Nodal counting on quantum graphs

DOI10.1088/0959-7174/14/1/011zbMath1063.81056arXivnlin/0305020OpenAlexW2057547316WikidataQ62596113 ScholiaQ62596113MaRDI QIDQ5461774

Uzy Smilansky, Joachim Weber, Sven Gnutzmann

Publication date: 26 July 2005

Published in: Waves in Random Media (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0305020

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) General mathematical topics and methods in quantum theory (81Q99)

Related Items (22)

Isospectral discrete and quantum graphs with the same flip counts and nodal counts ⋮ Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs ⋮ On the quotient quantum graph with respect to the regular representation ⋮ A theory of spectral partitions of metric graphs ⋮ Nodal statistics on quantum graphs ⋮ Quantum graphs which optimize the spectral gap ⋮ The nodal count {0,1,2,3,…} implies the graph is a tree ⋮ Eigenfunction statistics on quantum graphs ⋮ Minimizing optimal transport for functions with fixed-size nodal sets ⋮ Dynamics of nodal points and the nodal count on a family of quantum graphs ⋮ The number of nodal domains on quantum graphs as a stability index of graph partitions ⋮ The ergodicity landscape of quantum theories ⋮ Neumann domains on quantum graphs ⋮ On the hot spots of quantum graphs ⋮ A lower bound for nodal count on discrete and metric graphs ⋮ Eigenvalue and nodal properties on quantum graph trees* ⋮ No quantum ergodicity for star graphs ⋮ On the ground state for quantum graphs ⋮ On Pleijel's nodal domain theorem for quantum graphs ⋮ On fully supported eigenfunctions of quantum graphs ⋮ On the nodal structure of nonlinear stationary waves on star graphs ⋮ Rényi and Tsallis entropies related to eigenfunctions of quantum graphs

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