Tosio Kato’s work on non-relativistic quantum mechanics: part 1

We review the work of Tosio Kato on the mathematics of non-relativistic quantum mechanics and some of the research that was motivated by this. Topics in this first part include analytic and asymptotic eigenvalue perturbation theory, Temple–Kato inequality, self-adjointness results, and quadratic forms including monotone convergence theorems

Contributions to Mathematics and Statistics : Essays in honor of Seppo Hassi

This Festschrift contains thirteen articles in honor of the sixtieth birthday of Professor Seppo Hassi (University of Vaasa). It centers on three topics: functional analysis and operator theory, boundary value problems, and statistics, stochastics, and the history of mathematics. The collection contains four papers on the topic of functional analysis and operator theory. More precisely, it includes a paper treating the transformation of operator-valued Nevanlinna functions and the congruence of their associated realizing operators, a paper treating Parseval frames in the setting of Krein spaces, a paper treating algebraic inclusions of relations as well as the generalized inverses of relations, and a paper treating Krein-von Neumann and Friedrichs extensions by means of energy spaces. Boundary value problems are considered in six of the contributions. In particular, singular perturbations of the Dirac operator are treated by means of the technique of boundary triplets, the connection between sectorial Schrödinger L-systems and certain classes of Weyl-Titchmarsh functions is considered, PT-symmetric Hamiltonians are treated from the perspective of couplings of dual pairs, the Riesz basis property of indefinite Sturm-Liouville problems is considered, the stability properties of spectral characteristics of boundary value problems are investigated, and the completeness and minimality of systems of eigenfunctions and associated functions of ordinary differential operators are treated. Finally, the collection also contains three contributions connected with the topics of statistics, stochastics, and the history of mathematics. More precisely, a new statistic is introduced for the testing of cumulative abnormal returns in the case of partially overlapping event windows, a new characterization of Brownian motion is established, and, finally, a history of (the department of) mathematics and statistics at the University of Vaasa is presented.fi=vertaisarvioimaton|en=nonPeerReviewed

BCS Theory in the Weak Magnetic Field Regime for Systems with Nonzero Flux and Exponential Estimates on the Adiabatic Theorem in Extended Quantum Lattice Systems

In the main part of this PhD thesis, we consider a periodically realized microscopic superconductor described by BCS theory, which is subject to external electromagnetic fields. We show that the superconductor is properly described by Ginzburg--Landau theory in the macroscopic and weak magnetic field limit. The main novelty of our results is to allow for a non-vanishing magnetic flux through the unit cell of the lattice of periodicity. These main results are supplemented by various unpublished notes in the field of BCS theory. Furthermore, we preface the presentation of these results with a comprehensive introduction suitable for master's or PhD students. Thereby, we hope to contribute to filling the gap of missing introductory literature in the field. The thesis comprises a second topic, in which we provide ideas for setting up quantum lattice systems in order to prove exponential estimates for the adiabatic theorem. These notes are the result of studies in this field, which have been conducted during a research stay at the University of British Columbia (UBC) in Vancouver, Canada.Comment: PhD thesi

BCS theory in the weak magnetic field regime for systems with nonzero flux and exponential estimates on the adiabatic theorem in extended quantum lattice systems

In the main part of this PhD thesis, we consider a periodically realized microscopic superconductor described by BCS theory, which is subject to external electromagnetic fields. We show that the superconductor is properly described by Ginzburg--Landau theory in the macroscopic and weak magnetic field limit. The main novelty of our results is to allow for a non-vanishing magnetic flux through the unit cell of the lattice of periodicity. These main results are supplemented by various unpublished notes in the field of BCS theory. Furthermore, we preface the presentation of these results with a comprehensive introduction suitable for master's or PhD students. Thereby, we hope to contribute to filling the gap of missing introductory literature in the field. The thesis comprises a second topic, in which we provide ideas for setting up quantum lattice systems in order to prove exponential estimates for the adiabatic theorem. These notes are the result of studies in this field, which have been conducted during a research stay at the University of British Columbia (UBC) in Vancouver, Canada.Comment: PhD thesi

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions