A Note on the Analyticity of Density of States

@article{Kaminaga2012ANO,
  title={A Note on the Analyticity of Density of States},
  author={Masahiro Kaminaga and M. Krishna and S. Nakamura},
  journal={Journal of Statistical Physics},
  year={2012},
  volume={149},
  pages={496-504}
}
We consider the d-dimensional Anderson model, and we prove the density of states is locally analytic if the single site potential distribution is locally analytic and the disorder is large. We employ the random walk expansion of resolvents and a simple complex function theory trick. In particular, we discuss the uniform distribution case, and we obtain a sharper result using more precise computations. The method can be also applied to prove the analyticity of the correlation functions. 

Figures from this paper

Eigenfunction statistics for Anderson model with Hölder continuous single site potential
We consider random Schrödinger operators on ℓ2(ℤd)$\ell ^{2}(\mathbb {Z}^{d})$ with α-Hölder continuous (0<α≤1) single site distribution. In localized regime, we study the distribution of
Poisson Statistics for Anderson Model with Singular Randomness
In this work we consider the Anderson model on the $d$-dimensional lattice with the single site potential having singular distribution, mainly $\alpha$-H\"older continuous ones and show that the
Regularity of the Density of States of Random Schrödinger Operators
In this paper we solve a long standing open problem for Random Schrodinger operators on $L^2(\mathbb{R}^d)$ with i.i.d single site random potentials. We allow a large class of free operators,
Spectral statistics of random Schrödinger operator with growing potential
In this work we investigate the spectral statistics of random Schr\"{o}dinger operators $H^\omega=-\Delta+\sum_{n\in\mathbb{Z}^d}(1+|n|^\alpha)q_n(\omega)|\delta_n\rangle\langle\delta_n|$, $\alpha>0$
A Complete Bibliography of the Journal of Statistical Physics: 2000{2009
(2 + 1) [XTpXpH12, CTH11]. + [Zuc11b]. 0 [Fed17]. 1 [BELP15, CAS11, Cor16, Fed17, GDL10, GBL16, Hau16, JV19, KT12, KM19c, Li19, MN14b, Nak17, Pal11, Pan14, RT14, RBS16b, RY12, SS18c, Sug10, dOP18]. 1

References

SHOWING 1-10 OF 23 REFERENCES
Analyticity of the density of states and replica method for random schrödinger operators on a lattice
We analyze the density of states and some aspects of the replica method for Anderson's tight binding model on a lattice of arbitrary dimension, with diagonal disorder. We give heuristic arguments for
Smoothness of Correlations in the Anderson Model at Strong Disorder
Abstract.We study the higher-order correlation functions of covariant families of observables associated with random Schrödinger operators on the lattice in the strong disorder regime. We prove that
Spectral properties of disordered systems in the one-body approximation
The paper considers the Schrödinger equation for a single particle and its discrete analogues. Assuming that the coefficients of these equations are homogeneous and ergodic random fields, it is
A rigorous approach to Anderson localization
Abstract We summarize some features of a novel and mathematically rigorous approach to Anderson localization. Our approach can be used to show that, in the Anderson tight binding model, there is no
Regularity of the density of states in the Anderson model on a strip for potentials with singular continuous distributions
We derive regularity properties for the density of states in the Anderson model on a one-dimensional strip for potentials with singular continuous distributions. For example, if the characteristic
Remark on the continuity of the density of states of ergodic finite difference operators
We give an elementary proof that for a large class ofd-dimensional finite difference operators including tight-binding models for electron propagation and models for harmonic phonons with random
Smoothness of the integrated density of states on strips
Smoothness of the integrated density of states, k(E), of random Schrodinger operators, i.i.d. and non-i.i.d. cases, on a discrete strip lattice is investigated. It is proven that k(E) is C∞ if only
Harmonic analysis on SL(2,R) and smoothness of the density of states in the one-dimensional Anderson model
We consider infinite Jacobi matrices with ones off-diagonal, and independent identically distributed random variables with distributionF(v)dv on-diagonal. IfF has compact support and lies in some
Smoothness of the density of states in the Anderson model at high disorder
We prove smoothness of the density of states in the Anderson model at high disorder for a class of potential distributions that include the uniform distribution.
Lipschitz-Continuity of the Integrated Density of States for Gaussian Random Potentials
The integrated density of states of a Schrödinger operator with random potential given by a homogeneous Gaussian field whose covariance function is continuous, compactly supported and has positive
...
1
2
3
...