# The spectrum minimum for random Schroedinger operators with indefinite sign potentials

## Abstract

This paper sets out to study the spectral minimum for an operator belonging to the family of random Schroedinger operators of the form H{sub {lambda}}{sub ,{omega}}=-{delta}+W{sub per}+{lambda}V{sub {omega}}, where we suppose that V{sub {omega}} is of Anderson type and the single site is assumed to be with an indefinite sign. Under some assumptions we prove that there exists {lambda}{sub 0}>0 such that for any {lambda} set-membership sign [0,{lambda}{sub 0}], the minimum of the spectrum of H{sub {lambda}}{sub ,{omega}} is obtained by a given realization of the random variables.

- Authors:

- Departement de Mathematiques Physiques, I.P.E.I. Monastir, 5000 Monastir (Tunisia)

- Publication Date:

- OSTI Identifier:
- 20768718

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 47; Journal Issue: 1; Other Information: DOI: 10.1063/1.2162825; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; POTENTIALS; QUANTUM OPERATORS; RANDOMNESS; SCHROEDINGER EQUATION; SPECTRA

### Citation Formats

```
Najar, Hatem.
```*The spectrum minimum for random Schroedinger operators with indefinite sign potentials*. United States: N. p., 2006.
Web. doi:10.1063/1.2162825.

```
Najar, Hatem.
```*The spectrum minimum for random Schroedinger operators with indefinite sign potentials*. United States. doi:10.1063/1.2162825.

```
Najar, Hatem. Sun .
"The spectrum minimum for random Schroedinger operators with indefinite sign potentials". United States.
doi:10.1063/1.2162825.
```

```
@article{osti_20768718,
```

title = {The spectrum minimum for random Schroedinger operators with indefinite sign potentials},

author = {Najar, Hatem},

abstractNote = {This paper sets out to study the spectral minimum for an operator belonging to the family of random Schroedinger operators of the form H{sub {lambda}}{sub ,{omega}}=-{delta}+W{sub per}+{lambda}V{sub {omega}}, where we suppose that V{sub {omega}} is of Anderson type and the single site is assumed to be with an indefinite sign. Under some assumptions we prove that there exists {lambda}{sub 0}>0 such that for any {lambda} set-membership sign [0,{lambda}{sub 0}], the minimum of the spectrum of H{sub {lambda}}{sub ,{omega}} is obtained by a given realization of the random variables.},

doi = {10.1063/1.2162825},

journal = {Journal of Mathematical Physics},

number = 1,

volume = 47,

place = {United States},

year = {Sun Jan 15 00:00:00 EST 2006},

month = {Sun Jan 15 00:00:00 EST 2006}

}

DOI: 10.1063/1.2162825

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