Supersymmetric methods in random matrix theory
Supersymmetric methods in random matrix theory
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DissertationPrüfungsdatum
06.10.2021Datum der Veröffentlichung
02.12.2021Erstgutachter
Disertori, MargheritaZweitgutachter
Ferrari, PatrikMetadaten
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Inhalt
Randomness and chaos are key ingredients in the description of nature and are therefore central elements in mathematics and physics. A conducting metal becomes an insulator if there are enough random defects in its structure. This phase transition generated by randomness (also called Anderson transition) is a central point of study. It is an unproven conjecture that in dimension 3 there is such a phase transition between diffusive and isolated states while in dimension 1 there are proofs that only localization occurs.
This doctoral thesis provides insights into supersymmetric methods relevant for the study of two prominent random matrix models describing disordered materials: random Schrödinger operators and random band matrices.
The main idea in the following is - using the supersymmetric approach - to establish dual representations for the quantity of interest, which in turn can be studied via analytic tools, inspired by statistical mechanics.
This doctoral thesis provides insights into supersymmetric methods relevant for the study of two prominent random matrix models describing disordered materials: random Schrödinger operators and random band matrices.
The main idea in the following is - using the supersymmetric approach - to establish dual representations for the quantity of interest, which in turn can be studied via analytic tools, inspired by statistical mechanics.
Schlagwörter
Zufallsmatrizen, Supersymmetrie, Random Matrices, Supersymmetry
Klassifikation (DDC)
510 MathematikLager, Mareike: Supersymmetric methods in random matrix theory. - Bonn, 2021. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-64596
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-64596
@phdthesis{handle:20.500.11811/9441,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-64596,
author = {{Mareike Lager}},
title = {Supersymmetric methods in random matrix theory},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2021,
month = dec,
note = {Randomness and chaos are key ingredients in the description of nature and are therefore central elements in mathematics and physics. A conducting metal becomes an insulator if there are enough random defects in its structure. This phase transition generated by randomness (also called Anderson transition) is a central point of study. It is an unproven conjecture that in dimension 3 there is such a phase transition between diffusive and isolated states while in dimension 1 there are proofs that only localization occurs.
This doctoral thesis provides insights into supersymmetric methods relevant for the study of two prominent random matrix models describing disordered materials: random Schrödinger operators and random band matrices.
The main idea in the following is - using the supersymmetric approach - to establish dual representations for the quantity of interest, which in turn can be studied via analytic tools, inspired by statistical mechanics.},
url = {https://hdl.handle.net/20.500.11811/9441}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-64596,
author = {{Mareike Lager}},
title = {Supersymmetric methods in random matrix theory},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2021,
month = dec,
note = {Randomness and chaos are key ingredients in the description of nature and are therefore central elements in mathematics and physics. A conducting metal becomes an insulator if there are enough random defects in its structure. This phase transition generated by randomness (also called Anderson transition) is a central point of study. It is an unproven conjecture that in dimension 3 there is such a phase transition between diffusive and isolated states while in dimension 1 there are proofs that only localization occurs.
This doctoral thesis provides insights into supersymmetric methods relevant for the study of two prominent random matrix models describing disordered materials: random Schrödinger operators and random band matrices.
The main idea in the following is - using the supersymmetric approach - to establish dual representations for the quantity of interest, which in turn can be studied via analytic tools, inspired by statistical mechanics.},
url = {https://hdl.handle.net/20.500.11811/9441}
}
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