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AbstractWe consider the one-dimensional random Schrödinger operator $$H_{\omega} = H_0 + \sigma V_{\omega},$$Hω=H0+σVω,where the potential V has i.i.d. entries with bounded support. We prove that the IDS is Hölder continuous… Click to show full abstract
AbstractWe consider the one-dimensional random Schrödinger operator $$H_{\omega} = H_0 + \sigma V_{\omega},$$Hω=H0+σVω,where the potential V has i.i.d. entries with bounded support. We prove that the IDS is Hölder continuous with exponent $${1-c \sigma}$$1-cσ. This improves upon the work of Bourgain showing that the Hölder exponent tends to 1 as sigma tends to 0 in the more specific Anderson–Bernoulli setting.
Keywords:
lder continuity;
density states;
states one;
integrated density;
one dimensional;
continuity integrated
Journal Title: Communications in Mathematical Physics
Year Published: 2017
Link to full text (if available)
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Journal Title: Communications in Mathematical Physics
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!