# Ordered spectral statistics in 1D disordered supersymmetric quantum mechanics and Sinai diffusion with dilute absorbers

@article{Texier2012OrderedSS, title={Ordered spectral statistics in 1D disordered supersymmetric quantum mechanics and Sinai diffusion with dilute absorbers}, author={Christophe Texier}, journal={arXiv: Disordered Systems and Neural Networks}, year={2012} }

Some results on the ordered statistics of eigenvalues for one-dimensional random Schrodinger Hamiltonians are reviewed. In the case of supersymmetric quantum mechanics with disorder, the existence of low energy delocalized states induces eigenvalue correlations and makes the ordered statistics problem nontrivial. The resulting distributions are used to analyze the problem of classical diffusion in a random force field (Sinai problem) in the presence of weakly concentrated absorbers. It is shown…

## References

SHOWING 1-10 OF 33 REFERENCES

Sinai model in presence of dilute absorbers

- Physics, Mathematics
- 2009

We study the Sinai model for the diffusion of a particle in a one dimension random potential in presence of a small concentration $\rho$ of perfect absorbers using the asymptotically exact real space…

Statistical Distribution of Quantum Entanglement for a Random Bipartite State

- Mathematics, Physics
- 2011

We compute analytically the statistics of the Renyi and von Neumann entropies (standard measures of entanglement), for a random pure state in a large bipartite quantum system. The full probability…

TOPICAL REVIEW: Functionals of Brownian motion, localization and metric graphs

- Mathematics, Physics
- 2005

We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of Brownian motion arise in the study of…

One-dimensional classical diffusion in a random force field with weakly concentrated absorbers

- Physics
- 2009

A one-dimensional model of classical diffusion in a random force field with a weak concentration ? of absorbers is studied. The force field is taken as a Gaussian white noise with (x)=0 and…

The local structure of the spectrum of the one-dimensional Schrödinger operator

- Mathematics
- 1981

AbstractLet
$$H_V = - \frac{{d^{\text{2}} }}{{dt^{\text{2}} }} + q(t,\omega )$$
be an one-dimensional random Schrödinger operator in ℒ2(−V,V) with the classical boundary conditions. The random…

Breaking supersymmetry in a one-dimensional random Hamiltonian

- Physics, Mathematics
- 2008

The one-dimensional supersymmetric random Hamiltonian , where (x) is a Gaussian white noise of zero mean and variance g, presents particular spectral and localization properties at low energy: a…

A limit law for the ground state of Hill's equation

- Mathematics
- 1994

AbstractIt is proved that the ground state Λ(L) of (−1)x the Schrödinger operator with white noise potential, on an interval of lengthL, subject to Neumann, periodic, or Dirichlet conditions,…

Individual energy level distributions for one-dimensional diagonal and off-diagonal disorder

- Mathematics, Physics
- 2000

We study the distribution of the n-th energy level for two different one-dimensional random potentials. This distribution is shown to be related to the distribution of the distance between two…

One-dimensional disordered supersymmetric quantum mechanics: A brief survey

- Physics
- 1998

We consider a one-dimensional model of localization based on the Witten Hamiltonian of supersymmetric quantum mechanics. The low energy spectral properties are reviewed and compared with those of…

On the basic states of one-dimensional disordered structures

- Mathematics
- 1983

The purpose of this paper is to study a limit probability distribution of the set of the first κ eigenvalues λ1(ℒ)<λ2(ℒ)<...<λκ(ℒ) (with a fixed κ and ℒ→∞) of the boundary problem on the interval [0,…