Weakly resonant tunneling interactions for adiabatic quasi-periodic Schrödinger operators:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Paris
SMF
2006
|
| Series: | Mémoires de la SMF
104 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 105 S. |
| ISBN: | 9782856291887 |
Staff View
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Record in the Search Index
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| adam_text |
MEMOIRES DE LA SMF 104 WEAKLY RESONANT TUNNELING INTERACTIONS FOR
ADIABATIC QUASI-PERIODIC SCHRODINGER OPERATORS ALEXANDER FEDOTOV
FREDERIC KLOPP SOCIETE MATHEMATIQUE DE FRANCE 2006 PUBLIE AVEC LE
CONCOURS DU CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CONTENTS 1.
INTRODUCTION 1 2. THE RESULTS 7 2.1. THE PERIODIC OPERATOR 7 2.2. A
"GEOMETRIC" ASSUMPTION ON THE ENERGY REGION UNDER STUDY 8 2.3. THE
DEFINITIONS OF THE PHASE INTEGRALS AND THE TUNNELING COEFFICIENTS 8 2.4.
ERGODIC FAMILY 11 2.5. A COARSE DESCRIPTION OF THE LOCATION OF THE
SPECTRUM IN J 11 2.6. A PRECISE DESCRIPTION OF THE LOCATION OF THE
SPECTRUM IN J 12 2.7. THE LYAPUNOV EXPONENT AND THE NATURE OF THE
SPECTRUM IN J 14 2.8. NUMERICAL COMPUTATIONS 17 2.9. COMMENTS,
GENERALIZATIONS AND REMARKS 18 2.10. NOTATIONS 19 2.11. A READING GUIDE
TO THE PAPER 19 3. THE MONODROMY MATRIX 21 3.1. THE MONODROMY MATRICES
AND THE MONODROMY EQUATION 21 3.2. ASYMPTOTICS OF TWO MONODROMY MATRICES
22 4. ROUGH CHARACTERIZATION OF THE SPECTRUM AND A NEW MONODROMY MATRIX
27 4.1. THE SCALAR EQUATION 27 4.2. ROUGH CHARACTERIZATION OF THE
LOCATION OF THE SPECTRUM 28 4.3. A NEW MONODROMY MATRIX 30 5. THE
SPECTRUM IN THE "NON-RESONANT" CASE 33 5.1. COEFFICIENTS OF THE SCALAR
EQUATION 33 5.2. THE LOCATION OF THE SPECTRUM 39 5.3. COMPUTATION OF THE
INTEGRATED DENSITY OF STATES 40 5.4. COMPUTATION OF THE LYAPUNOV
EXPONENT 42 5.5. ABSOLUTELY CONTINUOUS SPECTRUM 46 CONTENTS 6. COMPUTING
THE MONODROMY MATRICES 51 6.1. TRANSITION MATRICES 52 6.2. RELATIONS
BETWEEN THE COEFFICIENTS A U AND B V OF THE MATRIX T V 54 6.3.
ASYMPTOTICS OF THE COEFFICIENTS OF THE MONODROMY MATRIX 60 7. PERIODIC
SCHRODINGER OPERATORS 63 7.1. ANALYTIC THEORY OF BLOCH SOLUTIONS 63 7.2.
MEROMORPHIC DIFFERENTIAL Q, 64 8. THE CONSISTENT SOLUTIONS 67 8.1.
STANDARD BEHAVIOR OF CONSISTENT SOLUTIONS 67 8.2. COMPLEX MOMENTUM AND
STOKES LINES FOR W(Q = A COS C, 69 8.3. TWO CONSISTENT SOLUTIONS 72 9.
TWO CONSISTENT BASES 75 9.1. ASYMPTOTICS OF /* 75 9.2. THE WRONSKIAN OF
/* AND /; 76 10. TRANSITION MATRICES 7 9 10.1. ELEMENTARY PROPERTIES OF
THE TRANSITION MATRICES 79 10.2. THE ASYMPTOTICS OF THE TRANSITION
MATRICES 80 10.3. THE PROOF OF THEOREM 6.1 81 10.4. GENERAL ASYMPTOTIC
FORMULAE 82 10.5. THE ASYMPTOTICS OF THE COEFFICIENT BO 84 10.6. THE
ASYMPTOTICS OF THE COEFFICIENT AO 87 11. PHASE INTEGRALS, TUNNELING
COEFFICIENTS AND THE ISO-ENERGY SURFACE . 89 11.1. THE COMPLEX MOMENTUM
ON THE INTEGRATION CONTOURS 89 11.2. INDEPENDENCE OF THE TUNNELING
COEFFICIENTS AND PHASE INTEGRALS ON THE BRANCH OF THE COMPLEX MOMENTUM
IN THEIR DEFINITIONS 90 11.3. PROOF OF THE INEQUALITIES (2.4) 91 11.4.
PROOF OF (2.9) .,. 91 11.5. PROOF OF LEMMA 10.3 91 11.6. THE ISO-ENERGY
CURVE 92 12. PROPERTIES OF THE FOURIER COEFFICIENTS 95 12.1. COMPUTING
THE SEMI-CLASSICAL FACTORS 95 12.2. PROOF OF (6.10)-(6.12) 97 12.3.
PROOF OF (3.23) 97 13. COMBINATIONS OF FOURIER COEFFICIENTS 99 13.1. THE
CONSTANT 9 AND THE COEFFICIENTS T H , T VFI , T VILT 99 13.2. THE PHASES
{ & V } V =O,TT AND {Z^^O,* 101 BIBLIOGRAPHY 103 MEMOIRES DE LA SMF 104 |
| adam_txt |
MEMOIRES DE LA SMF 104 WEAKLY RESONANT TUNNELING INTERACTIONS FOR
ADIABATIC QUASI-PERIODIC SCHRODINGER OPERATORS ALEXANDER FEDOTOV
FREDERIC KLOPP SOCIETE MATHEMATIQUE DE FRANCE 2006 PUBLIE AVEC LE
CONCOURS DU CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CONTENTS 1.
INTRODUCTION 1 2. THE RESULTS 7 2.1. THE PERIODIC OPERATOR 7 2.2. A
"GEOMETRIC" ASSUMPTION ON THE ENERGY REGION UNDER STUDY 8 2.3. THE
DEFINITIONS OF THE PHASE INTEGRALS AND THE TUNNELING COEFFICIENTS 8 2.4.
ERGODIC FAMILY 11 2.5. A COARSE DESCRIPTION OF THE LOCATION OF THE
SPECTRUM IN J 11 2.6. A PRECISE DESCRIPTION OF THE LOCATION OF THE
SPECTRUM IN J 12 2.7. THE LYAPUNOV EXPONENT AND THE NATURE OF THE
SPECTRUM IN J 14 2.8. NUMERICAL COMPUTATIONS 17 2.9. COMMENTS,
GENERALIZATIONS AND REMARKS 18 2.10. NOTATIONS 19 2.11. A READING GUIDE
TO THE PAPER 19 3. THE MONODROMY MATRIX 21 3.1. THE MONODROMY MATRICES
AND THE MONODROMY EQUATION 21 3.2. ASYMPTOTICS OF TWO MONODROMY MATRICES
22 4. ROUGH CHARACTERIZATION OF THE SPECTRUM AND A NEW MONODROMY MATRIX
27 4.1. THE SCALAR EQUATION 27 4.2. ROUGH CHARACTERIZATION OF THE
LOCATION OF THE SPECTRUM 28 4.3. A NEW MONODROMY MATRIX 30 5. THE
SPECTRUM IN THE "NON-RESONANT" CASE 33 5.1. COEFFICIENTS OF THE SCALAR
EQUATION 33 5.2. THE LOCATION OF THE SPECTRUM 39 5.3. COMPUTATION OF THE
INTEGRATED DENSITY OF STATES 40 5.4. COMPUTATION OF THE LYAPUNOV
EXPONENT 42 5.5. ABSOLUTELY CONTINUOUS SPECTRUM 46 CONTENTS 6. COMPUTING
THE MONODROMY MATRICES 51 6.1. TRANSITION MATRICES 52 6.2. RELATIONS
BETWEEN THE COEFFICIENTS A U AND B V OF THE MATRIX T V 54 6.3.
ASYMPTOTICS OF THE COEFFICIENTS OF THE MONODROMY MATRIX 60 7. PERIODIC
SCHRODINGER OPERATORS 63 7.1. ANALYTIC THEORY OF BLOCH SOLUTIONS 63 7.2.
MEROMORPHIC DIFFERENTIAL Q, 64 8. THE CONSISTENT SOLUTIONS 67 8.1.
STANDARD BEHAVIOR OF CONSISTENT SOLUTIONS 67 8.2. COMPLEX MOMENTUM AND
STOKES LINES FOR W(Q = A COS C, 69 8.3. TWO CONSISTENT SOLUTIONS 72 9.
TWO CONSISTENT BASES 75 9.1. ASYMPTOTICS OF /* 75 9.2. THE WRONSKIAN OF
/* AND /; 76 10. TRANSITION MATRICES 7 9 10.1. ELEMENTARY PROPERTIES OF
THE TRANSITION MATRICES 79 10.2. THE ASYMPTOTICS OF THE TRANSITION
MATRICES 80 10.3. THE PROOF OF THEOREM 6.1 81 10.4. GENERAL ASYMPTOTIC
FORMULAE 82 10.5. THE ASYMPTOTICS OF THE COEFFICIENT BO 84 10.6. THE
ASYMPTOTICS OF THE COEFFICIENT AO 87 11. PHASE INTEGRALS, TUNNELING
COEFFICIENTS AND THE ISO-ENERGY SURFACE . 89 11.1. THE COMPLEX MOMENTUM
ON THE INTEGRATION CONTOURS 89 11.2. INDEPENDENCE OF THE TUNNELING
COEFFICIENTS AND PHASE INTEGRALS ON THE BRANCH OF THE COMPLEX MOMENTUM
IN THEIR DEFINITIONS 90 11.3. PROOF OF THE INEQUALITIES (2.4) 91 11.4.
PROOF OF (2.9) .,. 91 11.5. PROOF OF LEMMA 10.3 91 11.6. THE ISO-ENERGY
CURVE 92 12. PROPERTIES OF THE FOURIER COEFFICIENTS 95 12.1. COMPUTING
THE SEMI-CLASSICAL FACTORS 95 12.2. PROOF OF (6.10)-(6.12) 97 12.3.
PROOF OF (3.23) 97 13. COMBINATIONS OF FOURIER COEFFICIENTS 99 13.1. THE
CONSTANT 9 AND THE COEFFICIENTS T H , T VFI , T VILT 99 13.2. THE PHASES
{ & V } V =O,TT AND {Z^^O,* 101 BIBLIOGRAPHY 103 MEMOIRES DE LA SMF 104 |
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| language | German |
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| spelling | Fedotov, Alexander Verfasser aut Weakly resonant tunneling interactions for adiabatic quasi-periodic Schrödinger operators Alexander Fedotov ; Frédéric Klopp Paris SMF 2006 VI, 105 S. txt rdacontent n rdamedia nc rdacarrier Mémoires de la SMF 104 Schrödinger operator Schrödinger-Gleichung (DE-588)4053332-3 gnd rswk-swf Quasiperiodizität (DE-588)4247312-3 gnd rswk-swf WKB-Methode (DE-588)4190133-2 gnd rswk-swf Schrödinger-Gleichung (DE-588)4053332-3 s Quasiperiodizität (DE-588)4247312-3 s WKB-Methode (DE-588)4190133-2 s b DE-604 Klopp, Frédéric Verfasser aut Mémoires de la SMF 104 (DE-604)BV000000921 104 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014866177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fedotov, Alexander Klopp, Frédéric Weakly resonant tunneling interactions for adiabatic quasi-periodic Schrödinger operators Mémoires de la SMF Schrödinger operator Schrödinger-Gleichung (DE-588)4053332-3 gnd Quasiperiodizität (DE-588)4247312-3 gnd WKB-Methode (DE-588)4190133-2 gnd |
| subject_GND | (DE-588)4053332-3 (DE-588)4247312-3 (DE-588)4190133-2 |
| title | Weakly resonant tunneling interactions for adiabatic quasi-periodic Schrödinger operators |
| title_auth | Weakly resonant tunneling interactions for adiabatic quasi-periodic Schrödinger operators |
| title_exact_search | Weakly resonant tunneling interactions for adiabatic quasi-periodic Schrödinger operators |
| title_exact_search_txtP | Weakly resonant tunneling interactions for adiabatic quasi-periodic Schrödinger operators |
| title_full | Weakly resonant tunneling interactions for adiabatic quasi-periodic Schrödinger operators Alexander Fedotov ; Frédéric Klopp |
| title_fullStr | Weakly resonant tunneling interactions for adiabatic quasi-periodic Schrödinger operators Alexander Fedotov ; Frédéric Klopp |
| title_full_unstemmed | Weakly resonant tunneling interactions for adiabatic quasi-periodic Schrödinger operators Alexander Fedotov ; Frédéric Klopp |
| title_short | Weakly resonant tunneling interactions for adiabatic quasi-periodic Schrödinger operators |
| title_sort | weakly resonant tunneling interactions for adiabatic quasi periodic schrodinger operators |
| topic | Schrödinger operator Schrödinger-Gleichung (DE-588)4053332-3 gnd Quasiperiodizität (DE-588)4247312-3 gnd WKB-Methode (DE-588)4190133-2 gnd |
| topic_facet | Schrödinger operator Schrödinger-Gleichung Quasiperiodizität WKB-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014866177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000921 |
| work_keys_str_mv | AT fedotovalexander weaklyresonanttunnelinginteractionsforadiabaticquasiperiodicschrodingeroperators AT kloppfrederic weaklyresonanttunnelinginteractionsforadiabaticquasiperiodicschrodingeroperators |