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The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…
We study the transport of a quantum particle through square lattices of various sizes by employing the tight-binding Hamiltonian from quantum percolation. Input and output semi-infinite chains are attached to the lattice either by diagonal…
All metamaterial applications are based upon the idea that extreme material properties can be achieved through appropriate dynamic homogenization of composites. This homogenization is almost always done for infinite domains and the results…
Transmission probabilities of the scattering problem with a position dependent mass are studied. After sketching the basis of the theory, within the context of the Schr\"{o}dinger equation for spatially varying effective mass, the simplest…
We describe the bound state and scattering properties of a quantum mechanical particle in a scalar $N$-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy…
Crossing symmetry asserts that particles are indistinguishable from anti-particles traveling back in time. In quantum field theory, this statement translates to the long-standing conjecture that probabilities for observing the two scenarios…
Reciprocity is a universal principle that has a profound impact on many areas of physics. A fundamental phenomenon in condensed-matter physics, optical physics and acoustics, arising from reciprocity, is the constructive interference of…
Within an effective Dirac-Weyl theory we solve the scattering problem for massless chiral fermions impinging on a cylindrical time-dependent potential barrier. The set-up we consider can be used to model the electron propagation in a…
If scattering amplitudes are ordinary complex numbers (not quaternions) there is a universal algebraic relationship between the six coherent cross sections of any three scatterers (taken singly and pairwise). A violation of this…
We discuss a model in which a quantum particle passes through $\delta$ potentials arranged in an increasingly sparse way. For infinitely many barriers we derive conditions, expressed in terms ergodic properties of wave function phases,…
The barrier distribution, originated from channel coupling effects in heavy-ion fusion reactions, has been extracted experimentally for many systems using either a fusion excitation function or an excitation function of large-angle…
Scattering matrices with block symmetry, which corresponds to scattering process on cavities with geometrical symmetry, are analyzed. The distribution of transmission coefficient is computed for different number of channels in the case of a…
Classical and quantum properties of scattering of charged particles in ultrathin crystals are considered. A comparison is made of these two ways of study of scattering process. In the classical consideration we remark the appearance of…
We study a question arising in inverse scattering theory: given a penetrable obstacle, does there exist an incident wave that does not scatter? We show that every penetrable obstacle with real-analytic boundary admits such an incident wave.…
Many systems occurring in real-world applications, such as controlling the motions of robots or modeling the spread of diseases, are switched impulsive systems. To ensure that the system state stays in a safe region (e.g., to avoid…
Recent experiments have revealed that the meniscus formed near a surface-piercing barrier can significantly alter the propagation and scattering of capillary-gravity surface waves, beyond what classic flat-surface models predict. In…
We consider simple models of tunneling of an object with intrinsic degrees of freedom. This important problem was not extensively studied until now, in spite of numerous applications in various areas of physics and astrophysics. We show…
The stationary phase method is often employed for computing tunneling {\em phase} times of analytically-continuous {\em gaussian} or infinite-bandwidth step pulses which collide with a potential barrier. The indiscriminate utilization of…
Superscattering, i.e., a phenomenon of the scattering cross section from a subwavelength object exceeding the single-channel limit, has important prospects in enhanced sensing/spectroscopy, solar cells, and biomedical imaging.…
We present model calculations for the Landauer conductance of tunnel junctions. The tunneling of free electrons through a rectangular potential barrier is considered. The conductance of a finite number of barriers was calculated using a…