scholarly journals Invariants of Isospectral Deformations and Spectral Rigidity

2012 ◽  
Vol 37 (3) ◽  
pp. 369-446 ◽  
Author(s):  
Georgi Popov ◽  
Peter Topalov
Keyword(s):  
Spectral Rigidity

scholarly journals Spectral Rigidity of Random Schrödinger Operators via Feynman–Kac Formulas

2020 ◽  
Vol 21 (7) ◽  
pp. 2259-2299
Author(s):  
Pierre Yves Gaudreau Lamarre ◽  
Promit Ghosal ◽  
Yuchen Liao
Keyword(s):  
Schrödinger Operators ◽  
Random Schrödinger Operators ◽  
Schrodinger Operators ◽  
Spectral Rigidity

scholarly journals Spectral rigidity and invariant distributions on Anosov surfaces

2014 ◽  
Vol 98 (1) ◽  
pp. 147-181 ◽  
Author(s):  
Gabriel P. Paternain ◽  
Mikko Salo ◽  
Gunther Uhlmann
Keyword(s):  
Invariant Distributions ◽  
Spectral Rigidity

THE SPECTRAL STATISTICS OF TRIANGULAR QUANTUM BILLIARDS

1995 ◽  
Vol 05 (06) ◽  
pp. 1599-1609 ◽  
Author(s):  
PAOLO BELLOMO
Keyword(s):  
Energy Range ◽  
Equilateral Triangle ◽  
Nearest Neighbor ◽  
Low Energy ◽  
Local Character ◽  
Energy Regime ◽  
Spectral Rigidity ◽  
Spectral Statistics ◽  
Spectral Distributions

We study the spectral statistics of three triangular quantum billiards. We show that for an ergodic billiard the nearest neighbor spacings distribution in the low energy regime is strongly influenced by a neighboring integrable domain (equilateral triangle). With increasing energy we observe a transition towards a more chaotic-like pattern. We also show that for all three triangles the properties of the spectral distributions depend heavily on the energy range considered. This is specially true for the spectral rigidity, because of its essentially local character. The features of the distributions do not depend strongly on the genus of classical billiards.

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