Density Functional Theory (DFT) has firmly established itself as the workhorse for atomic-level simulations of condensed phases, pure or composite materials and quantum chemical systems. This work offers a rigorous and detailed introduction to the foundations of this theory, up to and including such advanced topics as orbital-dependent functionals as well as both time-dependent and relativistic DFT. Given the many ramifications of contemporary DFT, the text concentrates on the self-contained presentation of the basics of the most widely used DFT variants: this implies a thorough discussion of the corresponding existence theorems and effective single particle equations, as well as of key approximations utilized in implementations. The formal results are complemented by selected quantitative results, which primarily aim at illustrating the strengths and weaknesses of particular approaches or functionals. The structure and content of this book allow a tutorial and modular self-study approach: the reader will find that all concepts of many-body theory which are indispensable for the discussion of DFT - such as the single-particle Green's function or response functions - are introduced step by step, along with the actual DFT material. The same applies to basic notions of solid state theory, such as the Fermi surface of inhomogeneous, interacting systems. In fact, even the language of second quantization is introduced systematically in an Appendix for readers without formal training in many-body theory.

Semiclassical Theory of Atoms presents a novel approach to theoretical atomic physics. The fundamental quantity in this new, powerful formalism is the effective potential, not the density. The starting point is the highly semiclassical approximation known as the Thomas-Fermi model. It is studied in great detail, and then refined in three steps by adding quantum corrections successively according to their importance. First, the strongly bound electrons are treated in detail. Second, the bulk of electrons is better described by introducing quantum corrections to the Thomas-Fermi treatment and by including the exchange interaction. At this stage, predicted binding energies, for instance, are correct to within a small fraction of a percent. Third, shell effects are introduced. The improved semiclassical treatment is then sufficiently refined to reproduce the systematics of the Periodic Table. It addresses the graduate student with a good knowledge of elementary quantum mechanics.

In its combination of an advanced teaching standpoint with an emphasis on new perspectives and recent advances in the study of liquids formed by simple molecules, Molecular Liquids: New Perspectives in Physics and Chemistry provides a clear, understandable guide through the complexities of the subject. A wide range of topics is covered in the areas of intermolecular forces, statistical mechanics, the microscopic dynamics of simple liquids, thermodynamics of solutions, nonequilibrium molecular dynamics, molecular models for transport and relaxation in fluids, liquid simulations, statistical band shape theories, conformational studies, fast-exchange dynamics, and hydrogen bonding. The experimental techniques covered include: neutron scattering, X-ray diffraction, IR, Raman, NMR, quasielastic neutron scattering, and high-precision, time-resolved coherent Raman spectroscopy.

In the beginning of the 1990's, in the course of the events which were rapidly cha- ing the political con?guration of the East European countries, the crisis which - vested the vast research apparatus of the former Soviet Union was entailing con- quences whose dimension and depth were immediately realized by the international scienti?c community. In the same years, however, the most important branch of nuclear energy - searchanddevelopment, inparticularthatconcerning?ssionreactor, wasworldwide undergoing a substantial reduction due to a variety of decisional situations. Yet, paradoxically, it was a very good fortune that a number of concerns on the future of nuclear research were shared by East- and West-European scientists, especially those who were working in advanced ?elds. In fact, the only hope for coping with an uncertain future was to erect bridges between similar institutions and employ safeguarding tactics linked to a long term collaboration strategy. A decade later, this proved to be a winning decision, since the revival of nuclear energy is presently starting from a basis of common intentions and a network of established cooperation, whose seeds are to be searched in those initial, individual e?orts.

This volume is published in honor of Friedrich Hund's 100th birthday. It is a modern review on matter at high densities and pressures in astrophysics from Hund's early contribution to present-day ideas. The relation between the equation of state and the structure of compact cosmic objects is discussed, and two main contributions deal with the equation of state of baryonic matter at nuclear densities and with the numerical solution of the general relativistic field equations for non-rotating and rapidly rotating neutron stars. In a final chapter the present state of asteroseismology is presented as a tool to explore the interior of cosmic objects by analyzing the observed free oscillations of the Earth, the Sun, and white dwarf stars.

Solitons are a well-known and intriguing aspect of nonlinear behavior in a continuous system such as a fluid: a wave propagates through the medium without distortion. Liquid crystals are highly ordered systems without a rigid, long-range structure. Solitons in liquid crystals (sometimes referred to as "walls") have a wide variety of remarkable properties that are becoming important for practical applications such as electroluminescent display. This book, the first review of the subject to be published, contains not only surveys of the existing literature, but presents new results as well.

Recent results from high-energy scattering and theoretical developments of string theory require a change in our understanding of the basic structure of space-time. This book is about the advancement of ideas on the stochastic nature of space-time from the 1930s onward. In particular, the author promotes the concept of space as a set of hazy lumps, first introduced by Karl Menger, and constructs a novel framework for statistical behaviour at the microlevel. The various chapters address topics such as space-time fluctuation and random potential, non-local fields, and the origin of stochasticity. Implications in astro-particle physics and cosmology are also explored. Audience: This volume will be of interest to physicists, chemists and mathematicians involved in particle physics, astrophysics and cosmology.

Modern nuclear physics is a well developed branch of physical science, with wide-ranging applications of its results in engineering and industry. At the same time, the development of a consistent theory of nuclei and nuclear processes presents certain problems. It is well known that the most important aim of nuclear physics is the study of nuclear structure and the explanation of properties on the basis of the interaction between nucleons which constitute nuclei. Difficulties of a modern theory of the nucleus are caused by both an insufficient knowledge of nuclear interactions and the multi particle character of nuclear systems. Experimental data on nuclear interactions do not contradict the hypothesis of the pair character of nuclear forces. However, the absence of rigorous meth ods of calculations of many particle nuclear systems with strong interaction makes it necessary to use macroscopic nuclear models to describe particular nuclear properties. Nuclear models have been developed in different ways, and the models themselves have been modified and complicated. In spite of the visible discrepancy, different models of the nucleus significantly supple ment one another. The development of nuclear models has led to considerable progress in the understanding of atomic nuclei. The current results of theo retical nuclear physics are reported in numerous scientific papers. The most important and relevant experimental and theoretical results can be found in many monographs, the best of which are written by well-known experts in the field."

Readers intent on mastering the basics should start by reading the first few overview chapters and then delve into the descriptions of specific current applications to see how they actually work. Important future applications are also outlined, including information storage, materials for computer memories, quantum computers, isotopic fibers, isotopic optoelectronics, and quantum electronics.

The twenty-second Coral Gables conference "UNIFIED SYMMETRY: In the Small and In the Large" continued with the efforts to unify the small and the large. The information gathered with the Huble telescope has in part, in the absence of the SCC , provided a basis for the physicists to unify cosmology and elementary particle physics. The congressional cancellation of the biggest experimental project on the frontiers of physics should not be regarded as an insurmountable obstacle to progress in theoretical physics. The physicists' rise to prominence was mostly reached through their creation of the nuclear era. The post cold war era has somewhat reduced the political, military, and, in part, the social role of the physicist. Some in the administration and the Congress would like physicists to focus on the directly utilitarian aspects of science. Thus, some people do not realize that this regimentation of science would inhibit the creativity. The contributions of solid state physics research to the advancement of technology is the result of physics freely pursued independently of its applications. Modern Physics beginning with Newton's theory of gravity has enabled us to create the space age, to contribute to various technologies, and to impact on our technological modus vivendi.

The 1990 Cargese Summer Institute on ZO-Physics was organized by the Univer- site Pierre et Marie Curie, Paris (M. Levy and J.-L. Basdevant), CERN (M. Jacob), the Universite Catholique de Louvain (D. Speiser and J. Weyers), and the Katholieke Universiteit te Leuven (R. Gastmans), which, since 1975, have joined their efforts and worked in common. It was the ninth Summer Institute on High Energy Physics orga- nized jointly at Cargese by these three universities. Because of the start-up of LEP in the summer of 1989, we broke with our tradition of having our Summer Institutes in the odd years. Indeed, it seemed to us that the many new data from LEP had to be presented in detail as soon as possible in order to prepare the young researchers in particle physics better for the experimental results with which they will be confronted in the coming years. The main theme of the school was therefore ZO-physics, with particular emphasis on the way the experiments at LEP are analyzed. We had one lecturer from each LEP experiment: they agreed among each other to present different topics in e+e- physics. Nevertheless, they made sure that all the major topics were discussed and that the results could be critically compared.

A NATO Advanced Studies Institute was held June 12-23, 1978, at the University of Wisconsin in Madison, Wisconsin. It was a topical Institute in theoretical nuclear physics and had the some what novel feature of focussing not on a single topic but on two closely allied ones: pion-nucleus and heavy-ion physics. These two fields. both dedicated to the investigation of short-wave length properties of nuclei, have many techniques and concepts in cornmon, and essentially become one in the topic of relativistic heavy-ion physics. The purpose of including both in a single Institute was to encourage the practitioners in each of these fields to learn from those in the other; to judge from the liveli ness of the questioning which ensued, the purpose was well-served indeed. Because the Institute was viewed as one which served both educational and research ends, the lecturers took particular pains to develop their subjects in a careful, coherent sequence. The result is a compendium of advanced techniques and current results in these two rapidly-expanding fields of nuclear theory which should serve interested physicists as an ideal introduction to the fields. In addition to the support provided by the Scientific Affairs Division of NATO, substantial financial assistance was provided by the U. S. National Science Foundation and the Graduate School of the University of Wisconsin."

Cosmic electrodynamics is the specific branch of plasma physics which studies electromagnetic phenomena -- mostly the role of electromagnetic forces in dynamics of highly-conducting compressible medium in the solar interior and atmosphere, solar wind, in the Earth's magnetosphere and magnetospheres of other planets as well as pulsars and other astrophysical objects. This textbook is written to be used at several different levels. It is aimed primarily at beginning graduate students who are assumed to have a knowledge of basic physics. Starting from the language of plasma physics, from Maxwell's equations, the author guides the reader into the more specialized concepts of cosmic electrodynamics. The main attention in the book is paid to physics rather than maths. However, the clear mathematical image of physical processes in space plasma is presented and spelled out in the surrounding text. There is not another way to work in modern astrophysics at the quantitative level. The book will also be useful for professional astronomers and for specialists, who investigate cosmic plasmas from space, as well as for everybody who is interested in modern astrophysics.

Over the past five de-:: ades researchers have sought to develop a new framework that would resolve the anomalies attributable to a patchwork formulation of relativistic quantum mechanics. This book chronicles the development of a new paradigm for describing relativistic quantum phenomena. What makes the new paradigm unique is its inclusion of a physically measurable, invariant evolution parameter. The resulting theory has been sufficiently well developed in the refereed literature that it is now possible to present a synthesis of its ideas and techniques. My synthesis is intended to encourage and enhance future research, and is presented in six parts. The environment within which the conventional paradigm exists is described in the Introduction. Part I eases the mainstream reader into the ideas of the new paradigm by providing the reader with a discussion that should look very familiar, but contains subtle nuances. Indeed, I try to provide the mainstream reader with familiar "landmarks" throughout the text. This is possible because the new paradigm contains the conventional paradigm as a subset. The foundation of the new paradigm is presented in Part II, fol owed by numerous applications in the remaining three parts. The reader should notice that the new paradigm handles not only the broad class of problems typically dealt with in conventional relativistic quantum theory, but also contains fertile research areas for both experimentalists and theorists. To avoid developing a theoretical framework without physical validity, numerous comparisons between theory and experiment are provided, and several predictions are made.

This volume deals with the basic knowledge and understanding of fundamental interactions of low energy electrons with molecules. It pro vides an up-to-date and comprehensive account of the fundamental in teractions of low-energy electrons with molecules of current interest in modern technology, especially the semiconductor industry. The primary electron-molecule interaction processes of elastic and in elastic electron scattering, electron-impact ionization, electron-impact dissociation, and electron attachment are discussed, and state-of-the art authoritative data on the cross sections of these processes as well as on rate and transport coefficients are provided. This fundamental knowledge has been obtained by us over the last eight years through a critical review and comprehensive assessment of "all" available data on low-energy electron collisions with plasma processing gases which we conducted at the National Institute of Standards and Technology (NIST). Data from this work were originally published in the Journal of Physical and Chemical Reference Data, and have been updated and expanded here. The fundamental electron-molecule interaction processes are discussed in Chapter 1. The cross sections and rate coefficients most often used to describe these interactions are defined in Chapter 2, where some recent advances in the methods employed for their measurement or calculation are outlined. The methodology we adopted for the critical evaluation, synthesis, and assessment of the existing data is described in Chapter 3. The critically assessed data and recommended or suggested cross sections and rate and transport coefficients for ten plasma etching gases are presented and discussed in Chapters 4, 5, and 6."

For 75 years the stopping of energetic ions in matter has been a subject of great theoretical and experimental interest. The theoretical treatment of the stopping of ions in matter is largely due to the work of Bohr, 1-3 Bethe,4-6 Bloch,7. s and Lindhard,9-12 and it has been reviewed by Bohr,3 Fano,13 17 20 Jackson,14 Sigmund,15 Ahlen,16 and Ziegler et al. - Soon after the discovery of energetic particle emission from radioactive materials, there was interest in how these corpuscles were slowed down in traversing matter. In 1900, Marie Curie stated 21 the hypothesis that Hies rayons alpha sont des projectiles materiels susceptibles de perdre de leur vitesse en travers ant la matiere. " Early attempts to evaluate this were incon- clusive for there was not yet an accurate proposed model of the atom. Enough experimental evidence was collected in the next decade to make stopping power theory one of the central concerns of those attempting to develop an atomic model. J. J. Thomson, director of the prestigious Cavendish Laboratory, and Niels Bohr, a fresh postdoctoral scientist at Rutherford's Manchester Laboratory, both published almost simultaneously22. 23 an analysis of the stopping of charged particles by matter, and each contained many of their divergent ideas on the model of an atom. Thomson ignored in his paper the Rutherford alpha-particle scattering 24 experiment of a year before. But the nuclear atom with a heavy positively 25 charged core was the basis of Bohr's ideas.

This book is based on contributions to the NATO Advanced Research Workshop on Recombination of Atomic Ions. This was held at the Slieve Donard Hotel in Newcastle, Northern Ireland, between 6 and 9 October 1991 and attracted 35 participants from 5 countries. The book is inter.~ed to serve as an in-depth review of work to this date on the subject of recombination of atomic ions both in collision with free electrons and with atoms. It contains contributions from almost all groups which have made significant contributions in this area during the last decade. In addition, a synopsis of the discussion session following each of the main subject areas is presented. The material is organized into several themes; an overview of the subject area, theoretical aspects of recombination, experimental measurements of electron-ion recombination and experimental measurement.s of recombination in ion-atom collisions. We would like to acknowledge the sponsorship of the NATO Scientific Affairs Division. We would like to thank the Northern Ireland Tourist Board and the Queen's University of Belfast for providing some additional funding. Finally we would like to thank all the contributors to these proceedings for their efforts in preparing the manuscripts and their assistance in the editing process.

The first presentation of the novel interdisciplinary optical remote sensing technique for various ionized diluted media, based on the collisional polarization of the spectoral emission. The book provides a methodology of the impact spectropolarimetic sensing of many solutions to many practical diagnostic problems.

Reviews of Plasma Physics Volume 22, contains two reviews. The first Cooperative Effects in Plasmas by the late B.B. Kadomtsev is based on the second edition of the author's book in Russian which originated from his written lectures for students of the Moscow Institute of Physics and Technology. Kadomtsev intended to publish the book in English and even initiated the translation himself. The book represents a review of the typical plasma cooperative phenomena that determine the behavior of laboratory and astrophysical plasmas. It is characterized by lively language. The first three sections of the review deal with linear and nonlinear phenomena in fluids without a magnetic field. An additional subsection 'Solitons' has been added to the third section. The next two sections address regular nonlinear phenomena in a plasma in a magnetic field. The second review by S.V. Bulanov et al is connected with the contents of the first. The physics of the laser-plasma interaction including such nonlinear processes as wave breaking, the acceleration of charged particles, electromagnetic wave self-focusing, the relativistic soliton and vortex generation, are considered analytically and illustrated using computer simulations.

The present volume contains the text of the invited talks delivered at the Eighth International Conference on Recent Progress in Many-Body Theories held at SchloB Seggau, Province of Styria, Austria, during the period August 22-26, 1994. The pro ceedings of the Fifth Conference (Oulu, Finland 1987), the Sixth Conference (Arad, Israel 1989) and the Seventh Conference (Minneapolis, USA 1991) have been published. by Plenum as the first three volumes of this series. Papers from the First Conference (Trieste, Italy 1978) comprise Nuclear Physics volume A328, Nos. 1 and 2, the Second Conference (Oaxtepec, Mexico 1979) was published by Springer-Verlag as volume 142 of "Lecture Notes in Physics," entitled "Recent Progress in Many Body Theories." Vol ume 198 of the same series contains the papers from the Third Conference (Altenberg, 1983). These volumes intend to cover a broad spectrum of current research topics in physics that benefit from the application of many-body theories for their elucidation. At the same time there is a focus on the development and refinement of many-body methods. One of the major aims of the conference series has been to foster the exchange of ideas among physicists working in such diverse areas as nuclear physics, quantum chemistry, complex systems, lattice Hamiltonians, quantum fluids and condensed matter physics. The present volume contains contributions from all these areas. th The conference was dedicated on the occasion of Ludwig Boltzmann's 150 birthday."

This volume contains the lectures and contributions presented at the NATO Advanced Study Institute (ASI) on "Frontier Topics in Nuclear Physics", held at Predeal in Romania from 24 August to 4 September 1993. The ASI stands in a row of 23 Predeal Summer Schools organized by the Institute of Atomic Physics (Bucharest) in Predeal or Poiana-Brasov during the last 25 years. The main topics of the ASI were cluster radioactivity, fission and fusion. the production of very heavy elements, nuclear structure described with microscopic and collective models, weak: interaction and double beta decay, nuclear astrophysics, and heavy ion reactions from low to ultrarelativistic energies. The content of this book is ordered according to these topics. The ASI started with a lecture by Professor Greiner on the "Present and future of nuclear physics", showing the most important new directions of research and the interdisciplinary relations of nuclear physics with other fields of physics. This lecture is printed in the first chapter of the book.

Not merely a discussion of small particles or clusters of atoms, molecules, but also the systems they constitute. The goal is to analyse the properties of such finite aggregates and their behaviour in gases and plasmas, and to investigate processes that involve such clusters, based on lectures and seminar problems for graduates. The main part of the book includes more than 200 problems, covering collisions, charge transfer, chemical reactions, condensed systems and their structures, kinetics of cluster growth, excited clusters, the transition from clusters to bulk particles, and small particles, dust, and aerosols in plasmas. Reference data for corresponding parameters of systems under consideration is given in the appendices. Of interest to physicists, astrophysicists, and chemists.

InMay1988,theFirstInternationalConferenceonDissociativeRecombination:Theory, ExperimentandApplicationswasheldatChateauLakeLouise,Alberta,Canada. Thismeeting gaveaconsiderableimpetustothissubject,whichisofparticularinterestforalargevarietyof fieldsincludinginterstellarclouds,planetaryatmospheres,gaslasers,plasmaprocessing,ion sourcesandthermonuclearplasmas. Sincethen,indeed,severalcollaborationswereinitiated betweenexperimentalistsworkingwithdifferenttechniques,betweentheoreticiansdealingwith molecularstructureononehandanddynamicsontheotherhandandalsobetween experimentalistsandtheoreticians. Duringthelastfouryears,therefore,alargenumberof studieswerecarriedoutandraisedanewsetofquestions. Moreparticularly,theresultsthat wereobtainedconcerningcontroversialspeciessuchasH!andHeir,castingsomedoubton theverymechanismsbywhichdissociativerecombinationproceeds. The Second International Conference on Dissociative Recombination: Theory, ExperimentandApplications heldat"I'AbbayedeSaintJacutdelaMer",Brittany,France, May3-8,1992,camethereforeattherighttimetosurveythecurrentstateofthesubject. The symposiumbroughttogetherleadinginvestigatorsinthefieldsofmolecularionrecombination research,atomicandmoleculartheoryandexperiment,plasmasphysics,astrochemistryand aeronomy. Speakerspresentedtalksreviewingtheirownworkandthesewerefollowedby livelydiscussionsessions. Freetimeperiodsallowedparticipantstodiscoveranenchanting peninsulaofNorthBrittanywhilepursuingstimulatingscientificdiscussions. Thepapersinthis volumearebasedonthesetalksandfurtherdiscussions,withtheexceptionofcontributions fromT. AmanoandB. M. McLaughlinwhowereunabletoattend. Alistofparticipantsas wellasasouvenirgroupphotoisgivenattheendofthebook. WeareindebtedtoNATOforitsfinancialsupportwhichcontributedtothegreat successofthissecondmeeting. TheUniversityofRennesIandtheBalzerscompanyarealso acknowledgedfortheiradditionalsupportManythankstothewholestaffoftheabbeyforits kindnessandeffortsinprovidinguswithapropitiousenvironmentforsuchaworkshop. We arealsogratefultoL. Caubetforhervaluableadministrativeassistanceduringthepreparation ofthemeeting. Finallyaspecialmentionmustbegiventoallthesessionchairpersonsfortheir skillinorchestratingthediscussions. Lookingforwardtoattendingthethirdmeeting. TheEditors Bertrand R. Rowe J. Bria/l A. Mitchell Andre Callosa DepartementdePhysique DepartmentofPhysics DepartementdePhysique AtomiqueetMoleculaire TheUniversityofWesternOntario AtomiqueetMoleculaire UniversitedeRennesI London,Canada,N6A3K7 UniversitedeRennesI CampusdeBeaulieu CampusdeBeaulieu 35042RennesCedex, 35042RennesCedex, France France v CONTENTS ORALCONTRIBUTIONS PolyatomicIonDissociativeRecombination . 1 D. R. Bates RecentDevelopmentsandPerspectivesintheTreatmentofDissociative RecombinationandRelatedProcesses...11 A. Giusti-Suzor, I. F Schneider, and 0. Dulieu CharacteristicsofSuperexcitedStatesofMoleculesandMQDTStudiesofNO+ DissociativeRecombination...25 H. Sun, K. Nakashima, and H. Nakamura CalculationsforAr +Xe*andArXe+ +e 35 A. P. Hickman, DL Huestis, and R. P. Saxon Electron-IonContinuum-ContinuumMixinginDissociativeRecombination 47 s. L. Guberman ATheoreticalStudyoftheHCO+andHCS+ElectronicDissociativeRecombinations. . 59 D. Talbi, and Y Ellinger DissociativeRecombinationofCH;:SomeBasicInformationfromElectronic 2 StructureCalculations. 67 WP. Kraemer TheoreticalProblemsintheDissociativeRecombinationofH~ +e...75 H. Takagi RecentMergedBeamsInvestigationsofHydrogenMolecularIonRecombination...87 J B. A. Mitchell, F B. Yousif, P. Van der Donk, and T. J Morgan vii FlowingAfterglowStudiesofElectron-IonRecombinationusingLangmuirProbesand OpticalSpectroscopy...99 NG. Adams RecentFlowingAfterglowMeasurements . 113 B. R. Rowe InfraredSpectroscopicStudiesoftheDissociativeRecombinationProcessesofH...127 3 T. Amano RecombinationofClusterIons . 135 R. Johnsen PredissociationofExcitedStatesofH . . 145 3 H. Helm AStudyofHe e,3I,;)BoundandContinuumStates...155 2 CJ Gillan, B. M McLaughlin. and P. G. Burke ElectronCollisionInducedExcitationsandDissociationofHeH+usingthe R-MatrixMethod . . 163 BK Sarpal, J Tennyson, and L. A. Morgan AssociativeIonisationofHydrogen:ExperimentswithFastMergedBeams...173 F Brouillard, andX Urbain TheoryoftheAsssociativeIonisationReactionbetweenTwoLaser-Excited . 187 SodiumAtoms 0. Du!ieu, A. Giusti-Suzor, andF Masnou-Seeuws ResonantTheoryofDissociativeAttachment...195 J. J. Fabrikant MicroscopicandMacroscopicTheoriesofTermolecularRecombinationbetween AtomicIons...205 MR. Flannery DissociativeRecombinationinPlanetaryIonospheres . . 219 JL. Fox ChemistryofSupernova1987a . 243 A. Dalgarno DissociativeRecombinationinInterstellarClouds . .

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 Schrodinger equation, a task that remained elusive for experimentally relevant conditions for many years. In this thesis the first numerically exact solutions of the time-dependent many-body Schrodinger equation for a bosonic Josephson junction are provided and compared to the approximate Gross-Pitaevskii and Bose-Hubbard theories. It is thereby shown that the dynamics of Bose-Einstein condensates is far more intricate than one would anticipate based on these approximations. A special conceptual innovation in this thesis are optimal lattice models. It is shown how all quantum lattice models of condensed matter physics that are based on Wannier functions, e.g. the Bose/Fermi Hubbard model, can be optimized variationally. This leads to exciting new physics."