Mathematical Results in Quantum Mechanics

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 physics Prominent contributors Shows the actual research topics in mathematical physics