Spectral Theory of Random Schrödinger Operators:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1990
|
| Schriftenreihe: | Probability and Its Applications
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Since the seminal work of P. Anderson in 1958, localization in disordered systems has been the object of intense investigations. Mathematically speaking, the phenomenon can be described as follows: the self-adjoint operators which are used as Hamiltonians for these systems have a ten dency to have pure point spectrum, especially in low dimension or for large disorder. A lot of effort has been devoted to the mathematical study of the random self-adjoint operators relevant to the theory of localization for disordered systems. It is fair to say that progress has been made and that the un derstanding of the phenomenon has improved. This does not mean that the subject is closed. Indeed, the number of important problems actually solved is not larger than the number of those remaining. Let us mention some of the latter: • A proof of localization at all energies is still missing for two dimen sional systems, though it should be within reachable range. In the case of the two dimensional lattice, this problem has been approached by the investigation of a finite discrete band, but the limiting pro cedure necessary to reach the full two-dimensional lattice has never been controlled. • The smoothness properties of the density of states seem to escape all attempts in dimension larger than one. This problem is particularly serious in the continuous case where one does not even know if it is continuous |
| Beschreibung: | 1 Online-Ressource (XXVI, 589 p) |
| ISBN: | 9781461244882 9781461288411 |
| DOI: | 10.1007/978-1-4612-4488-2 |
Internformat
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| 500 | |a Since the seminal work of P. Anderson in 1958, localization in disordered systems has been the object of intense investigations. Mathematically speaking, the phenomenon can be described as follows: the self-adjoint operators which are used as Hamiltonians for these systems have a ten dency to have pure point spectrum, especially in low dimension or for large disorder. A lot of effort has been devoted to the mathematical study of the random self-adjoint operators relevant to the theory of localization for disordered systems. It is fair to say that progress has been made and that the un derstanding of the phenomenon has improved. This does not mean that the subject is closed. Indeed, the number of important problems actually solved is not larger than the number of those remaining. Let us mention some of the latter: • A proof of localization at all energies is still missing for two dimen sional systems, though it should be within reachable range. In the case of the two dimensional lattice, this problem has been approached by the investigation of a finite discrete band, but the limiting pro cedure necessary to reach the full two-dimensional lattice has never been controlled. • The smoothness properties of the density of states seem to escape all attempts in dimension larger than one. This problem is particularly serious in the continuous case where one does not even know if it is continuous | ||
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Datensatz im Suchindex
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| author | Carmona, René |
| author_facet | Carmona, René |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-search | 515.7 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-4488-2 |
| format | Electronic eBook |
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| isbn | 9781461244882 9781461288411 |
| language | English |
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| spelling | Carmona, René Verfasser aut Spectral Theory of Random Schrödinger Operators by René Carmona, Jean Lacroix Boston, MA Birkhäuser Boston 1990 1 Online-Ressource (XXVI, 589 p) txt rdacontent c rdamedia cr rdacarrier Probability and Its Applications Since the seminal work of P. Anderson in 1958, localization in disordered systems has been the object of intense investigations. Mathematically speaking, the phenomenon can be described as follows: the self-adjoint operators which are used as Hamiltonians for these systems have a ten dency to have pure point spectrum, especially in low dimension or for large disorder. A lot of effort has been devoted to the mathematical study of the random self-adjoint operators relevant to the theory of localization for disordered systems. It is fair to say that progress has been made and that the un derstanding of the phenomenon has improved. This does not mean that the subject is closed. Indeed, the number of important problems actually solved is not larger than the number of those remaining. Let us mention some of the latter: • A proof of localization at all energies is still missing for two dimen sional systems, though it should be within reachable range. In the case of the two dimensional lattice, this problem has been approached by the investigation of a finite discrete band, but the limiting pro cedure necessary to reach the full two-dimensional lattice has never been controlled. • The smoothness properties of the density of states seem to escape all attempts in dimension larger than one. This problem is particularly serious in the continuous case where one does not even know if it is continuous Mathematics Functional analysis Differential equations, partial Functional Analysis Partial Differential Equations Mathematik Schrödinger-Gleichung (DE-588)4053332-3 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Hamilton-Operator (DE-588)4072278-8 gnd rswk-swf Hamilton-Operator (DE-588)4072278-8 s Spektraltheorie (DE-588)4116561-5 s 1\p DE-604 Schrödinger-Gleichung (DE-588)4053332-3 s 2\p DE-604 Lacroix, Jean Sonstige oth https://doi.org/10.1007/978-1-4612-4488-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Carmona, René Spectral Theory of Random Schrödinger Operators Mathematics Functional analysis Differential equations, partial Functional Analysis Partial Differential Equations Mathematik Schrödinger-Gleichung (DE-588)4053332-3 gnd Spektraltheorie (DE-588)4116561-5 gnd Hamilton-Operator (DE-588)4072278-8 gnd |
| subject_GND | (DE-588)4053332-3 (DE-588)4116561-5 (DE-588)4072278-8 |
| title | Spectral Theory of Random Schrödinger Operators |
| title_auth | Spectral Theory of Random Schrödinger Operators |
| title_exact_search | Spectral Theory of Random Schrödinger Operators |
| title_full | Spectral Theory of Random Schrödinger Operators by René Carmona, Jean Lacroix |
| title_fullStr | Spectral Theory of Random Schrödinger Operators by René Carmona, Jean Lacroix |
| title_full_unstemmed | Spectral Theory of Random Schrödinger Operators by René Carmona, Jean Lacroix |
| title_short | Spectral Theory of Random Schrödinger Operators |
| title_sort | spectral theory of random schrodinger operators |
| topic | Mathematics Functional analysis Differential equations, partial Functional Analysis Partial Differential Equations Mathematik Schrödinger-Gleichung (DE-588)4053332-3 gnd Spektraltheorie (DE-588)4116561-5 gnd Hamilton-Operator (DE-588)4072278-8 gnd |
| topic_facet | Mathematics Functional analysis Differential equations, partial Functional Analysis Partial Differential Equations Mathematik Schrödinger-Gleichung Spektraltheorie Hamilton-Operator |
| url | https://doi.org/10.1007/978-1-4612-4488-2 |
| work_keys_str_mv | AT carmonarene spectraltheoryofrandomschrodingeroperators AT lacroixjean spectraltheoryofrandomschrodingeroperators |