Zobrazeno 1 - 10
of 9 766
pro vyhledávání: '"complex potentials"'
Autor:
Cuenin, Jean-Claude
We prove eigenvalue bounds for Schr\"odinger operator $-\Delta_g+V$ on compact manifolds with complex potentials $V$. The bounds depend only on an $L^q$-norm of the potential, and they are shown to be optimal, in a certain sense, on the round sphere
Externí odkaz:
http://arxiv.org/abs/2411.16984
In this work we establish under certain hypotheses the $N \to +\infty$ asymptotic expansion of integrals of the form $$\mathcal{Z}_{N,\Gamma}[V] \, = \, \int_{\Gamma^N} \prod_{ a < b}^{N}(z_a - z_b)^\beta \, \prod_{k=1}^{N} \mathrm{e}^{ - N \beta V(z
Externí odkaz:
http://arxiv.org/abs/2411.10610
Autor:
Cuenin, Jean-Claude, Frank, Rupert L.
We explain in which sense Schr\"odinger operators with complex potentials appear to violate locality (or Weyl's asymptotics), and we pose three open problems related to this phenomenon.
Externí odkaz:
http://arxiv.org/abs/2409.11285
Akademický článek
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Akademický článek
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The limit point and limit circle classification of real Sturm-Liouville problems by H. Weyl more than 100 years ago was extended by A.R. Sims around 60 years ago to the case when the coefficients are complex. Here, the main result is a collection of
Externí odkaz:
http://arxiv.org/abs/2310.16128
Autor:
Song, Jin, Yan, Zhenya
Publikováno v:
Physica D 448 (2023) 133729
In this paper, we firstly extend the physics-informed neural networks (PINNs) to learn data-driven stationary and non-stationary solitons of 1D and 2D saturable nonlinear Schr\"odinger equations (SNLSEs) with two fundamental PT-symmetric Scarf-II and
Externí odkaz:
http://arxiv.org/abs/2310.02276
We quantify the subcriticality of the bilaplacian in dimensions greater than four by providing explicit repulsivity/smallness conditions on complex additive perturbations under which the spectrum remains stable. Our assumptions cover critical Rellich
Externí odkaz:
http://arxiv.org/abs/2309.06823
Autor:
Cuenin, Jean-Claude, Merz, Konstantin
We review some results and proofs on eigenvalue bounds for random Schr\"odinger operators with complex-valued potentials. We also include new Schatten norm estimates for the resolvent and use them to obtain bounds for sums of eigenvalues.
Commen
Commen
Externí odkaz:
http://arxiv.org/abs/2308.08889
Autor:
Kravchenko, Vladislav V.
Publikováno v:
Journal of Mathematical Physics, 2024; 65 (3): 033501
An approach for solving a variety of inverse coefficient problems for the Sturm-Liouville equation -y''+q(x)y={\lambda}y with a complex valued potential q(x) is presented. It is based on Neumann series of Bessel functions representations for solution
Externí odkaz:
http://arxiv.org/abs/2307.13086