Surface Localization in Impurity Band with Random Displacements and Long-Range Interactions
We study the random Schrödinger operators in a Euclidean space with the disorder generated by two complementary mechanisms: random substitution in a lower-dimensional layer and random displacements in the bulk, without additional assumptions regarding the reflection symmetry of the site potentials....
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/7192303 |
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| author | Victor Chulaevsky |
| author_facet | Victor Chulaevsky |
| author_sort | Victor Chulaevsky |
| collection | DOAJ |
| description | We study the random Schrödinger operators in a Euclidean space with the disorder generated by two complementary mechanisms: random substitution in a lower-dimensional layer and random displacements in the bulk, without additional assumptions regarding the reflection symmetry of the site potentials. The latter are assumed to be bounded and have a power-law decay. Complementing earlier results obtained in the strong disorder regime, we establish spectral and strong dynamical localization in the impurity zone near the bottom of spectrum for arbitrarily weak amplitudes of the random displacements, provided the concentration of impurities is sufficiently small. |
| format | Article |
| id | doaj-art-a6981a52e5de4e11a5fc507c021b4678 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-a6981a52e5de4e11a5fc507c021b46782025-08-20T03:38:39ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/71923037192303Surface Localization in Impurity Band with Random Displacements and Long-Range InteractionsVictor Chulaevsky0Département de Mathématiques, Université de Reims, Moulin de la Housse, BP 1039, 51687 Reims Cedex 2, FranceWe study the random Schrödinger operators in a Euclidean space with the disorder generated by two complementary mechanisms: random substitution in a lower-dimensional layer and random displacements in the bulk, without additional assumptions regarding the reflection symmetry of the site potentials. The latter are assumed to be bounded and have a power-law decay. Complementing earlier results obtained in the strong disorder regime, we establish spectral and strong dynamical localization in the impurity zone near the bottom of spectrum for arbitrarily weak amplitudes of the random displacements, provided the concentration of impurities is sufficiently small.http://dx.doi.org/10.1155/2018/7192303 |
| spellingShingle | Victor Chulaevsky Surface Localization in Impurity Band with Random Displacements and Long-Range Interactions Advances in Mathematical Physics |
| title | Surface Localization in Impurity Band with Random Displacements and Long-Range Interactions |
| title_full | Surface Localization in Impurity Band with Random Displacements and Long-Range Interactions |
| title_fullStr | Surface Localization in Impurity Band with Random Displacements and Long-Range Interactions |
| title_full_unstemmed | Surface Localization in Impurity Band with Random Displacements and Long-Range Interactions |
| title_short | Surface Localization in Impurity Band with Random Displacements and Long-Range Interactions |
| title_sort | surface localization in impurity band with random displacements and long range interactions |
| url | http://dx.doi.org/10.1155/2018/7192303 |
| work_keys_str_mv | AT victorchulaevsky surfacelocalizationinimpuritybandwithrandomdisplacementsandlongrangeinteractions |