Mathematical physics of quantum mechanics : selected and refereed lectures from QMath9 / Joachim Asch, Alain Joye (eds.).

By: QMath9 (2004 : Giens, France)
Contributor(s): Asch, Joachim | Joye, Alain
Material type: TextTextSeries: Lecture notes in physics: 690.Publisher: Berlin ; New York : Springer, ©2006Description: 1 online resource (xxi, 483 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 3540310266; 9783540310266; 9783540342731; 3540342737; 6610627061; 9786610627066Subject(s): Quantum theory -- Congresses | Mathematical physics -- Congresses | Théorie quantique -- Mathématiques -- Congrès | SCIENCE -- Physics -- Quantum Theory | Mathematical physics | Quantum theory | Physique | Mathematical physics | Quantum theory | Kwantummechanica | Mathematische fysica | Mathematische Physik | Quantenmechanisches System | Giens <2004>Genre/Form: Electronic books. | Conference papers and proceedings. | Giens (2004) | Kongress. | Online-Publikation. Additional physical formats: Print version:: Mathematical physics of quantum mechanics.DDC classification: 530.1201/51 LOC classification: QC174.12 | .Q24 2004Other classification: 33.23 | O413-532 | UD 8220 | 530 Online resources: Click here to access online
Contents:
Introduction -- Solving the ten martini problem / A. Avila and S. Jitomirskaya -- Swimming lessons for microbots / Y. Avron -- Landau-Zener formulae from adiabatic transition histories / V. Betz and S. Teufel -- Scattering theory of dynamic electrical transport / M. Büttiker and M. Moskalets -- The Landauer-Büttiker formula and resonant quantum transport / H.D. Cornean, A. Jensen and V. Moldoveanu -- Point interaction polygons : an isoperimetric problem / P. Exner -- Limit cycles in quantum mechanics / S.D. Głazek -- Cantor spectrum for quasi-periodic Schrödinger operators / J. Puig -- Adiabatic theorems and reversible isothermal processes / W.K. Abou-Salem and J. Fröhlich -- Quantum massless field in 1+1 dimensions / J. Dereziński and K.A. Meissner -- Stability of multi-phase equilibria / M. Merkli -- Ordering of energy levels in Heisenberg models and applications / B. Nachtergaele and S. Starr -- Interacting fermions in 2 dimensions / V. Rivasseau -- On the essential spectrum of the translation invariant Nelson model / J. Schach-Møller -- Bose-Einstein condensation as a quantum phase transition in an optical lattice / M. Aizenman [and others] -- Long time behaviour to the Schrödinger-Poisson-X[superscript [alpha]] systems / O. Bokanowski [and others] -- Towards the quantum Brownian motion / L. Erdős, M. Salmhofer and H.-T. Yau -- Bose-Einstein condensation and superradiance / J.V. Pulé, A.F. Verbeure and V.A. Zagrebnov -- Derivation of the Gross-Pitaevskii hierarchy / B. Schlein -- Towards a microscopic derivation of the phonon Boltzmann equation / H. Spohn -- On the quantization of Hall currents in presence of disorder / J.-M. Combes, F. Germinet and P.D. Hislop -- Equality of the bulk and edge Hall conductances in 2D / A. Elgart -- Generic subsets in spaces of measures and singular continuous spectrum / D. Lenz and P. Stollmann -- Low density expansion for Lyapunov exponents / H. Schulz-Baldes -- Poisson statistics for the largest eigenvalues in random matrix ensembles / A. Soshnikov -- Recent results on quantum map eigenstates / S. De Biévre -- Level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators / A. Fedotov and F. Klopp -- Low lying eigenvalues of Witten Laplacians and metastability [after Helffer-Klein-Nier and Helffer-Nier] / B. Helffer -- The mathematical formalism of a particle in a magnetic field / M. Măntoiu and R. Purice -- Fractal Weyl law for open chaotic maps / S. Nonnenmacher -- Spectral shift function for magnetic Schrödinger operators / G. Raikov -- Counting string/M vacua / S. Zelditch.
Action note: digitized 2011 committed to preserveSummary: At the QMath9 meeting, young scientists learn about the state of the art in the mathematical physics of quantum systems. Based on that event, this book offers a selection of outstanding articles written in pedagogical style comprising six sections which cover new techniques and recent results on spectral theory, statistical mechanics, Bose-Einstein condensation, random operators, magnetic Schrödinger operators and much more. For postgraduate students, Mathematical Physics of Quantum Systems serves as a useful introduction to the research literature. For more expert researchers, this book will be a concise and modern source of reference.
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Includes bibliographical references and index.

Introduction -- Solving the ten martini problem / A. Avila and S. Jitomirskaya -- Swimming lessons for microbots / Y. Avron -- Landau-Zener formulae from adiabatic transition histories / V. Betz and S. Teufel -- Scattering theory of dynamic electrical transport / M. Büttiker and M. Moskalets -- The Landauer-Büttiker formula and resonant quantum transport / H.D. Cornean, A. Jensen and V. Moldoveanu -- Point interaction polygons : an isoperimetric problem / P. Exner -- Limit cycles in quantum mechanics / S.D. Głazek -- Cantor spectrum for quasi-periodic Schrödinger operators / J. Puig -- Adiabatic theorems and reversible isothermal processes / W.K. Abou-Salem and J. Fröhlich -- Quantum massless field in 1+1 dimensions / J. Dereziński and K.A. Meissner -- Stability of multi-phase equilibria / M. Merkli -- Ordering of energy levels in Heisenberg models and applications / B. Nachtergaele and S. Starr -- Interacting fermions in 2 dimensions / V. Rivasseau -- On the essential spectrum of the translation invariant Nelson model / J. Schach-Møller -- Bose-Einstein condensation as a quantum phase transition in an optical lattice / M. Aizenman [and others] -- Long time behaviour to the Schrödinger-Poisson-X[superscript [alpha]] systems / O. Bokanowski [and others] -- Towards the quantum Brownian motion / L. Erdős, M. Salmhofer and H.-T. Yau -- Bose-Einstein condensation and superradiance / J.V. Pulé, A.F. Verbeure and V.A. Zagrebnov -- Derivation of the Gross-Pitaevskii hierarchy / B. Schlein -- Towards a microscopic derivation of the phonon Boltzmann equation / H. Spohn -- On the quantization of Hall currents in presence of disorder / J.-M. Combes, F. Germinet and P.D. Hislop -- Equality of the bulk and edge Hall conductances in 2D / A. Elgart -- Generic subsets in spaces of measures and singular continuous spectrum / D. Lenz and P. Stollmann -- Low density expansion for Lyapunov exponents / H. Schulz-Baldes -- Poisson statistics for the largest eigenvalues in random matrix ensembles / A. Soshnikov -- Recent results on quantum map eigenstates / S. De Biévre -- Level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators / A. Fedotov and F. Klopp -- Low lying eigenvalues of Witten Laplacians and metastability [after Helffer-Klein-Nier and Helffer-Nier] / B. Helffer -- The mathematical formalism of a particle in a magnetic field / M. Măntoiu and R. Purice -- Fractal Weyl law for open chaotic maps / S. Nonnenmacher -- Spectral shift function for magnetic Schrödinger operators / G. Raikov -- Counting string/M vacua / S. Zelditch.

At the QMath9 meeting, young scientists learn about the state of the art in the mathematical physics of quantum systems. Based on that event, this book offers a selection of outstanding articles written in pedagogical style comprising six sections which cover new techniques and recent results on spectral theory, statistical mechanics, Bose-Einstein condensation, random operators, magnetic Schrödinger operators and much more. For postgraduate students, Mathematical Physics of Quantum Systems serves as a useful introduction to the research literature. For more expert researchers, this book will be a concise and modern source of reference.

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