Related papers: The Flea on the Magnetic Elephant
This article is devoted to the semiclassical spectral analysis of the magnetic Laplacian in two dimensions. Assuming that the magnetic field is positive and has two symmetric radial wells, we establish an accurate tunnelling formula, that…
Motivated by the analysis of the tunneling effect for the magnetic Laplacian, we introduce an abstract framework for the spectral reduction of a self-adjoint operator to a hermitian matrix. We illustrate this framework by three…
We establish a tunneling formula for a Schr\"odinger operator with symmetric double-well potential and homogeneous magnetic field, in dimension two. Each well is assumed to be radially symmetric and compactly supported. We obtain an…
The two-dimensional magnetic Laplacian is considered. We calculate the leading term of the splitting between the first two eigenvalues of the operator in the semiclassical limit under the assumption that the magnetic field does not vanish…
This paper is devoted to semiclassical tunneling estimates induced on the circle by a double well electric potential in the case when a magnetic field is added. When the two electric wells are connected by two geodesics for the Agmon…
We investigate theoretically the effect of a magnetic field on intersubband polaritons in an asymmetric quantum well placed inside an optical resonator. It is demonstrated that the field-induced diamagnetic shift of electron subbands in the…
This paper deals with semiclassical asymptotics of the three-dimensional magnetic Laplacian in presence of magnetic confinement. Using generic assumptions on the geometry of the confinement, we exhibit three semiclassical scales and their…
We argue that the tunneling between two 2D electron gases in a weak magnetic field is of resonance character, and involves a long lifetime excitonic state of an electron and hole {\it uniformly spread} over cyclotron orbits. We find that…
We present a semiclassical study of a transport process, the tunneling, in the presence of a magnetic field and a dissipative environment. We have found that the problem can be mapped onto an effective one-dimensional one, and the tunneling…
This paper is devoted to the spectral analysis of the Neumann realization of the 2D magnetic Laplacian with semiclassical parameter h > 0 in the case when the magnetic field vanishes along a smooth curve which crosses itself inside a…
This paper is devoted to the spectral analysis of the Laplacian with constant magnetic field on a cone of aperture $\alpha$ and Neumann boundary condition. We analyze the influence of the orientation of the magnetic field. In particular,…
This article establishes, in an analytic framework and in two dimensions, the first WKB constructions describing the eigenfunctions of the pure magnetic Laplacian with low energy when the magnetic field has a unique minimum that is positive…
We investigate analytically the amplification of a weak magnetic field in a homogeneous and isotropic turbulent flow lacking reflectional symmetry (helical turbulence). We propose that the spectral distributions of magnetic energy and…
We investigate the tunneling properties of a two-species few-boson mixture in a one-dimensional triple well and harmonic trap. The mixture is prepared in an initial state with a strong spatial correlation for one species and a complete…
This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are…
The semiclassical magnetic Neumann Schr\"odinger operator on a smooth, bounded, and simply connected domain $\Omega$ of the Euclidean plane is considered. When $\Omega$ has a symmetry axis, the semiclassical splitting of the first two…
We show that the addition of a magnetic field parallel to the current induces self sustained intrinsic current oscillations in an asymmetric double barrier structure. The oscillations are attributed to the nonlinear dynamic coupling of the…
We give a mathematically rigorous construction of a magnetic Schr\"odinger operator corresponding to a field with flux through finitely many holes of the Sierpinski Gasket. The operator is shown to have discrete spectrum accumulating at…
Magnetoresistivity features connected with the spin level coincidences under tilted fields in a $\Gamma_8$ conduction band of the HgTe quantum well were found to align along straight trajectories in a $(B_\bot,B_{||})$ plane between the…
We demonstrate that, in a quasi-two-dimensional electron system confined to an AlAs quantum well and occupying two conduction-band minima (valleys), a parallel magnetic field can couple to the electrons' orbital motion and tune the energies…