This thesis investigates ultracold molecules as a resource for novel quantum many-body physics, in particular by utilizing their rich internal structure and strong, long-range dipole-dipole interactions. In addition, numerical methods based on matrix product states are analyzed in detail, and general algorithms for investigating the static and dynamic properties of essentially arbitrary one-dimensional quantum many-body systems are put forth. Finally, this thesis covers open-source impleme...

An illuminating portrayal of Richard Feynman—a giant of twentieth century physics—from his childhood tinkering with radios, to his vital work on the Manhattan Project and beyondRaised in Depression-era Rockaway Beach, physicist Richard Feynman was irreverent, eccentric, and childishly enthusiastic—a new kind of scientist in a field that was in its infancy. His quick mastery of quantum mechanics earned him a place at Los Alamos working on the Manhattan Project under...

A series of seminal technological revolutions has led to a new generation of electronic devices miniaturized to such tiny scales where the strange laws of quantum physics come into play. There is no doubt that, unlike scientists and engineers of the past, technology leaders of the future will have to rely on quantum mechanics in their everyday work. This makes teaching and learning the subject of paramount importance for further progress. Mastering quantum physics is a very non-trivial tas...

Around 1900, physicists started to discover particles like electrons, protons, and neutrons, and with these discoveries believed they could predict the internal behavior of the atom. However, once their predictions were compared to the results of experiments in the real world, it became clear that the principles of classical physics and mechanics were far from capable of explaining phenomena on the atomic scale. With this realization came the advent of quantum physics, one of the most impo...

Many regard Albert Einstein as the greatest physicist since Newton. What exactly did he do that is so important in physics? We provide an introduction to his physics at a level accessible to an undergraduate physics student. All equations are worked out in detail from the beginning. Einstein's doctoral thesis and his Brownian motion paper were decisive contributions to our understanding of matter as composed of molecules and atoms. Einstein was one of the founding fathers of quantum theory...

This book provides an advanced introduction to extended theories of quantum field theory and algebraic topology, including Hamiltonian quantization associated with some geometrical constraints, symplectic embedding and Hamilton-Jacobi quantization and Becci-Rouet-Stora-Tyutin (BRST) symmetry, as well as de Rham cohomology. It offers a critical overview of the research in this area and unifies the existing literature, employing a consistent notation.Although the results presented ap...

This monograph forms an interdisciplinary study in atomic, molecular, and quantum information (QI) science. Here a reader will find that applications of the tools developed in QI provide new physical insights into electron optics as well as properties of atoms & molecules which, in turn, are useful in studying QI both at fundamental and applied levels. In particular, this book investigates entanglement properties of flying electronic qubits generated in some of the well known processes cap...

At extremely low temperatures, clouds of bosonic atoms form what is known as a Bose-Einstein condensate. Recently, it has become clear that many different types of condensates -- so called fragmented condensates -- exist. In order to tell whether fragmentation occurs or not, it is necessary to solve the full many-body Schrödinger equation, a task that remained elusive for experimentally relevant conditions for many years. In this thesis the first numerically exact solutions of the time-dep...

This book develops two exciting areas of particle physics research. It applies the recent new insights about the usefulness of helicity amplitudes in understanding gauge theory to the long-standing effort to understand theories with both electric and magnetic charges. It is known that for some supersymmetric theories there is an exact duality that relates two descriptions of the physics, one where the electric charges are weakly coupled and another where the electric charges are strongly c...

This graduate-level text collects and synthesizes a series of ten lectures on the nuclear quantum many-body problem. Starting from our current understanding of the underlying forces, it presents recent advances within the field of lattice quantum chromodynamics before going on to discuss effective field theories, central many-body methods like Monte Carlo methods, coupled cluster theories, the similarity renormalization group approach, Green’s function methods and large-scale diagonalizati...

Although used with increasing frequency in many branches of physics, random matrix ensembles are not always sufficiently specific to account for important features of the physical system at hand. One refinement which retains the basic stochastic approach but allows for such features consists in the use of embedded ensembles.The present text is an exhaustive introduction to and survey of this important field. Starting with an easy-to-read introduction to general random matrix theory...

This book gives an introduction to quantum mechanics with the matrix method. Heisenberg's matrix mechanics is described in detail. The fundamental equations are derived by algebraic methods using matrix calculus. Only a brief description of Schrödinger's wave mechanics is given (in most books exclusively treated), to show their equivalence to Heisenberg's matrix method. In the first part the historical development of Quantum theory by Planck, Bohr and Sommerfeld is sketched, followed by th...