| Автор | Christophe Texier |
| Дата выпуска | 2000-09-08 |
| dc.description | We study the distribution of the nth energy level for two different one-dimensional random potentials. This distribution is shown to be related to the distribution of the distance between two consecutive nodes of the wavefunction. We first consider the case of a white noise potential and study the distributions of energy levels both in the positive and the negative part of the spectrum. It is demonstrated that, in the limit of a large system (L∞), the distribution of the nth energy level is given by a scaling law which is shown to be related to the extreme value statistics of a set of independent variables. In the second part we consider the case of a supersymmetric random Hamiltonian (potential V(x) = φ(x)<sup>2</sup> + φ'(x)). First we study the case where φ(x) is a white noise with zero mean. In particular, it is shown that the ground state energy, which behaves on average like exp (-L<sup>1/3</sup>) in agreement with previous work, is not a self-averaging quantity in the limit L∞ as is seen in the case of diagonal disorder. Then we consider the case when φ(x) has a non-zero mean value. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | Individual energy level distributions for one-dimensional diagonal and off-diagonal disorder |
| Тип | paper |
| DOI | 10.1088/0305-4470/33/35/303 |
| Print ISSN | 0305-4470 |
| Журнал | Journal of Physics A: Mathematical and General |
| Том | 33 |
| Первая страница | 6095 |
| Последняя страница | 6128 |
| Аффилиация | Christophe Texier; Département de Physique Théorique, Université de Genève, 24 quai Ernest Ansermet, CH-1211 Genève 4, Switzerland |
| Выпуск | 35 |
