Zobrazeno 1 - 10
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pro vyhledávání: '"Helffer, B."'
Autor:
Helffer, B., Kachmar, A.
Inspired by a recent paper$^*$ by C. Fefferman, J. Shapiro and M. Weinstein, we investigate quantum tunneling for a Hamiltonian with a symmetric double well and a uniform magnetic field. In the simultaneous limit of strong magnetic field and deep pot
Externí odkaz:
http://arxiv.org/abs/2208.13030
Autor:
Helffer, B., Kachmar, A.
Motivated by the study of high energy Steklov eigenfunctions, we examine the semi-classical Robin Laplacian. In the two dimensional situation, we determine an effective operator describing the asymptotic distribution of the negative eigenvalues, and
Externí odkaz:
http://arxiv.org/abs/2102.07187
For $\mathbb N^*:=\mathbb N \setminus \{0\}$, we consider the collection $\mathfrak M(N)$ of all the $N$ rows, for which, for $n=1,\cdots,N$, the $n-th$ row consists of an increasing sequence $(a_j^n)_j$ of real numbers. For $\mathfrak A \in \mathfra
Externí odkaz:
http://arxiv.org/abs/1908.02752
Autor:
Helffer, B, Nourrigat, Jean
The aim of this paper is to review and compare the spectral properties of (the closed extension of) --$\Delta$ + U (V $\ge$ 0) and --$\Delta$ + iV in L 2 (R^d) for C $\infty$ real potentials U or V with polynomial behavior. The case with magnetic fie
Externí odkaz:
http://arxiv.org/abs/1709.08542
Akademický článek
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Autor:
Grebenkov, D. S., Helffer, B.
Publikováno v:
SIAM J. Math. Anal. 50, 622-676 (2018)
We investigate a two-dimensional Schr\"odinger operator, $-h^2 \Delta +iV(x)$, with a purely complex potential $iV(x)$. A rigorous definition of this non-selfadjoint operator is provided for bounded and unbounded domains with common boundary conditio
Externí odkaz:
http://arxiv.org/abs/1608.01925
Publikováno v:
SIAM J. Math. Anal. 49, 1844-1894 (2017)
We consider a suitable extension of the complex Airy operator, $-d^2/dx^2 + ix$, on the real line with a transmission boundary condition at the origin. We provide a rigorous definition of this operator and study its spectral properties. In particular
Externí odkaz:
http://arxiv.org/abs/1603.06992
Autor:
Bonnaillie-Noël, Virginie, Helffer, B.
In this article, we propose a state of the art concerning the nodal and spectral minimal partitions. First we focus on the nodal partitions and give some examples of Courant sharp cases. Then we are interested in minimal spectral partitions. Using th
Externí odkaz:
http://arxiv.org/abs/1506.07249
Publikováno v:
Gazette de la Société Mathématique de France; jul2024, Issue 181, p76-83, 8p
We consider spectral minimal partitions. Continuing work of the the present authors about problems for planar domains, [23], we focus on the sphere and obtain a sharp result for 3-partitions which is related to questions from harmonic analysis, in pa
Externí odkaz:
http://arxiv.org/abs/0903.3326