25 citations · 114 across the 27 of their papers we have counts for
14 papers · 1 filter
Eigenvalue Fluctuations of 1-dimensional random Schrödinger operators
Takuto Mashiko, Yuma Marui, Naoki Maruyama +1
As an extension to the paper by Breuer, Grinshpon, and White \cite{B}, we study the linear statistics for the eigenvalues of the Schrödinger operator with random decaying potential…
Limiting distribution of extremal eigenvalues of d-dimensional random Schrödinger operator
Kaito Kawaai, Yugo Maruyama, Fumihiko Nakano
We consider Schrödinger operator with random decaying potential on and showed that, (i) IDS coincides with that of free Laplacian in general cases, and (ii) th…
Shape of eigenvectors for the decaying potential model
Fumihiko Nakano
We consider the 1d Schrödinger operator with decaying random potential, and study the joint scaling limit of the eigenvalues and the measures associated with the corresponding eige…
The scaling limit of eigenfunctions for 1d random Schrödinger operator
Fumihiko Nakano
We report our results on the scaling limit of the eigenvalues and the corresponding eigenfunctions for the 1-d random Schrödinger operator with random decaying potential. The formu…
A self-adjointness criterion for the Schrödinger operator with infinitely many point interactions and its application to random operators
Masahiro Kaminaga, Takuya Mine, Fumihiko Nakano
We prove the Schrödinger operator with infinitely many point interactions in is self-adjoint if the support of the interactions is decomposed into unifor…
Clock statistics for 1d Schrödinger operators
Victor Chulaevsky, Fumihiko Nakano
We study the 1d Schrödinger operators with alloy type random supercritical decaying potential and prove the clock convergence for the local statistics of eigenvalues. We also consi…
Fluctuation of density of states for 1d Schrödinger operators
Fumihiko Nakano
We consider the 1d Schrödinger operator with random decaying potential and compute the 2nd term asymptotics of the density of states, which shows substantial differences between th…
Poisson statistics for 1d Schrödinger operators with random decaying potentials
Shinichi Kotani, Fumihiko Nakano
We consider the 1d Schrödinger operators with random decaying potentials where the spectrum is pure point(sub-critical case). We show that the point process composed of the rescale…
Level statistics for one-dimensional Schrödinger operators and Gaussian beta ensemble
Fumihiko Nakano
We study the level statistics for two classes of 1-dimensional random Schrödinger operators : (1) for operators whose coupling constants decay as the system size becomes large, and…
Level statistics of one-dimensional Schrödinger operators with random decaying potential
Shinichi Kotani, Fumihiko Nakano
We study the level statistics of one-dimensional Schrödinger operator with random potential decaying like at infinity. We consider the point process consisting of th…
The distribution of localization centers in some discrete random systems
Fumihiko Nakano
As a supplement of our previous work, we consider the localized region of the random Schroedinger operators on and study the point process composed of their eigenv…
The repulsion between localization centers in the Anderson model
Fumihiko Nakano
In this note we show that, a simple combination of deep results in the theory of random Schrödinger operators yields a quantitative estimate of the fact that the localization cente…
Spin of the ground state and the flux phase problem on the ring
Fumihiko Nakano
As a continuation of our previous work, we derive the optimal flux phase which minimizes the ground state energy in the one-dimensional many particle systems, when the number of pa…
The flux phase problem on the ring
Fumihiko Nakano
We give a simple proof to derive the optimal flux which minimizes the ground state energy in one dimensional Hubbard model, provided the number of particles is even.