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Mathematical Concepts of Quantum Mechanics
The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include: many-body systems, modern perturbation theory, path integrals, the theory of resonances, adiabatic theory, geometrical phases, Aharonov-Bohm effect, density functional theory, open systems, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. Some of the sections could be used for introductions to geometrical methods in Quantum Mechanics, to quantum information theory and to quantum electrodynamics and quantum field theory.
Quantum Dissipative Systems
Starting from first principles, this book introduces the fundamental concepts and methods of dissipative quantum mechanics and explores related phenomena in condensed matter systems. Major experimental achievements in cooperation with theoretical advances have brightened the field and brought it to the attention of the general community in natural sciences. Nowadays, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book -- originally published in 1990 and republished in 1999 and and 2008 as enlarged second and third editions -- delves significantly deeper than ever before into the fundamental concepts, methods and applications of quantum dissi...
Introduction to Spectral Theory
The intention of this book is to introduce students to active areas of research in mathematical physics in a rather direct way minimizing the use of abstract mathematics. The main features are geometric methods in spectral analysis, exponential decay of eigenfunctions, semi-classical analysis of bound state problems, and semi-classical analysis of resonance. A new geometric point of view along with new techniques are brought out in this book which have both been discovered within the past decade. This book is designed to be used as a textbook, unlike the competitors which are either too fundamental in their approach or are too abstract in nature to be considered as texts. The authors' text fills a gap in the marketplace.
Sixteenth International Congress on Mathematical Physics
The International Congress on Mathematical Physics is the flagship conference in this exciting field. Convening every three years, it gives a survey on the progress achieved in all branches of mathematical physics. It also provides a superb platform to discuss challenges and new ideas. The present volume collects material from the XVIth ICMP which was held in Prague, August 2009, and features most of the plenary lectures and invited lectures in topical sessions as well as information on other parts of the congress program. This volume provides a broad coverage of the field of mathematical physics, from dominantly mathematical subjects to particle physics, condensed matter, and application of mathematical physics methods in various areas such as astrophysics and ecology, amongst others.
Free Speech on Campus
Can free speech coexist with an inclusive campus environment? Hardly a week goes by without another controversy over free speech on college campuses. On one side, there are increased demands to censor hateful, disrespectful, and bullying expression and to ensure an inclusive and nondiscriminatory learning environment. On the other side are traditional free speech advocates who charge that recent demands for censorship coddle students and threaten free inquiry. In this clear and carefully reasoned book, a university chancellor and a law school dean—both constitutional scholars who teach a course in free speech to undergraduates—argue that campuses must provide supportive learning environments for an increasingly diverse student body but can never restrict the expression of ideas. This book provides the background necessary to understanding the importance of free speech on campus and offers clear prescriptions for what colleges can and can’t do when dealing with free speech controversies.
The Mystics of Mile End
A Jewish family navigates faith, loss, and the chaos of modern life in this “remarkable debut . . . with a profound sense of empathy” (Simon Van Booy, author of Everything Beautiful Began After). In the half-Hasidic, half-hipster Montreal neighborhood of Mile End, eleven-year-old Lev Meyer is discovering that there may be a place for Judaism in his life. As he learns about science in his day school, Lev begins his own extracurricular study of the Bible’s Tree of Knowledge with neighbor Mr. Katz, who is building his own Tree out of trash. Meanwhile his sister Samara is secretly studying for her Bat Mitzvah with next-door neighbor and Holocaust survivor, Mr. Glassman. All the while his f...
Thermal Relaxation for Particle Systems in Interaction with Several Bosonic Heat Reservoirs
The present publication is concerned with the study of thermodynamic properties of a quantum mechanical system composed of a small particle system (such as a spin chain) and several quantized massless boson fields (as photon gasses or phonon fields) at positive temperature. As the text at hand is a contribution to the area of mathematical physics it unites mathematical concepts of the thermodynamics of a quantum system with the mathematically rigorous treatment of problems in positive temperature quantum physics. The dissertation character of this publication is reflected by the fact that recent research work of the author is displayed along with a review of established results in the field of statistical quantum mechanics. An extended introductory part serves as thorough familiarization of non-experts with the field of studies. The required technical tools for the mathematical treatment of the system under consideration are carefully compiled apart from the main text.
On My Right Michael, On My Left Gabriel
Introduction : angelic greetings or Shalom Aleichem -- At home with the angels : Babylonian ritual sources -- Out and about with the angels : Palestinian ritual sources -- No angels? early rabbinic sources -- In the image of God, not angels : rabbinic sources -- In the image of the angels : liturgical sources -- Israel among the angels : Late rabbinic sources -- Jewish mystics and the angelic realms : early mystical sources -- Conclusion : angels in Judaism and the religions of late antiquity -- Appendix A : table -- Appendix B : description of table.
Osnat and Her Dove
Osnat was born five hundred years ago – at a time when almost everyone believed in miracles. But very few believed that girls should learn to read. Yet Osnat's father was a great scholar whose house was filled with books. And she convinced him to teach her. Then she in turn grew up to teach others, becoming a wise scholar in her own right, the world's first female rabbi! Some say Osnat performed miracles – like healing a dove who had been shot by a hunter! Or saving a congregation from fire! But perhaps her greatest feat was to be a light of inspiration for other girls and boys; to show that any person who can learn might find a path that none have walked before.
Extended States for the Schrödinger Operator with Quasi-Periodic Potential in Dimension Two
The authors consider a Schrödinger operator H=−Δ+V(x⃗ ) in dimension two with a quasi-periodic potential V(x⃗ ). They prove that the absolutely continuous spectrum of H contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves ei⟨ϰ⃗ ,x⃗ ⟩ in the high energy region. Second, the isoenergetic curves in the space of momenta ϰ⃗ corresponding to these eigenfunctions have the form of slightly distorted circles with holes (Cantor type structure). A new method of multiscale analysis in the momentum space is developed to prove these results. The result is based on a previous paper on the quasiperiodic polyharmonic operator (−Δ)l+V(x⃗ ), l>1. Here the authors address technical complications arising in the case l=1. However, this text is self-contained and can be read without familiarity with the previous paper.
