Quantum ergodicity and delocalization of Schrödinger Eigenfunctions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
EMS Press
[2022]
|
| Ausgabe: | 1. Auflage |
| Schriftenreihe: | Zurich lectures in advanced mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 134 Seiten 24 cm x 17 cm |
| ISBN: | 9783985470150 3985470154 |
Internformat
MARC
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|---|---|---|---|
| 001 | BV048597911 | ||
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| 005 | 20221215 | ||
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| 100 | 1 | |a Anantharaman, Nalini |d 1976- |e Verfasser |0 (DE-588)1227362226 |4 aut | |
| 245 | 1 | 0 | |a Quantum ergodicity and delocalization of Schrödinger Eigenfunctions |c Nalini Anantharaman |
| 250 | |a 1. Auflage | ||
| 264 | 1 | |a Berlin |b EMS Press |c [2022] | |
| 300 | |a 134 Seiten |c 24 cm x 17 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Zurich lectures in advanced mathematics | |
| 653 | |a Schrödinger operators on manifolds and graphs | ||
| 653 | |a quantum chaos | ||
| 653 | |a Laplacian | ||
| 653 | |a quantum ergodicity | ||
| 710 | 2 | |a European Mathematical Society Publishing House ETH-Zentrum SEW A27 |0 (DE-588)1066118477 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-98547-515-5 |w (DE-604)BV048319890 |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-033973503 | ||
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Datensatz im Suchindex
| _version_ | 1804184641602584576 |
|---|---|
| adam_text | CONTENTS
1
INTRODUCTION
.......................................................................................................
1
1.1
HISTORY
OF
THE
PROBLEM
............................................................................
1
1.2
CONJECTURES,
SCOPE
OF
THE
BOOK
................................................................
3
2
HIGH
FREQUENCY
DELOCALISATION
........................................................................
15
2.1
L
P
-NORMS
AS
MEASURES
OF
DELOCALISATION?
...............................................
16
2.2
THE
SHNIRELMAN
THEOREM
.........................................................................
18
2.3
OVERVIEW
OF
PSEUDO-DIFFERENTIAL
OPERATORS
............................................
20
2.4
THE
GEODESIC
FLOW
AND
THE
ERGODICITY
ASSUMPTION
................................
32
2.5
PROOF
OF
THE
QUANTUM
ERGODICITY
THEOREM
............................................
34
3
ENTROPY
AND
SUPPORT
OF
SEMICLASSICAL
MEASURES
..........................................
37
3.1
QUANTUM
UNIQUE
ERGODICITY
CONJECTURE
.................................................
37
3.2
STATEMENT
OF
RESULTS
.................................................................................
38
3.3
WHAT
IS
ENTROPY?
.....................................................................................
41
3.4
PROOF
OF
THE
ENTROPY
RESULT
(THEOREM
3.1)
...............................................
45
3.5
A
FEW
WORDS
ON
DYATLOV
AND
JIN
S
RESULT
...............................................
55
4
QUANTUM
ERGODICITY
ON
REGULAR
GRAPHS
........................................................
57
4.1
REGULAR
GRAPHS:
QUANTUM
ERGODICITY
......................................................
58
4.2
HARMONIC
ANALYSIS
ON
THE
(Q
+
L)-REGULAR
TREE
.....................................
66
4.3
PROOF
OF
THEOREM
4.2
..............................................................................
71
5
QUANTUM
ERGODICITY
ON
THE
SPHERE
..
........................................................
81
6
QUANTUM
ERGODICITY
ON
NON-REGULAR
GRAPHS
...............................................
85
6.1
INTRODUCTION
...............................................................................................
85
6.2
A
PROOF
BASED
ON
THE
NON-BACKTRACKING
RANDOM
WALK
...........................
89
6.3
ADAPTATION
TO
NON-REGULAR
GRAPHS
...........................................................
99
6.4
TREES
OF
FINITE
CONE
TYPE AND
THEIR
STOCHASTIC
PERTURBATIONS
....................
107
6.5
THE
MEASURE
(A}
Y
:
ONE
EXAMPLE
................................................................
115
7
BACKHAUSZ
AND
SZEGEDY
S
THEOREM
...................................................................
117
7.1
GAUSSIANITY
OF
EIGENFUNCTIONS
.....................................................................
117
7.2
ELEMENTS
OF
THE
PROOF
.................................................................................
120
REFERENCES
...................................................................................................................
127
|
| adam_txt |
CONTENTS
1
INTRODUCTION
.
1
1.1
HISTORY
OF
THE
PROBLEM
.
1
1.2
CONJECTURES,
SCOPE
OF
THE
BOOK
.
3
2
HIGH
FREQUENCY
DELOCALISATION
.
15
2.1
L
P
-NORMS
AS
MEASURES
OF
DELOCALISATION?
.
16
2.2
THE
SHNIRELMAN
THEOREM
.
18
2.3
OVERVIEW
OF
PSEUDO-DIFFERENTIAL
OPERATORS
.
20
2.4
THE
GEODESIC
FLOW
AND
THE
ERGODICITY
ASSUMPTION
.
32
2.5
PROOF
OF
THE
QUANTUM
ERGODICITY
THEOREM
.
34
3
ENTROPY
AND
SUPPORT
OF
SEMICLASSICAL
MEASURES
.
37
3.1
QUANTUM
UNIQUE
ERGODICITY
CONJECTURE
.
37
3.2
STATEMENT
OF
RESULTS
.
38
3.3
WHAT
IS
ENTROPY?
.
41
3.4
PROOF
OF
THE
ENTROPY
RESULT
(THEOREM
3.1)
.
45
3.5
A
FEW
WORDS
ON
DYATLOV
AND
JIN
'
S
RESULT
.
55
4
QUANTUM
ERGODICITY
ON
REGULAR
GRAPHS
.
57
4.1
REGULAR
GRAPHS:
QUANTUM
ERGODICITY
.
58
4.2
HARMONIC
ANALYSIS
ON
THE
(Q
+
L)-REGULAR
TREE
.
66
4.3
PROOF
OF
THEOREM
4.2
.
71
5
QUANTUM
ERGODICITY
ON
THE
SPHERE
.
.
81
6
QUANTUM
ERGODICITY
ON
NON-REGULAR
GRAPHS
.
85
6.1
INTRODUCTION
.
85
6.2
A
PROOF
BASED
ON
THE
NON-BACKTRACKING
RANDOM
WALK
.
89
6.3
ADAPTATION
TO
NON-REGULAR
GRAPHS
.
99
6.4
TREES
OF
FINITE
CONE
TYPE AND
THEIR
STOCHASTIC
PERTURBATIONS
.
107
6.5
THE
MEASURE
(A}
Y
:
ONE
EXAMPLE
.
115
7
BACKHAUSZ
AND
SZEGEDY
'
S
THEOREM
.
117
7.1
GAUSSIANITY
OF
EIGENFUNCTIONS
.
117
7.2
ELEMENTS
OF
THE
PROOF
.
120
REFERENCES
.
127 |
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| author | Anantharaman, Nalini 1976- |
| author_GND | (DE-588)1227362226 |
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| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)1336532834 (DE-599)DNB1262414369 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 1. Auflage |
| format | Book |
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| id | DE-604.BV048597911 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T21:09:11Z |
| indexdate | 2024-07-10T09:42:34Z |
| institution | BVB |
| institution_GND | (DE-588)1066118477 |
| isbn | 9783985470150 3985470154 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033973503 |
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| owner | DE-188 DE-11 |
| owner_facet | DE-188 DE-11 |
| physical | 134 Seiten 24 cm x 17 cm |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | EMS Press |
| record_format | marc |
| series2 | Zurich lectures in advanced mathematics |
| spelling | Anantharaman, Nalini 1976- Verfasser (DE-588)1227362226 aut Quantum ergodicity and delocalization of Schrödinger Eigenfunctions Nalini Anantharaman 1. Auflage Berlin EMS Press [2022] 134 Seiten 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier Zurich lectures in advanced mathematics Schrödinger operators on manifolds and graphs quantum chaos Laplacian quantum ergodicity European Mathematical Society Publishing House ETH-Zentrum SEW A27 (DE-588)1066118477 pbl Erscheint auch als Online-Ausgabe 978-3-98547-515-5 (DE-604)BV048319890 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033973503&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20220713 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Anantharaman, Nalini 1976- Quantum ergodicity and delocalization of Schrödinger Eigenfunctions |
| title | Quantum ergodicity and delocalization of Schrödinger Eigenfunctions |
| title_auth | Quantum ergodicity and delocalization of Schrödinger Eigenfunctions |
| title_exact_search | Quantum ergodicity and delocalization of Schrödinger Eigenfunctions |
| title_exact_search_txtP | Quantum ergodicity and delocalization of Schrödinger Eigenfunctions |
| title_full | Quantum ergodicity and delocalization of Schrödinger Eigenfunctions Nalini Anantharaman |
| title_fullStr | Quantum ergodicity and delocalization of Schrödinger Eigenfunctions Nalini Anantharaman |
| title_full_unstemmed | Quantum ergodicity and delocalization of Schrödinger Eigenfunctions Nalini Anantharaman |
| title_short | Quantum ergodicity and delocalization of Schrödinger Eigenfunctions |
| title_sort | quantum ergodicity and delocalization of schrodinger eigenfunctions |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033973503&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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