Related papers: Semiclassical resonances under local magnetic fiel…
We develop the complex scaling for a manifold with an asymptotically cylindrical end under an assumption on the analyticity of the metric with respect to the axial coordinate of the end. We allow for arbitrarily slow convergence of the…
This paper is concerned with the magnetic Laplacian $P^h (\A)=(h D+\A)^2$ in semiclassical analysis, where $h$ is a semiclassical parameter. We study the $L^2$ Neumann and Dirichlet problems for the equation $P^h(\A)u=0$ in a bounded…
Non-autonomous perturbations of isochronous systems in the plane are considered. It is assumed that the intensity of perturbations decays with time, and the frequency is asymptotically constant with the limiting value satisfying a resonance…
We consider a quantum graph as a model of graphene in constant magnetic field and describe the density of states in terms of relativistic Landau levels satisfying a Bohr--Sommerfeld quantization condition. That provides semiclassical…
Semiclassical methods are extremely valuable in the study of transport and thermodynamical properties of ballistic microstructures. By expressing the conductance in terms of classical trajectories, we demonstrate that quantum interference…
In a system with Dirac cones, spatial modulation in material parameters induces a pseudo magnetic field, which acts like an external magnetic field. Here, we derive a concise formula to count the pseudo Landau levels in the simplest setup…
Using a semiclassical ansatz we analytically predict for the fidelity of delta-kicked rotors the occurrence of revivals and the disappearance of intermediate revival peaks arising from the breaking of a symmetry in the initial conditions. A…
We consider in the whole plane the Hamiltonian coupling of semilinear Schroedinger equations which have critical growth in the sense of Moser. We prove that the (nonempty) set S of ground state solutions is compact up to translations.…
We have studied the time evolution of magnetization of a high spin magnetic cluster in the ground state, in the presence of a sinusoidal axial magnetic field and a static transverse field by explicitly solving time dependent schr\"odinger…
We investigate novel Landau level structures of semi-metals with nodal ring dispersions. When the magnetic field is applied parallel to the plane in which the ring lies, there exist almost non-dispersive Landau levels at the Fermi level…
We derive a general quasiclassical approach for long-range magnetic-field quantization effects in superconductors. The method is applied to superclean d-wave superconductors in the mixed state. We study the delocalized states with energies…
In this paper, we define and study semi-classical analysis and semi-classical limits on compact nil-manifolds. As an application, we obtain properties of quantum limits for sub-Laplacians in this context, and more generally for positive…
Exploring the relationship between geometry and the resonant frequencies of a shape is of interest to pure and applied mathematicians. These resonant frequencies are related to the spectrum of the Laplacian, a partial differential operator.…
This work is a continuation of our recent study of non-relativistic charged particles, confined to a sphere enclosing a magnetic dipole at its center. In this sequel, we extend our computations in two significant ways. The first is to a…
The magnetic Laplacian on hyperbolic surfaces provides a rich analytic framework in which a variety of quantum phenomena emerge. The present note, written for the \emph{Proceedings of the Journ\'ees EDP 2025}, is a concise overview of the…
For a class of non compact Riemannian manifolds with ends, we give pseudo-differential expansions of bounded functions of the semi-classical Laplacian and study related Lp boundedness properties.
Selftrapping has been traditionally studied on the assumption that quasiparticles interact with harmonic phonons and that this interaction is linear in the displacement of the phonon. To complement recent semiclassical studies of…
We investigate the scalar-wave resonances of systems composed of identical Neumann-type inclusions arranged periodically around a circular ring. Drawing on natural similarities with the undamped Rayleigh-Bloch waves supported by infinite…
The semiclassical orbitals of a relativistic electron on a rotating sphere threaded by an intense magnetic dipole field are examined. Several physically distinct regimes emerge, depending on the relative sizes of the mass, total energy,…
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…