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pro vyhledávání: '"Harrell II, Evans M."'
We use methods of direct optimization as in [9] to find the minimizers of the fundamental gap of Sturm-Liouville operators on an interval, under the constraint that the potential is of single-well form and that the weight function is of single-barrie
Externí odkaz:
http://arxiv.org/abs/2407.02459
We study the problem of minimizing or maximizing the fundamental spectral gap of Schr\"odinger operators on metric graphs with either a convex potential or a ``single-well'' potential on an appropriate specified subset. (In the case of metric trees,
Externí odkaz:
http://arxiv.org/abs/2401.04344
Autor:
Harrell II, Evans M., Maltsev, Anna V.
Quantum graphs without interaction which contain equilateral cycles possess "topological" bound states which do not correspond to zeroes of one of the two variants of the secular equation for quantum graphs. Instead, their eigenvalues lie in the set
Externí odkaz:
http://arxiv.org/abs/2311.18030
On a compact metric graph, we consider the spectrum of the Laplacian defined with a mix of standard and Dirichlet vertex conditions. A Cheeger-type lower bound on the gap $\lambda_2 - \lambda_1$ is established, with a constant that depends only on th
Externí odkaz:
http://arxiv.org/abs/2301.07149
We analyze the heat kernel associated to the Laplacian on a compact metric graph, with standard Kirchoff-Neumann vertex conditions. An explicit formula for the heat kernel as a sum over loops, developed by Roth and Kostrykin, Potthoff, and Schrader,
Externí odkaz:
http://arxiv.org/abs/2204.06619
We characterize the potential-energy functions $V(x)$ that minimize the gap $\Gamma$ between the two lowest Sturm-Liouville eigenvalues for \[ H(p,V) u := -\frac{d}{dx} \left(p(x)\frac{du}{dx}\right)+V(x) u = \lambda u, \quad\quad x\in [0,\pi ], \] w
Externí odkaz:
http://arxiv.org/abs/1807.08328
We present asymptotically sharp inequalities, containing a second term, for the Dirichlet and Neumann eigenvalues of the Laplacian on a domain, which are complementary to the familiar Berezin-Li-Yau and Kr\"oger inequalities in the limit as the eigen
Externí odkaz:
http://arxiv.org/abs/1806.10366
Autor:
Harrell II, Evans M., Maltsev, Anna V.
We discuss explicit landscape functions for quantum graphs. By a "landscape function" $\Upsilon(x)$ we mean a function that controls the localization properties of normalized eigenfunctions $\psi(x)$ through a pointwise inequality of the form $$ |\ps
Externí odkaz:
http://arxiv.org/abs/1803.01186
Akademický článek
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Autor:
Harrell II, Evans M., Stubbe, Joachim
We present asymptotically sharp inequalities for the eigenvalues $\mu_k$ of the Laplacian on a domain with Neumann boundary conditions, using the averaged variational principle introduced in \cite{HaSt14}. For the Riesz mean $R_1(z)$ of the eigenvalu
Externí odkaz:
http://arxiv.org/abs/1607.02207