Related papers: Magnetic WKB Constructions
We study the effect of a magnetic field on the behaviour of a conducting elastic rod subject to a novel set of boundary conditions that, in the case of a transversely isotropic rod, give rise to exact helical post-buckling solutions. The…
Quantum wires occupy a unique status among the semiconducting nanostructures with reduced dimensionality -- no other system seems to have engaged researchers with as many appealing features to pursue. This paper aims at a core issue related…
We study interacting electrons in a periodic potential and a uniform magnetic field ${\bf B}$ taking the spin-orbit interaction into account. We first establish a perturbation expansion for those electrons with respect to the Bloch states…
The purpose of this paper is to prove optimal estimates for solutions of the Kohn-Laplacian for certain classes of model domains in several complex variables. This will be achieved by applying a type of singular integral operator whose…
This thesis deals with the systematic treatment of quantum-mechanical systems in post-Newtonian gravitational fields. Starting from clearly spelled-out assumptions, employing a framework of geometric background structures defining the…
We study the inflationary generation of helical cosmological magnetic fields in a higher-dimensional generalization of the electromagnetic theory. For this purpose, we also include a parity breaking piece to the electromagnetic action. The…
We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for…
We construct solutions to the nonlinear magnetic Schr\"odinger equation $$ \left\{ \begin{aligned} - \varepsilon^2 \Delta_{A/\varepsilon^2} u + V u &= \lvert u\rvert^{p-2} u & &\text{in}\ \Omega,\\ u &= 0 & &\text{on}\ \partial\Omega,…
We obtain the rigorous WKB expansion to all orders for the radial Kepler problem, using the residue calculus in evaluating the WKB quantization condition in terms of a complex contour integral in the complexified coordinate plane. The…
To give a general description of the influences of electric fields or currents on magnetization dynamics, we developed a semiclassical theory for the magnetization implicitly coupled to electronic degrees of freedom. In the absence of…
The feasibility of obtaining exact analytical results in the realm of QED in the presence of a background electromagnetic field is almost exclusively limited to a few tractable cases, where the Dirac equation in the corresponding background…
We consider a restricted baby Skyrme-Maxwell scenario enlarged via the inclusion of a nontrivial magnetic permeability. We then proceed with the minimization of its total energy by means of the Bogomol'nyi-Prasad-Sommerfield (BPS)…
We perform a rigorous mathematical analysis of the bending modes of a linear triatomic molecule that exhibits the Renner-Teller effect. Assuming the potentials are smooth, we prove that the wave functions and energy levels have asymptotic…
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…
Orbital magnetism is a purely quantum phenomenon that reflects intrinsic electronic properties of solids, yet its microscopic description in interacting multiband systems remains incomplete. We develop a general quantum many-body framework…
We consider Kramers-Fokker-Planck operators with general degenerate coefficients. We prove semiclassical hypocoercivity estimates for a large class of such operators. Then, we manage to prove Eyring-Kramers formulas for the bottom of the…
We study the quantum Hamilton-Jacobi (QHJ) equation of the recently obtained exactly solvable models, related to the newly discovered exceptional polynomials and show that the QHJ formalism reproduces the exact eigenvalues and the…
For uniform arrangements of magnetic fields, strings, or domain walls (together with the cosmological constant and non-relativistic matter), exact solutions to the Einstein equations are shown to lead to a universe with ellipsoidal…
Considering both the nonlinear invariant terms constructed by the electromagnetic field and the Riemann tensor in gravity action, we obtain a new class of $(n+1)$-dimensional magnetic brane solutions in third order Lovelock-Born-Infeld…
In the context of the semiclassical treatment of Hawking radiation we prove the universality of the reduced canonical momentum for the system of a massive shell self gravitating in a spherical gravitational field within the Painlev\'e…