Actions for Quantum theory from small to large scales [electronic resource] : lecture notes of the Les Houches Summer School: Volume 95, August 2010

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Quantum theory from small to large scales [electronic resource] : lecture notes of the Les Houches Summer School: Volume 95, August 2010 / [edited by] Jürg Frohlich [and others].

Conference Author
Ecole d'été de physique théorique (Les Houches, Haute-Savoie, France) (95th : 2010)
Published
Oxford : Oxford University Press, 2012.
Physical Description
1 online resource (xxv, 691 pages) : illustrations, portraits
Additional Creators
Fröhlich, Jürg
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Contents
Machine generated contents note: pt. I Long lectures -- 1.Lecture notes on quantum Brownian motion / Laszlo Erdos -- Preface -- 1.1.Overview of the rigorous derivations of diffusions -- 1.2.Some facts on stochastic processes -- 1.3.Classical mechanics of a single particle -- 1.4.Quantum mechanics of a single particle -- 1.5.Random Schrodinger operators -- 1.6.Main result -- 1.7.Feynman graphs (without repetition) -- 1.8.Key ideas of the proof of the diffusion (Theorems 1.13 and 1.14) -- 1.9.Integration of general Feynman graphs -- 1.10.Feynman graphs with repetitions -- 1.11.Computation of the main term -- 1.12.Conclusions -- 1.13.Appendix: Inequalities -- 1.14.Appendix: Power counting for integration of Feynman diagrams -- References -- 2.The temporal ultraviolet limit / Eugene Trubowitz -- 2.1.Introduction -- 2.2.Motivation for the stationary phase approximation -- 2.3.Bounds on the stationary phase approximation -- 2.4.Functional integrals -- 2.5.A simple high temperature expansion -- 2.6.Appendix: Complex Gaussian integrals -- References -- 3.Locality in quantum systems / Matthew B. Hastings -- Preface -- 3.1.Introduction and notation -- 3.2.Locality and Lieb-Robinson bounds -- 3.3.Correlation decay -- 3.4.Topological order -- 3.5.Fourier transforms -- 3.6.Quasi-adiabatic continuation -- 3.7.Lieb-Schultz-Mattis in higher dimensions -- 3.8.What is a phase? -- 3.9.Stability of topologically ordered phase -- Acknowledgements -- References -- 4.Entropic fluctuations in quantum statistical mechanics---an introduction / C.-A. Pillet -- 4.1.Introduction -- 4.2.Prologue: a thermally driven classical harmonic chain -- 4.3.Algebraic quantum statistical mechanics of finite systems -- 4.4.Entropic functionals and fluctuation relations of finite quantum systems -- 4.5.Open quantum systems -- 4.6.The thermodynamic limit and the large time limit -- 4.7.Fermionic systems -- 4.8.Appendix: Large deviations -- 4.9.Vitali convergence theorem -- References -- 5.Quantum phase transitions: introduction and some open problems / Achim Rosch -- Preface -- 5.1.Quantum criticality and scaling -- 5.2.Field driven QPT as Bose-Einstein condensation -- 5.3.Order parameter theories and perturbative renormalization group -- 5.4.Beyond the standard models -- Acknowledgements -- References -- 6.Cold quantum gases and Bose-Einstein condensation / Robert Seiringer -- 6.1.Introduction -- 6.2.Quantum many-body systems -- 6.3.BEC for interacting systems -- 6.4.Dilute Bose gases -- 6.5.Dilute Bose gases in traps -- Acknowledgements -- References -- 7.SUSY statistical mechanics and random band matrices / Thomas Spencer -- 7.1.An overview -- 7.2.Classical models of quantum dynamics -- 7.3.Introduction to random matrix ensembles and SUSY -- 7.4.Averaging Det(Ee - H)-1 -- 7.5.The density of states for GUE -- 7.6.Statistical mechanics, sigma models, and Goldstone modes -- 7.7.Hyperbolic symmetry -- 7.8.Phase transition for A SUSY hyperbolic sigma model -- 7.9.Efetov's sigma model -- 7.10.Appendix: Gaussian and Grassmann integration -- 7.11.Appendix: Formal perturbation theory -- 7.12.Appendix: Bounds on Green's functions of divergence form -- Acknowledgements -- References -- pt. II Short lectures -- 8.Mass renormalization in nonrelativistic quantum electrodynamics / Volker Bach -- 8.1.Mass renormalization in NR QED---overview of results -- 8.2.Renormalization group based on the smooth Feshbach-Schur map -- Acknowledgements -- References -- 9.Long-time diffusion for a quantum particle / Wojciech De Roeck -- 9.1.Introduction -- 9.2.The models -- 9.3.Weak coupling limit -- 9.4.Long-time behaviour -- References -- 10.The ground state construction of the two-dimensional Hubbard model on the honeycomb lattice / Alessandro Giuliani -- 10.1.Introduction -- 10.2.The model and the main results -- 10.3.The noninteracting system -- 10.4.Perturbation theory and Grassmann integration -- 10.5.The determinant expansion -- 10.6.The multi-scale integration: the ultraviolet regime -- 10.7.The multi-scale integration: the infrared regime -- 10.8.Conclusions -- 10.9.Appendix: Dimensional estimates of the propagators -- 10.10.Appendix: Truncated expectations and determinants -- 10.11.Appendix: Symmetry properties -- Acknowledgements -- References -- 11.On transport in quantum devices / Gian Michele Graf -- Preface -- 11.1.Quantum pumps -- 11.2.Transport statistics -- References -- 12.Renormalization group and problem of radiation / Israel Michael Sigal -- 12.1.Overview -- 12.2.Nonrelativistic QED -- 12.3.Resonances -- 12.4.Existence of the ground and resonance states -- 12.5.Generalized Pauli-Fierz transformation -- 12.6.Renormalization group map -- 12.7.A Banach space of Hamiltonians -- 12.8.Action of renormalization map -- 12.9.Renormalization group -- 12.10.Related results -- 12.11.Conclusion -- 12.12.Comments on literature -- 12.13.Appendix: Hamiltonian of the standard model -- 12.14.Translationally invariant Hamiltonians -- 12.15.Proof of Theorem 12.5 -- 12.16.Smooth Feshbach-Schur Map -- 12.17.Pull-through formulae -- 12.18.Supplement: creation and annihilation operators -- Acknowledgements -- References -- 13.Bell inequalities / Michael Marc Wolf -- 14.Universality of generalized Wigner matrices / Horng-Tzer Yau -- 14.1.Introduction -- 14.2.Local semicircle law -- 14.3.Universality of Gaussian divisible ensembles via Dyson Brownian motion -- 14.4.Green function comparison theorem -- References.
Summary
This title collects lecture courses and seminars given at the Les Houches Summer School 2010 on 'Quantum Theory: From Small to Large Scales'. It reviews the state-of-the-art developments in this field by touching on different research topics from an interdisciplinary perspective.
Subject(s)
ISBN
9780191741203 (ebook)
Note
Selected conference papers.
Bibliography Note
Includes bibliographical references.
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