This book builds bridges between two yet separated branches of theoretical and mathematical chemistry: Chemical Graph Theory and Electronic Structure Calculations. Although either of the fields have developed their own techniques, problems, methods, and favorite benchmark cases independent from each other, the authors have managed to bring them together by using the localization-delocalization matrix (LDM). The LDM is a novel molecular descriptor that fingerprints a molecule by condensing the complicated electronic information in one, mathematically manageable, object. In this book, the authors introduce the readers to modeling techniques based on LDMs. Their technique offers a high accuracy as well as robust predictive power, often dramatically surpassing the potential of either of the constituting methods on their own.

The book presents the winners of the Abel Prize in mathematics for the period 2018–2022:

This is volume 2 of Planets, Stars and Stellar Systems, a six-volume compendium of modern astronomical research, covering subjects of key interest to the main fields of contemporary astronomy. This volume on “Astronomical Techniques, Software, and Data” edited by Howard E. Bond presents accessible review chapters on Astronomical Photometry, Astronomical Spectroscopy, Infrared Astronomy Fundamentals, Astronomical Polarimetry: Polarized Views of Stars and Planets, Sky Surveys,Techniques of Radio Astronomy,Radio and Optical Interferometry: Basic Observing Techniques and Data Analysis, Absolute Calibration of Spectrophotometric Standard Stars,Virtual Observatories, Data Mining, and Astroinformatics, Statistical Methods for Astronomy, Numerical Techniques in Astrophysics.

The goal of this book is to expose the reader to the indispensable role that mathematics plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics as diverse as algebras, classical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups, manifolds, Lie groups and their representations, Clifford algebras and their representations, and fibre bundles and their applications to differential geometry and gauge theories.

It is with great emotion that we present here this volume dedicated to the memory of Bernard Jouvet, Docteur es Sciences, Directeur des Recher­ ches at the Centre National pour la Recherche Scientifique. The life and the career as a physicist of Professor Jouvet are evoked in the following pages by Professor F. Cerulus, a friend of long standing of Professor Jouvet. The contributions have been written by physicists who were friends, collaborators or former students of Professor Jouvet. I express here my gratitude for their contributions.

In my original proposal to Springer for a book on Quantal Density Functional Theory, I had envisaged one that was as complete in its presentation as possible, describing the basic theory as well as the approximation methods and a host of applications. However,after workingon the bookforabout ?ve years, I realizedthat the goal was too ambitious, and that I would be writing for another ?ve years for it to be achieved. Fortunately,there was a natural breakin the material, and I proposed to my editor, Dr. Claus Ascheron, that we split the book into two components: the ?rst on the basic theoretical framework, and the second on approximation methods and applications. Dr. Ascheron consented, and I am thankful to him for agreeing to do so. Hence, we published Quantal Density Functional Theory in 2004, and are now publishing Quantal Density Functional Theory II: Approximation Methods and Applications. One signi?cant advantage of this, as it turns out, is that I have been able to incorporate in each volume the most recent understandings available. This volume, like the earlier one, is aimed at advanced undergraduates in physics and chemistry, graduate students and researchers in the ?eld. It is written in the same pedagogical style with details of all proofs and numerous ?gures provided to explain the physics.

In the last 40 years geophysicists have found that it is possible to construct images and even determine important physical characteristics of rocks that can yield information about oil and gas bearing structures in the earth. To make these images and extract this information requires the application of an advanced understanding of the mathematical physics of wave propagation. The oil and gas industry labels a major collection of the necessary seismic data processing methods by the name seismic "migration".

Low-dimensional semiconductors have become a vital part of today's semiconductor physics, and excitons in these systems are ideal objects that bring textbook quantum mechanics to life. Furthermore, their theoretical understanding is important for experiments and optoelectronic devices. The author develops the effective-mass theory of excitons in low-dimensional semiconductors and describes numerical methods for calculating the optical absorption including Coulomb interaction, geometry, and external fields. The theory is applied to Fano resonances in low-dimensional semiconductors and the Zener breakdown in superlattices. Comparing theoretical results with experiments, the book is essentially self-contained; it is a hands-on approach with detailed derivations, worked examples, illustrative figures, and computer programs. The book is clearly structured and will be valuable as an advanced-level self-study or course book for graduate students, lecturers, and researchers.

This book provides a succinct overview of recent progress in characterization of heat carriers describing atomic motion in liquids. Unlike solids and gases where heat carriers are typically described by phonons and real atomic particles, the nature of effective heat carriers in liquids is still elusive.

Der beliebte Grundkurs Theoretische Physik deckt in sieben Bänden alle für Bachelor/Master- oder Diplom-Studiengänge maßgeblichen Gebiete ab. Jeder Band vermittelt gut durchdacht das im jeweiligen Semester nötige theoretische-physikalische Rüstzeug. Zahlreiche Übungsaufgaben mit ausführlichen Lösungen dienen der Vertiefung des Stoffes.

Simulation of materials at the atomistic level is an important tool in studying microscopic structures and processes. The atomic interactions necessary for the simulations are correctly described by Quantum Mechanics, but the size of systems and the length of processes that can be modelled are still limited. The framework of Gaussian Approximation Potentials that is developed in this thesis allows us to generate interatomic potentials automatically, based on quantum mechanical data. The resulting potentials offer several orders of magnitude faster computations, while maintaining quantum mechanical accuracy. The method has already been successfully applied for semiconductors and metals.

This book aims to coherently present applications of group analysis to integro-differential equations in an accessible way. The book will be useful to both physicists and mathematicians interested in general methods to investigate nonlinear problems using symmetries.

In addition to traditional topics, this book includes: selective measurements, Wigner's Theorem of symmetry transformations, generators of quantum transformations, supersymmetry, details on the spectra of Hamiltonians and stability of quantum systems, Bose-Fermi oscillators, coherent states, hyperfine structure of the H-atom for any angular momentum, the non-relativistic Lamb shift, anomalous magnetic moment of the electron, Ramsey oscillatory fields methods, measurement, interference and the role of the environment, the AB effect, geometric phases, including non-adiabatic and non-cyclic, Schrödinger's cat and quantum decoherence, quantum teleportation and cryptography, quantum dynamics of the Stern-Gerlach effect, Green functions, path integrals, including constrained dynamics, quantum dynamical principle and variations, systematics of multi-electron atoms, stability of matter, collapse of "bosonic matter" and the role of spin, intricacies of scattering, quantum description of relativistic particles for any spin and mass, spinors, helicity, the Spin and Statistics Theorem. It also contains numerous problems some of which are challenging enough for research.

HISTORICAL PRELUDE Ettore Majorana's fame solidly rests on testimonies like the following, from the evocative pen of Giuseppe Cocconi. At the request of Edoardo Amaldi, he wrote from CERN (July 18, 1965): "In January 1938, after having just graduated, I was invited, essen­ tially by you, to come to the Institute of Physics at the University in Rome for six months as a teaching assistant, and once I was there I would have the good fortune of joining Fermi, Bernardini (who had been given a chair at Camerino a few months earlier) and Ageno (he, too, a new graduate), in the research of the products of disintegration of /-L "mesons" (at that time called mesotrons or yukons), which are produced by cosmic rays [ . . . ] "It was actually while I was staying with Fermi in the small laboratory on the second floor, absorbed in our work, with Fermi working with a piece of Wilson's chamber (which would help to reveal mesons at the end of their range) on a lathe and me constructing a jalopy for the illumination of the chamber, using the flash produced by the explosion of an aluminum ribbon short circuited on a battery, that Ettore Majorana came in search of Fermi. I was introduced to him and we exchanged few words. A dark face. And that was it.

The aim of this book is twofold: to provide an introduction for newcomers to state of the art computer simulation techniques in space plasma physics and an overview of current developments. Computer simulation has reached a stage where it can be a highly useful tool for guiding theory and for making predictions of space plasma phenomena, ranging from microscopic to global scales. The various articles are arranged, as much as possible, according to the - derlying simulation technique, starting with the technique that makes the least number of assumptions: a fully kinetic approach which solves the coupled set of Maxwell’s equations for the electromagnetic ?eld and the equations of motion for a very large number of charged particles (electrons and ions) in this ?eld. Clearly, this is also the computationally most demanding model. Therefore, even with present day high performance computers, it is the most restrictive in terms of the space and time domain and the range of particle parameters that can be covered by the simulation experiments. It still makes sense, therefore, to also use models, which due to their simp- fying assumptions, seem less realistic, although the e?ect of these assumptions on the outcome of the simulation experiments needs to be carefully assessed.