Neumann Domains on Quantum Graphs

Lior Alon, Ram Band

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء

ملخص

The Neumann points of an eigenfunction f on a quantum (metric) graph are the interior zeros of f. The Neumann domains of f are the sub-graphs bounded by the Neumann points. Neumann points and Neumann domains are the counterparts of the well-studied nodal points and nodal domains. We prove bounds on the number of Neumann points and properties of the probability distribution of this number. Two basic properties of Neumann domains are presented: the wavelength capacity and the spectral position. We state and prove bounds on those as well as key features of their probability distributions. To rigorously investigate those probabilities, we establish the notion of random variables for quantum graphs. In particular, we provide conditions for considering spectral functions of quantum graphs as random variables with respect to the natural density on N.

اللغة الأصليةالإنجليزيّة
الصفحات (من إلى)3391-3454
عدد الصفحات64
دوريةAnnales Henri Poincare
مستوى الصوت22
رقم الإصدار10
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - أكتوبر 2021

All Science Journal Classification (ASJC) codes

  • !!Statistical and Nonlinear Physics
  • !!Nuclear and High Energy Physics
  • !!Mathematical Physics

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