European Mathematical Society, Zürich, Switzerlandm, 2017. — 597 p. — (EMS Series of Congress Reports). — ISBN:3037191759.This volume is dedicated to Pavel Exner on the occasion of his 70th anniversary. It collects contributions by numerous scientists with expertise in mathematical physics and in particular in problems arising from quantum mechanics. The questions addressed in the contributions cover a large range of topics. A lot of attention was paid to differential operators with zero range interactions, which are often used as models in quantum mechanics. Several authors considered problems related to systems with mixed-dimensions such as quantum waveguides, quantum layers and quantum graphs. Eigenvalues and eigenfunctions of Laplace and Schr?dinger operators are discussed too, as well as systems with adiabatic time evolution. Although most of the problems treated in the book have a quantum mechanical background, some contributions deal with issues which go well beyond this framework; for example the Cayley-Hamilton theorem, approximation formulae for contraction semigroups or factorization of analytic operator-valued Fredholm functions. As for the mathematical tools involved, the book provides a wide variety of techniques from functional analysis and operator theory. Altogether the volume presents a collection of research papers which will be of interest to any active scientist working in one of the above mentioned fields. Contents Relative partition function of Coulomb plus delta interaction Inequivalence of quantum Dirac elds of different masses and the underlying general structures involved On a class of Schrödinger operators exhibiting spectral transition On the quantum mechanical three-body problem with zero-range interactions On the index of meromorphic operator-valued functions and some applications Trace formulae for Schrödinger operators with singular interactions An improved bound for the non-existence of radial solutions of the Brezis–Nirenberg problem in Hn Twisted waveguide with a Neumann window Example of a periodic Neumann waveguide with a gap in its Two-dimensional time-dependent point interactions On resonant spectral gaps in quantum graphs Adiabatic theorem for a class of stochastic differential equations on a Hilbert space Eigenvalues of Schrödinger operators with complex surface potentials A lower bound to the spectral threshold in curved quantum layers To the spectral theory of vector-valued Sturm–Liouville operators with summable potentials and point interactions Spectral asymptotics for the Dirichlet Laplacian with a Neumann window via a Birman–Schwinger analysis of the Dirichlet-to-Neumann operator Dirichlet eigenfunctions in the cube, sharpening the Courant nodal inequality A mathematical modeling of electron–phonon interaction for small wave numbers close to zero The modied unitary Trotter–Kato and Zeno product formulas revisited Spectral asymptotics induced by approaching and diverging planar circles Spectral estimates for the Heisenberg Laplacian on cylinders Variational proof of the existence of eigenvalues for star graphs On the boundedness and compactness of weighted Green operators of second-order elliptic operators Abstract graph-like spaces and vector-valued metric graphs A Cayley–Hamiltonian theorem for periodic nite band matrices Path topology dependence of adiabatic time evolution On quantum graph lters with at passbands Comments on the Chernoff n-lemm
Чтобы скачать этот файл зарегистрируйтесь и/или войдите на сайт используя форму сверху.