Zobrazeno 1 - 10
of 34
pro vyhledávání: '"Bosch, Hanne van den"'
We consider Dirac-type operators on manifolds with boundary, and set out to determine all local smooth boundary conditions that give rise to (strongly) regular self-adjoint operators. By combining the general theory of boundary value problems for Dir
Externí odkaz:
http://arxiv.org/abs/2412.17396
We study one- and two-dimensional periodic tight-binding models under the presence of a potential that grows to infinity in one direction, hence preventing the particles to escape in this direction (the soft wall). We prove that a spectral flow appea
Externí odkaz:
http://arxiv.org/abs/2403.02462
We study the linearized Vlasov-Poisson equation in the gravitational case around steady states that are decreasing and continuous functions of the energy. We identify the absolutely continuous spectrum and give criteria for the existence of oscillati
Externí odkaz:
http://arxiv.org/abs/2305.05749
We consider four-component Dirac operators on domains in the plane. With suitable boundary conditions, these operators describe graphene quantum dots. The most general boundary conditions are defined by a matrix depending on four real parameters. For
Externí odkaz:
http://arxiv.org/abs/2211.07568
We estimate the lowest eigenvalue in the gap of the essential spectrum of a Dirac operator with mass in terms of a Lebesgue norm of the potential. Such a bound is the counterpart for Dirac operators of the Keller estimates for the Schr\"odinger opera
Externí odkaz:
http://arxiv.org/abs/2210.03091
We prove phase-space mixing for solutions to Liouville's equation for integrable systems. Under a natural non-harmonicity condition, we obtain weak convergence of the distribution function with rate $\langle \mathrm{time} \rangle^{-1}$. In one dimens
Externí odkaz:
http://arxiv.org/abs/2201.07019
Publikováno v:
Communications in Mathematical Physics 401 (2023) 227--273
We study the spectral stability of the nonlinear Dirac operator in dimension $1+1$, restricting our attention to nonlinearities of the form $f(\langle\psi,\beta \psi\rangle_{\mathbb{C}^2}) \beta$. We obtain bounds on eigenvalues for the linearized op
Externí odkaz:
http://arxiv.org/abs/2102.11703
We study stability properties of kinks for the (1+1)-dimensional nonlinear scalar field theory models \begin{equation*} \partial_t^2\phi -\partial_x^2\phi + W'(\phi) = 0, \quad (t,x)\in\mathbb{R}\times\mathbb{R}. \end{equation*} The orbital stability
Externí odkaz:
http://arxiv.org/abs/2008.01276
We investigate the self-adjointness of the two-dimensional Dirac operator $D$, with quantum-dot and Lorentz-scalar $\delta$-shell boundary conditions, on piecewise $C^2$ domains with finitely many corners. For both models, we prove the existence of a
Externí odkaz:
http://arxiv.org/abs/1902.05010
In this paper we study the existence and non-existence of minimizers for a type of (critical) Poincar\'{e}-Sobolev inequalities. We show that minimizers do exist for smooth domains in $\mathbb{R}^d$, an also for some polyhedral domains. On the other
Externí odkaz:
http://arxiv.org/abs/1810.05698