing an analog model based on Bose-Einstein condensates subject to a synthetic vector potential. The breaking of the irrotationality constraint superfluids allows us study simple planar geometries and obtain intuitive insight into amplified scattering processes at ergosurfaces. When boundary ...

For the magnetic Hamiltonian with singular vector potentials, we analytically continue resolvent to a logarithmic neighborhood of positive real axis and prove estimates there. As applications, obtain asymptotic locations resonances local smoothing estimate for solutions corresponding Schr\"odinger equation.

The vector decomposition theorem of Helmholtz leads to a form of the Coulomb gauge in which the potentials are expressed in a form that is totally instantaneous. The scalar potential is expressed in terms of the instantaneous charge density, the vector potential in terms of the instantaneous magnetic field.

We study connections between four different types of results that are concerned with vector-valued functions u : Ω → R of class L(Ω) on a domain Ω ⊂ R: Coercivity results in H(Ω) relying on div and curl, the Helmholtz decomposition, the construction of vector potentials, and the global div-curl lemma. Key-words: Friedrichs inquality, coercivity, div-curl lemma, compensated compactness