Spectral Theory for Magnetic Schrödinger Operators in Exterior Domains with Exploding and Oscillating Long-Range Potentials

2020 ◽  
pp. 209-244
Author(s):  
Kiyoshi Mochizuki
Keyword(s):  
Long Range ◽  
Spectral Theory ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Exterior Domains

scholarly journals LOCALIZATION FOR ONE DIMENSIONAL LONG RANGE RANDOM HAMILTONIANS

1999 ◽  
Vol 11 (01) ◽  
pp. 103-135 ◽  
Author(s):  
VOJKAN JAKŠIĆ ◽  
STANISLAV MOLCHANOV
Keyword(s):  
Long Range ◽  
Spectral Properties ◽  
Schrödinger Operators ◽  
Pure Point ◽  
Random Schrödinger Operators ◽  
Schrodinger Operators ◽  
One Dimensional ◽  
Free Part ◽  
Random Hamiltonians

We study spectral properties of random Schrödinger operators hω=h0+vω(n) on l2(Z) whose free part h0 is long range. We prove that the spectrum of hω is pure point for typical ω whenever the off-diagonal terms of h0 decay as |i-j|-γ for some γ>8.

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