A Numerical Renormalization Group Approach to Dissipative ...

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Page 1:
A Numerical Renormalization Group A
Page 4 and 5:
Contents Contents i Introduction 1
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CONTENTS iii 12.4.3 Intermediate Co
Page 9 and 10:
Introduction The miniaturization of
Page 11:
Table of Contents 3 treatment of th
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Chapter 1 Kondo Effect 1.1 Kondo Ef
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1.1 Kondo Effect in Metals 9 Figure
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1.2 Kondo Effect in Quantum Dots 11
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Chapter 2 Coherent Control of Singl
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2.1 Quantum Dots 15 Figure 2.2: Sca
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2.2 Color Centers in Diamond 17 An
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20 CHAPTER 3. Molecular Electronics
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Page 32 and 33:
Page 35 and 36:
Chapter 4 Fermionic Baths In the fi
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4.3 Mapping the Hamiltonian on a Se
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4.3 Mapping the Hamiltonian on a Se
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4.4 Iterative Diagonalization 33 4.
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4.4 Iterative Diagonalization 35 Fi
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Chapter 5 Bosonic Baths One disting
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5.1 Star Hamiltonian 39 Figure 5.2:
Page 49 and 50:
5.2 Chain Hamiltonian 41 For an ill
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Chapter 6 Density Matrix Numerical
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6.2 Reduced Density Matrix 45 magne
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6.2 Reduced Density Matrix 47 where
Page 58 and 59:
50 CHAPTER 7. Complete Basis A comm
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52 CHAPTER 7. Complete Basis Figure
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54 CHAPTER 7. Complete Basis G(ω)
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Chapter 8 Time-dependence In this c
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8.2 Time Evolution Formula 59 we en
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8.3 Transforming ˆρeq Now we empl
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8.4 Implementing the Algorithm 63 I
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Chapter 9 Finite Temperatures 9.1 S
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9.3 Spectral Functions 67 density m
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Chapter 10 Improving Accuracy In th
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10.3 Damping and Broadening 71 A↑
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10.4 Self-Energy Trick 73 A↑(ω)
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10.5 High-Accuracy NRG Spectral Fun
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Chapter 11 Ferromagnetic Kondo Mode
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11.1.2 Underscreened Kondo Effect 8
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11.1.3 Single Molecule Magnets 83 c
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11.3 Nonequilibrium Magnetization 8
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11.3.1 Isotropic Kondo Exchange 87
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11.3.2 Anisotropic Kondo Exchange 8
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11.4 Summary 91 spin at time t < 0
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94 CHAPTER 12. Fermionic vs. Bosoni
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100 CHAPTER 12. Fermionic vs. Boson
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Page 116 and 117:
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Page 125 and 126:
Chapter 13 Two Spins in a Bosonic B
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13.1 Generalized Two-Spin Boson Mod
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13.2.2 Qualitative Understanding of
Page 131 and 132: 13.2.2 Qualitative Understanding of
Page 133 and 134: 13.3.1 Static Entanglement Entropy
Page 135 and 136: 13.3.2 Subohmic System: Scaling of
Page 137 and 138: 13.4.1 Decoherence Without Transver
Page 139 and 140: 13.4.2 Beating and Decoherence: Bre
Page 141 and 142: 13.4.3 Synchronization of Spin Dyna
Page 143 and 144: 13.4.4 Vanishing Ising Interaction
Page 151 and 152: 13.4.6 Generation of Highly Entangl
Page 153 and 154: Chapter 14 Decoherence in an Aharan
Page 155 and 156: 14.1.1 Mapping to Symmetric/Antisym
Page 157 and 158: 14.2.1 Implementing the Kubo Formal
Page 159 and 160: 14.4 “Diagonal” AC Conductance
Page 161 and 162: 14.4.2 Renormalization of GLL(ωac)
Page 163 and 164: 14.5.2 “Polaron Shift” of Peak
Page 165 and 166: 14.5.3 Multiple Phonon Excitations
Page 167: 14.6 Summary 159 ReGLR/(g 2 ph e2
Page 170 and 171: 162 CHAPTER 14. Decoherence in an A
Page 172 and 173: 164 BIBLIOGRAPHY [12] P. Nozières
Page 174 and 175: 166 BIBLIOGRAPHY [36] D. D. Awschal
Page 176 and 177: 168 BIBLIOGRAPHY [58] A. Hewson: Th
Page 178 and 179: 170 BIBLIOGRAPHY [81] A. Isidori, D
Page 180 and 181: 172 BIBLIOGRAPHY [104] M. Heyl and
Page 184 and 185: 176 BIBLIOGRAPHY [152] D. Braun:
Page 186 and 187: 178 BIBLIOGRAPHY [174] T. L. Schmid
Page 188 and 189: 180 BIBLIOGRAPHY [198] M. E. Fisher
Page 191 and 192: Appendix A Details of the Mapping t
Page 193 and 194: Using the definition of ˆ f † m+
Page 195 and 196: Appendix B Detailed Derivation of S
Page 197 and 198: B.1 Full Density Matrix 189 Fig. B.
Page 199 and 200: B.1 Full Density Matrix 191 m frequ
Page 201 and 202: B.2 Single Shell Approximation 193
Page 203 and 204: Appendix C Details of Bosonization
Page 205 and 206: C.3 Bosonic Reorganization of Fock
Page 207 and 208: C.5 Derivation of the Bosonization
Page 209: C.5 Derivation of the Bosonization
Page 212 and 213: 204 APPENDIX D. Derivation of Scali
Page 215 and 216: Appendix E Mapping the Two-Spin Bos
Page 217: nian (E.1) thus reads in terms of f
Page 221: Publications Part of the results pr
Page 225: Acknowledgments I would like to tak
Page 228 and 229: Der dritte Teil der Arbeit beinhalt
Page 230 and 231: Darüber hinaus haben wir dargelegt
Page 233:
Erklärung Hiermit erkläre ich, da
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