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pro vyhledávání: '"Assal, Marouane"'
We analyze the properties of the spectral shift function (SSF) for some dispersive self-adjoint operators under suitable compact perturbations. New mechanisms allowing the SSF to have singularities at the thresholds are exhibited, based on the degene
Externí odkaz:
http://arxiv.org/abs/2409.13942
We consider a 1D $2\times 2$ matrix-valued operator \eqref{System0} with two semiclassical Schr\"odinger operators on the diagonal entries and small interactions on the off-diagonal ones. When the two potentials cross at a turning point with contact
Externí odkaz:
http://arxiv.org/abs/2402.19219
This paper is concerned with the asymptotics of resonances in the semiclassical limit $h\to 0^+$ for $2\times 2$ matrix Schr\"odinger operators in one dimension. We study the case where the two underlying classical Hamiltonian trajectories cross tang
Externí odkaz:
http://arxiv.org/abs/2211.11651
We study the distribution of resonances for discrete Hamiltonians of the form $H_0+V$ near the thresholds of the spectrum of $H_0$. Here, the unperturbed operator $H_0$ is a multichannel Laplace type operator on $\ell^2(\mathbb Z; \mathfrak{G}) \cong
Externí odkaz:
http://arxiv.org/abs/2203.01352
We study the spectrum of the semiclassical Witten Laplacian $\Delta_{f}$ associated to a smooth function $f$ on ${\mathbb R}^d$. We assume that $f$ is a confining Morse--Bott function. Under this assumption we show that $\Delta_{f}$ admits exponentia
Externí odkaz:
http://arxiv.org/abs/2202.02208
Autor:
Assal, Marouane
We establish semiclassical resolvent estimates for Schr\"odinger operators with long-range matrix-valued potentials. As an application we prove resonance free domains both in trapping and non-trapping situations. Our results generalize the well-known
Externí odkaz:
http://arxiv.org/abs/2009.03867
Autor:
Assal, Marouane, Fujiié, Setsuro
We study the asymptotic distribution of the eigenvalues of a one-dimensional two-by-two semiclassical system of coupled Schr\"odinger operators in the presence of two potential wells and with an energy-level crossing. We provide Bohr-Sommerfeld quant
Externí odkaz:
http://arxiv.org/abs/1910.01195
Autor:
Assal, Marouane
Dans ce travail, nous nous intéressons à l’analyse spectrale des systèmes d’opérateurs pseudodifférentiels semi-classiques. Dans la première partie, nous étudions la généralisation du théorème d’Egorov en temps longs dans le cas où
Externí odkaz:
http://www.theses.fr/2017BORD0586/document
Akademický článek
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We establish a semiclassical trace formula in a general framework of microhyperbolic hermitian systems of $h$-pseudodifferential operators, and apply it to the study of the spectral shift function associated to a pair of selfadjoint Schr\"odinger ope
Externí odkaz:
http://arxiv.org/abs/1702.07880