Related papers: Semiclassical WKB Problem for the non-self-adjoint…
Wave equations with energy-dependent potentials appear in many areas of physics, ranging from nuclear physics to black hole perturbation theory. In this work, we use the semi-classical WKB method to first revisit the computation of bound…
This paper is concerned with the efficient numerical computation of solutions to the 1D stationary Schr\"odinger equation in the semiclassical limit in the highly oscillatory regime. A previous approach to this problem based on explicitly…
This article concerns the long-time dynamics of quantum particles in the semi-classical regime. First, we show that for the nonlinear Hartree equation with short-range interaction potential, small-data solutions obey dispersion bounds and…
We study the resonant set of a two-level Schr\"odinger operator with a linear conical intersection. This model operator can be decomposed into a direct sum of first order systems on the real half-line. For these ordinary differential…
We justify the WKB analysis for the semiclassical nonlinear Schr\"{o}dinger equation with a subquadratic potential. This concerns subcritical, critical, and supercritical cases as far as the geometrical optics method is concerned. In the…
We study the coupled system of Maxwell and Dirac equations from a semiclassical point of view. A rigorous nonlinear WKB-analysis, locally in time, for solutions of (critical) order $O(\sqrt{\epsilon})$ is performed, where the small…
We revisit the well known Bohr-Sommerfeld quantization rule (BS) of order 2 for a self-adjoint 1-D h-Pseudo-differential operator within the algebraic and microlocal framework of Helffer and Sjoestrand; BS holds precisely when Gram matrix…
We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schr\"odinger equation, of relevance…
We are interested in a WKB analysis of the Logarithmic Non-Linear Schr\"odinger Equation with "Riemann-like" variables in an analytic framework in semiclassical regime. We show that the Cauchy problem is locally well posed uniformly in the…
We generalize Wentzel-Kramers-Brillouin (WKB) semi-classical equations for pseudospin-1 $\alpha-\mathcal{T}_3$ materials with arbitrary hopping parameter $0 < \alpha < 1$, which includes the dice lattice and graphene as two limiting cases.…
The semiclassical limit of the focusing Nonlinear (cubic) Schr\" odinger Equation (NLS) corresponds to the singularly perturbed Zakharov Shabat (ZS) system that defines the direct and inverse scattering transforms (IST). In this paper, we…
In this paper the spectral and scattering properties of a family of self-adjoint Dirac operators in $L^2(\Omega; \mathbb{C}^4)$, where $\Omega \subset \mathbb{R}^3$ is either a bounded or an unbounded domain with a compact $C^2$-smooth…
We provide new information concerning the pseudospectra of the complex harmonic oscillator. Our analysis illustrates two different techniques for getting resolvent norm estimates. The first uses the JWKB method and extends for this…
We have developed a complete semiclassical Wentzel-Kramers-Brillouin (WKB) theory for $\alpha-\mathcal{T}_3$ model which describes a wide class of existing pseudospin-1 Dirac cone materials. By expanding the sought wave functions in a…
We derive a determinant formula for the WKB exponential of singularly perturbed Zakharov-Shabat system that corresponds to the semiclassical (zero dispersion) limit of the focusing Nonlinear Schr\" odinger equation. The derivation is based…
We study the eigenvalues of the self-adjoint Zakharov-Shabat operator corresponding to the defocusing nonlinear Schrodinger equation in the inverse scattering method. Real eigenvalues exist when the square of the potential has a simple…
We study the spectrum of a periodic non-self-adjoint Dirac operator, and its dependence on a semiclassical parameter is also considered. Several bounds on the spectrum are obtained which provide sharp spectral enclosure estimates.…
This paper is concerned with a 1D Schr\"odinger scattering problem involving both oscillatory and evanescent regimes, separated by jump discontinuities in the potential function, to avoid "turning points". We derive a non-overlapping domain…
We analyze the eigenvalue problem for the semiclassical Dirac (or Zakharov-Shabat) operator on the real line with general analytic potential. We provide Bohr-Sommerfeld quantization conditions near energy levels where the potential exhibits…
Rigorous pointwise asymptotics are established for semiclassical soliton ensembles (SSEs) of the focusing nonlinear Schroedinger equation using techniques of asymptotic analysis of matrix Riemann-Hilbert problems. The accumulation of poles…