Mathematical Results In Quantum Mechanics Proceedings Of The Qmath10 Conference

The 10th Quantum Mathematics International Conference (Qmath10) gave an opportunity to bring together specialists interested in that part of mathematical physics which is in close connection with various aspects of quantum theory. It was also meant to introduce young scientists and new tendencies in the field.This collection of carefully selected papers aims to reflect recent techniques and results on Schrödinger operators with magnetic fields, random Schrödinger operators, condensed matter and open systems, pseudo-differential operators and semiclassical analysis, quantum field theory and relativistic quantum mechanics, quantum information, and much more. The book serves as a concise and well-documented tool for the more experimented scientists, as well as a research guide for postgraduate students.

The 10th Quantum Mathematics International Conference (Qmath10) gave an opportunity to bring together specialists interested in that part of mathematical physics which is in close connection with various aspects of quantum theory. It was also meant to introduce young scientists and new tendencies in the field.This collection of carefully selected papers aims to reflect recent techniques and results on SchrAdinger operators with magnetic fields, random SchrAdinger operators, condensed matter and open systems, pseudo-differential operators and semiclassical analysis, quantum field theory and relativistic quantum mechanics, quantum information, and much more. The book serves as a concise and well-documented tool for the more experimented scientists, as well as a research guide for postgraduate students.

The book provides a comprehensive overview on the state of the art of the quantum part of mathematical physics. In particular, it contains contributions to the spectral theory of Schrödinger and random operators, quantum field theory, relativistic quantum mechanics and interacting many-body systems. It also presents an overview on the achievements in mathematical physics since the last conference QMath11 held at Hradec Kralove, Czechia in 2010. Contents:Plenary Talks:A Bound for the Eigenvalue Counting Function for Higher-Order Krein Laplacians on Open Sets (F Gesztesy, M Mitrea, S Sukhtaiev and A Laptev)Trace Formulae for the Asymptotic Density of Eigenvalue Clusters for the Perturbed Landau Hamiltonian (T Lungenstrass and G D Raikov)On Long Range Behaviour of van der Waals Force (I Anapolitanos and I M Sigal)Quantum Spin Correlations and Random Loops (D Ueltschi)Equidistribution Estimates for Eigenfunctions and Eigenvalue Bounds for Random Operators (D Borisov, M Tautenhahn and I Veselić)Invited Section Talks:Vector Quantum Fields (J Dereziński)On the BCS Gap Equation for Superfluid Fermionic Gases (G Bräunlich, C Hainzl and R Seiringer)Improved Hardy Inequality in Twisted Tubes (H Kovařík)Microscopic Foundations of Ohm and Joule's Laws — The Relevance of Thermodynamics (J-B Bru and W de Siqueira Pedra)The Quantum Marginal Problem (C Schilling)Hartree-Fock Dynamics for Weakly Interacting Fermions (N Benedikter, M Porta and B Schlein)Contributed Talks:On the Ground State Energy of the Multipolaron in the Strong Coupling Limit (I Anapolitanos and B Landon)A Variation on Smilansky's Model (D Barseghyan and P Exner)Deriving the Gross-Pitaevskii Equation (N Benedikter)Boundary Triplets Approach for Dirac Operator (A A Boitsev)Bose-Einstein Condensation on Quantum Graphs (J Bolte and J Kerner)Description of Quantum and Classical Dynamics via Feynman Formulae (Ya A Butko)Asymptotic Observables, Propagation Estimates and the Problem of Asymptotic Completeness in Algebraic QFT (W Dybalski)Recent Probabilistic Results on Covariant Schrödinger Operators on Infinite Weighted Graphs (B Güneysu and O Milatovic)Resolvent Expansion for the Discrete One-Dimensional Schrödinger Operator (K Ito and A Jensen)Spectral Asymptotics for a δ′ Interaction Supported by an Infinite Curve (M Jex)Asymptotically Predefined Spectral Gaps for the Neumann Laplacian in Periodic Domains (A Khrabustovskyi)Graph Model for the Stokes Flow (M O Kovaleva and I Yu Popov)Point Contacts and Boundary Triples (V Lotoreichik, H Neidhardt and I Yu Popov)Trace Formulas for Singular and Additive Non-Selfadjoint Perturbations (M M Malamud and H Neidhardt)On δ′-Couplings at Graph Vertices (S S Manko)Stochastic Calculus and Non-Relativistic QED (B Güneysu, O Matte and J S Møller)Estimates for Numbers of Negative Eigenvalues of Laplacian for Y-Type Chain of Weakly Coupled Ball Resonators (A S Melikhova)On Thermodynamical Couplings of Quantum Mechanics and Macroscopic Systems (A Mielke)Almost Sure Purely Singular Continuous Spectrum for Quasicrystal Models (C Seifert)Adiabatic Theorems With and Without Spectral Gap Condition for Non-Semisimple Spectral Values (J Schmid)An Eigenvalue Counting Theorem with Applications to Random Schrödinger Operators (D Schmidt)System of Fermions with Zero-Range Interactions (A Teta) Readership: Graduate students, professionals and researchers in mathematical physics, quantum mechanics and field theory, quantum information, quantum chaos and physics of social systems. Key Features:Collection of state-of-the-art papers in mathematical physicsProminent contributorsShows the actual research topics in mathematical physicsKeywords:Schrödinger Operator;Spectral Theory;Random Operators;Quantum Field Theory;Relativistic Quantum Mechanics;Interacting Many-Body Systems

The volume collects papers from talks given at QMath11 - Mathematical Results in Quantum Physics, which was held in Hradec Kralove, September 2010. These papers bring new and interesting results in quantum mechanics and information, quantum field theory, random systems, quantum chaos, as well as in the physics of social systems. Part of the contribution is dedicated to Ari Laptev on the occasion of his 60th birthday, in recognition of his mathematical results and his service to the community. The QMath conference series has played an important role in mathematical physics for more than two decades, typically attracting many of the best results achieved in the last three-year period, and the meeting in Hradec Kralove was no exception.

This book constitutes the proceedings of the QMath 7 Conference on Mathematical Results in Quantum Mechanics held in Prague, Czech Republic in June, 1998. The volume addresses mathematicians and physicists interested in contemporary quantum physics and associated mathematical questions, presenting new results on Schrödinger and Pauli operators with regular, fractal or random potentials, scattering theory, adiabatic analysis, and interesting new physical systems such as photonic crystals, quantum dots and wires.

This book collects lecture courses and seminars given at the Les Houches Summer School 2010 on "Quantum Theory: From Small to Large Scales". Fundamental quantum phenomena appear on all scales, from microscopic to macroscopic. Some of the pertinent questions include the onset of decoherence, the dynamics of collective modes, the influence of external randomness and the emergence of dissipative behaviour. Our understanding of such phenomena has been advanced by the study of model systems and by the derivation and analysis of effective dynamics for large systems and over long times. In this field, research in mathematical physics has regularly contributed results that were recognized as essential in the physics community. During the last few years, the key questions have been sharpened and progress on answering them has been particularly strong. This book reviews the state-of-the-art developments in this field and provides the necessary background for future studies. All chapters are written from a pedagogical perspective, making the book accessible to master and PhD students and researchers willing to enter this field.

Annotation. The volume collects papers from talks given at QMath11 - Mathematical Results in Quantum Physics, which was held in Hradec Králové, September 2010. These papers bring new and interesting results in quantum mechanics and information, quantum field theory, random systems, quantum chaos, as well as in the physics of social systems. Part of the contribution is dedicated to Ari Laptev on the occasion of his 60th birthday, in recognition of his mathematical results and his service to the community. The QMath conference series has played an important role in mathematical physics for more than two decades, typically attracting many of the best results achieved in the last three-year period, and the meeting in Hradec Králové was no exception. Book jacket.

The papers in this volume cover important topics in spectral theory and geometric analysis such as resolutions of smooth group actions, spectral asymptotics, solutions of the Ginzburg-Landau equation, scattering theory, Riemann surfaces of infinite genus and tropical mathematics.