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math-ph2009
Lower bound on the density of states for periodic Schrödinger operators
Sergey Morozov, Leonid Parnovski, Irina Pchelintseva
We consider Schrödinger operators with smooth periodic potentials in Euclidean spaces of dimension bigger than 1 and prove a uniform lower bound on the density of states for large…
math-ph2008
Discrete spectrum in a critical coupling case of Jacobi matrices with spectral phase transitions by uniform asymptotic analysis
Serguei Naboko, Irina Pchelintseva, Luis O. Silva
For a two-parameter family of Jacobi matrices exhibiting first-order spectral phase transitions, we prove discreteness of the spectrum in the positive real axis when the parameters…