Related papers: Integral formulation of Dirac singular waveguides
Consider the wave propagation in a two-layered medium consisting of a homogeneous compressible air or fluid on top of a homogeneous isotropic elastic solid. The interface between the two layers is assumed to be an unbounded rough surface.…
We give a geometrical derivation of the Dirac equation by considering a spin-1/2 particle travelling with the speed of light in a cubic spacetime lattice. The mass of the particle acts to flip the multi-component wavefunction at the lattice…
The propagation of a dissipative solitary wave across an interface is studied in a binary complex plasma. The experiments were performed under microgravity conditions in the PK-3 Plus Laboratory on board the International Space Station…
Problems of pulse excitation in an acoustic waveguide with a flexible wall and in an acoustic half-space with a flexible wall are studied. In both cases the flexible wall is described by a thin plate equation. The solutions are written as…
In this work, we perform a statistical study on Dirac Billiards in the extreme quantum limit (a single open channel on the leads). Our numerical analysis uses a large ensemble of random matrices and demonstrates the preponderant role of…
We simplify and generalize an approach proposed by Di Vecchia and Ravndal to describe a massive Dirac particle in external vector and scalar fields. Two different path integral representations for the propagator are derived systematically…
Physical self-adjoint extensions and their spectra of the one-dimensional Dirac type Hamiltonian operator in which both the mass and velocity are constant except for a finite jump at one point of the real axis are correctly found. Different…
Boundary integral equation is derived for the problem of scattering of electromagnetic waves by 3D homogeneous body of arbitrary shape.
In this work we analyze the complex scaling method applied to the problem of time-harmonic scalar wave propagation in junctions between `leaky,' or open dielectric waveguides. In [arXiv:2302.04353, arXiv:2310.05816, arXiv:2401.04674,…
At the interface between two massless Dirac models with opposite helicity a paradoxical situation arises: A transversally impinging electron can seemingly neither be transmitted nor reflected, due to the locking between spin and momentum.…
We study large traveling surface waves within a two-dimensional finite depth, free boundary, homogeneous, incompressible and viscous fluid governed by Darcy's law. The fluid is bound by a gravitational force to a flat rigid bottom and meets…
We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. We assume that the wave speed is constant, and that the initial conditions and forcing terms are radially…
We investigate a two-dimensional transmission model consisting of a wave equation and a Kirchhoff plate equation with dynamical boundary controls under geometric conditions. The two equations are coupled through transmission conditions…
The low-energy excitations in many condensed matter and metamaterial systems can be well described by the Dirac equation. The mass term associated with these collective excitations, also known as the Dirac mass, can take any value and is…
We find the density matrix corresponding to the vacuum state of a massless Dirac field in two dimensions reduced to a region of the space formed by several disjoint intervals. We calculate explicitly its spectral decomposition. The…
The interaction of a solitary wave front with an interface formed by two strongly-nonlinear non-cohesive granular lattices displays rich behaviour, characterized by the breakdown of continuum equations of motion in the vicinity of the…
The two-component approach to the one-dimensional Dirac equation is applied to the Woods-Saxon potential. The scattering and bound state solutions are derived and the conditions for a transmission resonance (when the transmission…
A domain wall separating two different topological phases of the same crystal can support the propagation of backscattering-immune guided waves. In valley-Hall and quantum-Hall crystal waveguides, this property stems from symmetry…
A semi-infinite crack loaded by a general asymmetric system of forces in an infinite bi-material plane is considered. A boundary integral formulation is derived using the fundamental reciprocal identity (Betti formula). The resulting…
The aim of this work is to find exact solutions of the one-dimensional Dirac equation that do not belong to the already known conventional class. We write the spinor wavefunction as a bounded infinite sum in a complete basis set, which is…