The fate of the Lifshitz tail for condensed bosons

1992 ◽  
Vol 4 (7) ◽  
pp. 1729-1742 ◽  
Author(s):  
D K K Lee ◽  
J M F Gunn
Keyword(s):  
Lifshitz Tail

scholarly journals Supersymmetric Cluster Expansions and Applications to Random Schrödinger Operators

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Luca Fresta
Keyword(s):  
Density Of States ◽  
Local Density ◽  
Schrödinger Operators ◽  
Random Schrödinger Operators ◽  
Schrodinger Operators ◽  
Local Density Of States ◽  
Weak Disorder ◽  
Cluster Expansions ◽  
Strong Disorder ◽  
Lifshitz Tail

AbstractWe study discrete random Schrödinger operators via the supersymmetric formalism. We develop a cluster expansion that converges at both strong and weak disorder. We prove the exponential decay of the disorder-averaged Green’s function and the smoothness of the local density of states either at weak disorder and at energies in proximity of the unperturbed spectrum or at strong disorder and at any energy. As an application, we establish Lifshitz-tail-type estimates for the local density of states and thus localization at weak disorder.

scholarly journals Ergodicity and dynamical localization for Delone–Anderson operators

2015 ◽  
Vol 27 (09) ◽  
pp. 1550020 ◽  
Author(s):  
François Germinet ◽  
Peter Müller ◽  
Constanza Rojas-Molina
Keyword(s):  
Density Of States ◽  
Dynamical Localization ◽  
Integrated Density Of States ◽  
Tail Behavior ◽  
Geometric Complexity ◽  
Multi Scale ◽  
Ergodic Properties ◽  
The Family ◽  
Delone Sets ◽  
Lifshitz Tail

We study the ergodic properties of Delone–Anderson operators, using the framework of randomly colored Delone sets and Delone dynamical systems. In particular, we show the existence of the integrated density of states and, under some assumptions on the geometric complexity of the underlying Delone sets, we obtain information on the almost-sure spectrum of the family of random operators. We then exploit these results to study the Lifshitz-tail behavior of the integrated density of states of a Delone–Anderson operator at the bottom of the spectrum. Furthermore, we use Lifshitz-tail estimates as an input for the multi-scale analysis to prove dynamical localization.

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