ASYMPTOTICS OF THE EIGENVALUES OF THE ANDERSON HAMILTONIAN WITH WHITE NOISE POTENTIAL IN TWO DIMENSIONS

被引：12

作者：

Chouk, Khalil ^{[1
]}

van Zuijlen, Willem ^{[2
]}

机构：

[1] Univ Edinburgh, Sch Math, Edinburgh, Midlothian, Scotland

[2] Weierstrass Inst Appl Anal & Stochast, Berlin, Germany

来源：

ANNALS OF PROBABILITY | 2021年 / 49卷 / 04期

基金：

欧洲研究理事会;

关键词：

Anderson Hamiltonian; white noise; paracontrolled distributions; operators with Dirichlet boundary conditions; MODEL;

D O I：

10.1214/20-AOP1497

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper we consider the Anderson Hamiltonian with white noise potential on the box [0, L](2) with Dirichlet boundary conditions. We show that all of the eigenvalues divided by logL, converge as L -> infinity, almost surely to the same deterministic constant which is given by a variational formula.

引用

页码：1917 / 1964

页数：48

共 50 条

[21] Moment asymptotics for the parabolic Anderson problem with a perturbed lattice potential
Fukushima, Ryoki
Ueki, Naomasa
JOURNAL OF FUNCTIONAL ANALYSIS, 2011, 260 (03) : 724 - 744
[22] Maxwell eigenvalues and discrete compactness in two dimensions
Demkowicz, L
Monk, P
Schwab, C
Vardapetyan, L
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2000, 40 (4-5) : 589 - 605
[23] Stabilization of Hamiltonian systems perturbed by white noise
Dunyak, JP
Freidlin, MI
PROCEEDINGS OF THE 36TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-5, 1997, : 2809 - 2814
[24] Feynman-Kac formula for parabolic Anderson model in Gaussian potential and fractional white noise
Han, Yuecai
Wu, Guanyu
JOURNAL OF MATHEMATICAL PHYSICS, 2024, 65 (02)
[25] Large time asymptotics for the parabolic Anderson model driven by spatially correlated noise
Huang, Jingyu
Le, Khoa
Nualart, David
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2017, 53 (03): : 1305 - 1340
[26] Remnants of Anderson localization in prethermalization induced by white noise
Lorenzo, S.
Apollaro, T.
Palma, G. M.
Nandkishore, R.
Silva, A.
Marino, J.
PHYSICAL REVIEW B, 2018, 98 (05)
[27] Asymptotics of the eigenvalues of a discrete Schrodinger operator with zero-range potential
Lakaev, S. N.
Holmatov, Sh. Yu.
IZVESTIYA MATHEMATICS, 2012, 76 (05) : 946 - 966
[28] Dirac eigenvalues for a softcore Coulomb potential in d dimensions
Hall, Richard L.
Zorin, Petr
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2012, 45 (11)
[29] Inverse problems for the Pauli Hamiltonian in two dimensions
Kang H.
Uhlmann G.
Journal of Fourier Analysis and Applications, 2004, 10 (2) : 201 - 215
[30] Inverse problems for the Pauli Hamiltonian in two dimensions
Kang, KB
Uhlman, G
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2004, 10 (02) : 201 - 215

← 1 2 3 4 5 →