Related papers: Semiclassical WKB Problem for the non-self-adjoint…
We introduce a general framework for the study of the diffraction of waves by cone points at high frequencies. We prove that semiclassical regularity propagates through cone points with an almost sharp loss even when the underlying operator…
In designing and optimizing new-generation nanomaterials and related quantum devices, dissipation versus decoherence phenomena are often accounted for via local scattering models, such as relaxation-time and Boltzmann-like schemes. Here we…
Nonlinear charge transport in strongly coupled semiconductor superlattices is described by Wigner-Poisson kinetic equations involving one or two minibands. Electron-electron collisions are treated within the Hartree approximation whereas…
We study nonlinear magneto-optical responses of metals by a semiclassical Boltzmann equation approach. We derive general formulas for linear and second order nonlinear optical effects in the presence of magnetic fields that include both…
We study the approximate analytical solutions of the Dirac equation for the generalized Woods-Saxon potential with the pseudo-centrifugal term. In the framework of the spin and pseudospin symmetry concept, the approximately analytical bound…
In this paper we consider an inverse problem for the $n$-dimensional random Schr\"{o}dinger equation $(\Delta-q+k^2)u = 0$. We study the scattering of plane waves in the presence of a potential $q$ which is assumed to be a Gaussian random…
We examine spectra of Dirac operators on compact hyperbolic surfaces. Particular attention is devoted to symmetry considerations, leading to non-trivial multiplicities of eigenvalues. The relation to spectra of Maass-Laplace operators is…
In the context of some deformed canonical commutation relations leading to isotropic nonzero minimal uncertainties in the position coordinates, a Dirac equation is exactly solved for the first time, namely that corresponding to the Dirac…
The Wentzel-Kramers-Brillouin semiclassical method is formulated for quasiparticles with quartic-in-momentum dispersion which presents the simplest case of a soft energy-momentum dispersion. It is shown that matching wave functions in the…
We study the focusing intercritical NLS \begin{align}\label{abstract_nls} i\pt_t u+\Delta_{x,y}u=-|u|^\alpha u\tag{NLS} \end{align} on the semiperiodic waveguide manifold $\R^d_x\times \T_y$ with $d\geq 5$ and…
The paper deals with the semi-Dirac operator in a half-space arising in the description of quasiparticles in quantum mechanics as well as in semi-metals materials and related structures. It completely shows the self-adjointness, computes…
We develop direct and inverse scattering theory for Jacobi operators which are short range perturbations of quasi-periodic finite-gap operators. We show existence of transformation operators, investigate their properties, derive the…
We consider the self-adjoint operator $H=H_0+V$, where $H_0$ is the free semi-classical Dirac operator on $R^3$. We suppose that the smooth matrix-valued potential $V=O(<x>^{-\delta}), \delta>0,$ has an analytic continuation in a complex…
The Dirac equation is considered in the background of potentials of several types, namely scalar and vector-potentials as well as "Dirac-oscillator" potential or some of its generalisations. We investigate the radial Dirac equation within a…
The supersymmetric WKB (SWKB) condition is supposed to be exact for all known exactly solvable quantum mechanical systems with the shape invariance. Recently, it was claimed that the SWKB condition was not exact for the extended radial…
The use of the sine-Gordon equation as a model of magnetic flux propagation in Josephson junctions motivates studying the initial-value problem for this equation in the semiclassical limit in which the dispersion parameter $\e$ tends to…
The main goal of this paper is to put together: a) the Whitham theory applicable to slowly modulated $N$-phase nonlinear wave solutions to the focusing nonlinear Schr\"odinger (fNLS) equation, and b) the Riemann-Hilbert Problem approach to…
In order to extend the spectral action principle to non-compact spaces, we propose a framework for spectral triples where the algebra may be non-unital but the resolvent of the Dirac operator remains compact. We show that an example is…
The Heisenberg evolution of a given unitary operator corresponds classically to a fixed canonical transformation that is viewed through a moving coordinate system. The operators that form the bases of the Weyl representation and its Fourier…
The paper concerns scattering of plane waves by a bounded obstacle with complex valued impedance boundary conditions. We study the spectrum of the Neumann-to-Dirichlet operator for small wave numbers and long wave asymptotic behavior of the…