This thesis explores ultracold quantum gases of bosonic and fermionic atoms in optical lattices. The highly controllable experimental setting discussed in this work, has opened the door to new insights into static and dynamical properties of ultracold quantum matter. One of the highlights reported here is the development and application of a novel time-resolved spectroscopy technique for quantum many-body systems. By following the dynamical evolution of a many-body system after a quantum quench, the author shows how the important energy scales of the underlying Hamiltonian can be measured with high precision. This achievement, its application, and many other exciting results make this thesis of interest to a broad audience ranging from quantum optics to condensed matter physics. A lucid style of writing accompanied by a series of excellent figures make the work accessible to readers outside the rapidly growing research field of ultracold atoms.

This book explains the usage and application of Molecular Quantum Dynamics, the methodology where both the electrons and the nuclei in a molecule are treated with quantum mechanical calculations. This volume of Lecture Notes in Chemistry addresses graduate students and postdocs in the field of theoretical chemistry, as well as postgraduate students, researchers and teachers from neighboring fields, such as quantum physics, biochemistry, biophysics, or anyone else who is interested in this rising method in theoretical chemistry, and who wants to gain experience in the opportunities it can offer. It can also be useful for teachers interested in illustrative examples of time-dependent quantum mechanics as animations of realistic wave packets have been designed to assist in visualization. Assuming a basic knowledge about quantum mechanics, the authors link their explanations to recent experimental investigations where Molecular Quantum Dynamics proved successful and necessary for the understanding of the experimental results. Examples including reactive scattering, photochemistry, tunneling, femto- and attosecond chemistry and spectroscopy, cold chemistry or crossed-beam experiments illustrate the power of the method. The book restricts complicated formalism to the necessary and in a self-contained and clearly explained way, offering the reader an introduction to, and instructions for, practical exercises. Continuative explanation and math are optionally supplemented for the interested reader. The reader learns how to apply example simulations with the MCTDH program package (Multi Configuration Time Dependent Hartree calculations). Readers can thus obtain the tools to run their own simulations and apply them to their problems. Selected scripts and program code from the examples are made available as supplementary material. This book bridges the gap between the existing textbooks on fundamental theoretical chemistry and research monographs focusing on sophisticated applications. It is a must-read for everyone who wants to gain a sound understanding of Molecular Quantum Dynamics simulations and to obtain basic experience in running their own simulations.

Many, perhaps most textbooks of quantum mechanics present a Copenhagen, single system angle; fewer present the subject matter as an instrument for treating ensembles, but the two methods have been silently coexisting since the mid-Thirties. This lingering dichotomy of purpose for a major physical discipline has much shrouded further insights into the foundations of quantum theory. Quantum Reprogramming resolves this long-standing dichotomy by examining the mutual relation between single systems and ensembles, assigning each its own tools for treating the subject at hand: i.e., Schrodinger-Dirac methods for ensembles versus period integrals for single systems. A unified treatment of integer and fractional quantum Hall effects and a finite description of the electron's anomalies are mentioned as measures of justification for the chosen procedure of resolving an old-time dichotomy. The methods of presentation are, in part, elementary, with repetitive references needed to delineate differences with respect to standard methods. The parts on period integrals are developed with a perspective on elementary methods in physics, thus leading up to some standard results of de Rham theory and algebraic topology. Audience: Students of physics, mathematics, philosophers as well as outsiders with a general interest in the conceptual development of physics will find useful reading in these pages, which will stimulate further inquiry and study. "

An understanding of quantum mechanics is vital to all students of physics, chemistry and electrical engineering, but requires a lot of mathematical concepts, the details of which are given with great clarity in this book. Various concepts have been derived from first principles, so it can also be used for self-study. The chapters on the JWKB approximation, time-independent perturbation theory and effects of magnetic field stand out for their clarity and easy-to-understand mathematics. Two complete chapters on the linear harmonic oscillator provide a very detailed discussion of one of the most fundamental problems in quantum mechanics. Operator algebra is used to show the ease with which one can calculate the harmonic oscillator wave functions and study the evolution of the coherent state. Similarly, three chapters on angular momentum give a detailed account of this important problem. Perhaps the most attractive feature of the book is the excellent balance between theory and applications and the large number of applications in such diverse areas as astrophysics, nuclear physics, atomic and molecular spectroscopy, solid-state physics, and quantum well structures.

Advanced spectroscopic techniques allow the probing of very small systems and very fast phenomena, conditions that can be considered "extreme" at the present status of our experimentation and knowledge. Quantum dots, nanocrystals and single molecules are examples of the former and events on the femtosecond scale examples of the latter. The purpose of this book is to examine the realm of phenomena of such extreme type and the techniques that permit their investigations.

Each author has developed a coherent section of the program

starting at a somewhat fundamental level and ultimately reaching the frontier of knowledge in the field in a systematic and didactic fashion. The formal lectures are complemented by additional seminars.

Kinetic Theory: Classical, Quantum, and Relativistic Descriptions goes beyond the scope of other works in the field with its thorough treatment of applications in a wide variety of disciplines. Its clear exposition and emphasis on concrete examples will make it not only an excellent graduate text but also a valuable resource for researchers in such disciplines as aerospace, mechanical, and chemical engineering; astrophysics, solid state and laser physics and devices, plasma physics, and controlled and thermonuclear fusion. Among the topics covered are: - The Liouville equation and analyses of the Liouville equation, including two independent derivations - The Boltzmann equation and Boltzmann's H-theorem - Analysis of the linearized collision operator - Fluid dynamics and irreversibility - Assorted kinetic equations with applications to plasmas and neutral fluids - Elements of quantum kinetic theory, including the Green's-function formalism and the Wigner-Moyal equation - Relativistic kinetic theory and Lorentz invariants - Kinetic properties of metals and amorphous media - Monte-Carlo analysis in kinetic theory - Kinetic study of shock waves This third revised edition features a new section on constants of motion and symmetry and a new appendix on the Lorentz-Legendre expansion. Each chapter concludes with a variety of problems, many of which provide self-contained descriptions of related topics; lists of such "topical problems" are included in the Table of Contents. Numerous appendices supply vector formulas and tensor notation, properties of special functions, physical constants, references, and a historical time chart.

It may tum out that, like certain other phenomena studied by sociologists, bouts of interest in the foundations of quantum mechanics tend to come in 60-year cycles. It is hardly surprising that in the first decade or so of the subject the conceptual puzzles generated by this strange new way of looking at the world should have generated profound interest, not just among professional physicists themselves but also among philosophers and informed laymen; but this intense interest was followed by a fallow period in the forties and fifties when the physics establishment by and large took the view that the only puzzles left were the product either of incompetent application of the formalism or of bad philosophy, and only a few brave individualists like the late David Bohm dared to suggest that maybe there really was something there after all to worry about. As Bell and Nauenberg, surveying the scene in 1966, put it: "The typical physicist feels that [these questions 1 have long ago been answered, and that he will fully understand how if ever he can spare twenty minutes to think about it. " But gradually, through the sixties and seventies, curiosity did revive, and the last ten years or so have seen a level of interest in foundational questions, and an involvement in them by some of the leading figures of contemporary physics, which is probably unparalleled since the earliest days.

This thesis reports on the final measurement of the flavor-mixing phase in decays of strange-bottom mesons (B_s) into J/psi and phi mesons performed in high-energy proton-antiproton collisions recorded by the Collider Experiment at Fermilab. Interference occurs between direct decays and decays following virtual particle-antiparticle transitions (B_s-antiB_s). The phase difference between transition amplitudes ("mixing phase") is observable and extremely sensitive to contributions from non-standard-model particles or interactions that may be very hard to detect otherwise - a fact that makes the precise measurement of the B_s mixing phase one of the most important goals of particle physics. The results presented include a precise determination of the mixing phase and a suite of other important supplementary results. All measurements are among the most precise available from a single experiment and provide significantly improved constraints on the phenomenology of new particles and interactions.

This book tackles quantum gravity via the so-called background field method and its effective action functional. The author presents an explicitly covariant and effective technique to calculate the de Witt coefficients and to analyze the Schwinger-de Wit asymptotic expansion of the effective action. He also investigates the ultraviolet behaviour of higher-derivative quantum gravity.The book addresses theoretical physicists, graduate students as well as researchers, but should also be of interest to physicists working in mathematical or elementary particle physics.

Solitary wave physics plays a significant role from modern optical physics to optical communication, optical switching and optical storage. This book gives an updated overview of optical solitons, as a reference and guide for advanced students and scientists working in the field.

Each of this book's 32 essays discusses a chosen topic, at a level that is generally within that of a four-year degree course in Physics. The essays supplement (indeed sometimes correct) treatments usually given, or supplies reasoning that tends to fall through the cracks. The author uses his life long experience of tutorial teaching at Oxford to know what topics often need such discussion, for clarification, or for avoidance of common confusions. The book contains accounts of even-standard topics, accounts that offer an unusual emphasis, or a fresh insight, or more than customary rigour, or a cross-link to apparently unrelated material. The student (and their teachers) who really wants to understand physics will find this book indispensable. Often the outcome of tutorial discussion has been an understanding that lies a little to the side of what is presented in standard texts. Such understanding is presented here in the essays. The topics covered are diverse and have something useful to say across most areas of a physics degree.

This volume presents a selection of 434 letters from and to the Dutch physicist and Nobel Prize winner Hendrik Antoon Lorentz (1853-1928), covering the period from 1883 until a few months before his death in February 1928. The sheer size of the available correspondence (approximately 6000 letters from and to Lorentz) preclude a full publication. The letters included in this volume have been selected according to various criteria, the most important of which is scientific importance. A second criterion has been the availability of letters both from and to Lorentz, so that the reader can follow the exchange between Lorentz and his correspondent. Within such correspondences a few unimportant items, dealing with routine administrative or organizational matters, have been omitted. An exception to the scientific criterion is the exchange of letters between Lorentz and Albert Einstein, Max Planck, Woldemar Voigt, and Wilhelm Wien during World War I: these letters have been included because they shed important light on the disruption of the scientific relations during the war and on the political views of these correspondents as well as of Lorentz. similar reasons the letters exchanged with Einstein and Planck on post-war political issues have been included. Biographical sketch Hendrik Antoon Lorentz was born on July 18, 1853 in the Dutch town of Arnhem. He was the son of a relatively well-to-do owner of a nursery.

Beautifully illustrated and engagingly written, Twelve Lectures in Quantum Mechanics presents theoretical physics with a breathtaking array of examples and anecdotes. Basdevant's style is clear and stimulating, in the manner of a brisk classroom lecture that students can follow with ease and enjoyment. Here is a sample of the book's style, from the opening of Chapter 1: If one were to ask a passer-by to quote a great formula of physics, chances are that the answer would be E = mc2. In fact, of the three watershed years for physics toward the beginning of the 20th century - 1905: the Special Relativity of Einstein, Lorentz and Poincare; 1915: the General Relativity of Einstein, with its extraordinary reflections on gravitation, space and time; and 1925: the development of Quantum Mechanics; it is surely the last which has the most profound implications for the development of science and technology. There is no way around it: all physics is quantum, from elementary particles, to stellar physics and the Big Bang, not to mention semiconductors and solar cells. and Chair of the Department of Physics at the Ecole Polytechnique, and Director of Research for the CNRS. Specializing in the theoretical physics of elementary particles, quantum field theory and astrophysics, Prof. Basdevant works in the Leprince-Ringuet Laboratory at the Ecole Polytechnique.

Practical quantum computing still seems more than a decade away, and researchers have not even identified what the best physical implementation of a quantum bit will be. There is a real need in the scientific literature for a dialogue on the topic of lessons learned and looming roadblocks. This reprint from Quantum Information Processing is dedicated to the experimental aspects of quantum computing and includes articles that 1) highlight the lessons learned over the last 10 years, and 2) outline the challenges over the next 10 years. The special issue includes a series of invited articles that discuss the most promising physical implementations of quantum computing. The invited articles were to draw grand conclusions about the past and speculate about the future, not just report results from the present.

At the outset of the research leading to this book I held a position somewhere close to 'the standard Copenhagen interpretation' of QM. I was strongly attracted to, in particular, the philosophy of Niels Bohr. However, being aware of some of the problematic sides and ambiguities of his views and of new developments which have taken place in QM after his time, the main challenge would be to develop a more up to date version version of his approach and express it in a philosophically unobjectionable way. Traces of this original attitude can still be found in views I hold nowadays. For instance, I think that I now know a satisfactory and correct way of dealing with features like 'complementarity', and I still see this as a relevant subject. In many other respects, however, there have been major changes in my position. In fact, during certain stages of my research my views simply started moving and kept on doing so at an irritating pace and for uncomfortably long periods of time. I learned, for example that at least some of the classical ideas about theory structure are much better than I had realized, and cannot just be pushed aside for anything even as impressive as empirical success.

4. 2 Variance of Quantum Matrix Elements. 125 4. 3 Berry's Trick and the Hyperbolic Case 126 4. 4 Nonhyperbolic Case . . . . . . . 128 4. 5 Random Matrix Theory . . . . . 128 4. 6 Baker's Map and Other Systems 129 4. 7 Appendix: Baker's Map . . . . . 129 5 Error Terms 133 5. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . 133 5. 2 The Riemann Zeta Function in Periodic Orbit Theory 135 5. 3 Form Factor for Primes . . . . . . . . . . . . . . . . . 137 5. 4 Error Terms in Periodic Orbit Theory: Co-compact Case. 138 5. 5 Binary Quadratic Forms as a Model . . . . . . . . . . . . 139 6 Co-Finite Model for Quantum Chaology 141 6. 1 Introduction. . . . . . . . 141 6. 2 Co-finite Models . . . . . 141 6. 3 Geodesic Triangle Spaces 144 6. 4 L-Functions. . . . . . . . 145 6. 5 Zelditch's Prime Geodesic Theorem. 146 6. 6 Zelditch's Pseudo Differential Operators 147 6. 7 Weyl's Law Generalized 148 6. 8 Equidistribution Theory . . . . . . . . . 150 7 Landau Levels and L-Functions 153 7. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . 153 7. 2 Landau Model: Mechanics on the Plane and Sphere. 153 7. 3 Landau Model: Mechanics on the Half-Plane 155 7. 4 Selberg's Spectral Theorem . . . . . . . . . . . 157 7. 5 Pseudo Billiards . . . . . . . . . . . . . . . . . 158 7. 6 Landau Levels on a Compact Riemann Surface 159 7. 7 Automorphic Forms . . . . . 160 7. 8 Maass-Selberg Trace Formula 162 7. 9 Degeneracy by Selberg. . . . 163 7. 10 Hecke Operators . . . . . . . 163 7. 11 Selberg Trace Formula for Hecke Operators 167 7. 12 Eigenvalue Statistics on X . . . . 169 7. 13 Mesoscopic Devices. . . . . . . . 170 7. 14 Hall Conductance on Leaky Tori 170 7.

This book explores alternative ways of accomplishing secure information transfer with incoherent multi-photon pulses in contrast to conventional Quantum Key Distribution techniques. Most of the techniques presented in this book do not need conventional encryption. Furthermore, the book presents a technique whereby any symmetric key can be securely transferred using the polarization channel of an optical fiber for conventional data encryption. The work presented in this book has largely been practically realized, albeit in a laboratory environment, to offer proof of concept rather than building a rugged instrument that can withstand the rigors of a commercial environment.

This book is based upon the lectures delivered from 18 to 22 June 2007 at the INFN-LaboratoriNazionali di Frascati School on Attractor Mechanism, directed by Stefano Bellucci, with the participation of prestigious lecturers, including S. Ferrara, M. Gnaydin, P. Levay, T. Mohaupt, and A. Zichichi. All lectures were given at a pedagogical, introductory level, a feature which is re?ected in the s- ci?c "?avor" of this volume, which has also bene?ted much from the extensive discussions and related reworking of the various contributions. This is the fourth volume in a series of books on the general topics of sup- symmetry, supergravity, black holes, and the attractor mechanism. Indeed, based on previous meetings, three volumes have already been published: BELLUCCI S. (2006). Supersymmetric Mechanics - Vol. 1: Supersymmetry, NoncommutativityandMatrixModels.(vol.698, pp.1-229).ISBN:3-540-33313-4. Berlin, Heidelberg: Springer Verlag (Germany). Springer Lecture Notes in Physics Vol. 698. BELLUCCIS., S.FERRARA, A.MARRANI.(2006).SupersymmetricMech- ics - Vol. 2: The Attractor Mechanism and Space Time Singularities. (vol. 701, pp. 1-242). ISBN-13: 9783540341567. Berlin, Heidelberg: Springer Verlag (G- many). Springer Lecture Notes in Physics Vol. 701. BELLUCCIS.(2008).SupersymmetricMechanics-Vol.3: AttractorsandBlack HolesinSupersymmetricGravity.(vol.755, pp.1-373).ISBN-13:9783540795223. Berlin, Heidelberg: Springer Verlag (Germany). Springer Lecture Notes in Physics 755. In this volume, we have included two contributions originating from short p- sentations of recent original results given by participants, i.e., Wei Li and Filipe Moura.

As the growing number of conference proceedings, preprints, periodicals and popular journal articles are being joined by various electronic forms of dissemination of research, the series Progress in Low Temperature Physics assumes a particular responsibility in providing excellent reviews, guiding the reading of the literature and providing direction for future research possibilities. In this most recent volume, the main theme is research on superfluid and adsorbed phases of helium.

In five chapters the following topics are dealt with. Chapter one is a review of one of the essential characteristics of superfluid 4He, the Landau critical velocity. Chapter two reviews the amazing properties of coherent spin dynamics in superfluid 3He. The next chapter examines a unique situation with a number of thermodynamic transitions between superfluid states and discusses the current experimental and theoretical situation. Properties of phases of 3He adsorbed on graphite are discussed in the following chapter, and in a complementary final chapter a review is presented on the properties of multilayer 3He-4He mixture films.

Exploring various transport-simulation methods and applications for properties of nanometer-scale systems, this account illustrates how quantum mechanics have become an increasingly important field of scientific research. Beginning with a short review of quantum transport, followed by various calculation methods for nanosystems based on scattering approaches, non-equilibrium Green's function, master equation, and time-dependent wave-packet diffusion, this report broaches all aspects of nanosystems, from the fundamental to more advanced topics. With numerous examples that describe quantum transport calculations, this is an essential resource for promoting an easier understanding for graduate students and researchers of the field.

This book is unique in covering phenomena in photon- matter interactions in a unified way over a range of many orders in energy. The quantum field theoretic approach to the fully relativistic theory of quantum electrodynamics (QED) is presented together with the non- relativistic theory in both confined and unconfined geometries. The predictions of QED have been verified to a greater accuracy than any other physical theory. Moreover QED is a paradigm for other gauge theories and is presented in such a way that the generalisation to other gauge theories is natural. Gauge and Poincare symmetry properties and the non-existence of a photon wave function are thoroughly discussed. Starting from the Dirac equation the non-relativistic interaction of the electron with the electromagnetic field is derived as an effective Hamiltonian of multipole expansions. Much of quantum optics is based on the lowest order dipole approximation. From this point on the treatment of fully relativistic QED and quantum optics is done in parallel. Applications of perturbation theory such as Compton and Moller scattering and the theory photdetection are given. After the impressive successes of QED, the limitation of the theory and the necessity of electroweak theory and quantumchromodynamics are discussed. The remaining chapters are devoted to quantum optics inside cavaties. Various approaches to open systems such as master equations are discussed within the context of active systems (e.g. the laser) and passive systems. Semi- classical approximarions are shown to imply a rich non- linear dynamics including chaos for certain parameter regimes. The effect of fluctuations on such non-linear dynamics is also studied. The final chapter is devoted to highly non- classical states of the light field such as photon number, squeezed and two photon entangled states. The latter are studied for the important system of parametric down conversion and the localisation properties of photons are characterised in terms of asympotic tails in photodetection probabilities as a function of time delay. The range of the book has wider benefits. Workers in quantum optics will gain a deeper understanding of the foundations of their subject and field theorists will see concrete examples of open systems, which are beginning to impinge on fundamental theories.

This volume reviews recent developments in conformal quantum field theory in D-dimensions, and focuses on two main aims. Firstly, the promising trend is followed toward constructing an exact solution for a certain class of models. Work on the conformal Ward identities in a D-dimensional space in the late '70s suggests a parallel with the null-vectors which determine the minimal models in the two-dimensional field theory. Recent research has also indicated the possible existence of an infinite parameter algebra analogous to the Virasoro algebra in spaces of higher dimensions D>=3. Each of these models contains parameters similar to the central charge of the two-dimensional theory, due to special fields which occur in the commutator of the components of the energy-momentum tensor. As a first step, a special formalism is suggested which allows finding an exact solution of these models for any space dimension. Then it is shown that in each model closed differential equations can be obtained for higher correlators, as well as the algebraic equations for scale dimensions of fields, and dimensionless parameters similar to the central charge. Secondly, this work aims to give a survey of some special aspects of conformal quantum field theory in D-dimensional space. Included are the survey of conformal methods of approximate calculation of critical indices in a three-dimensional space, an analysis and solution of a renormalised system of Schwinger-Dyson equations, a derivation of partial wave expansions, among other topics. Special attention is given to the development of the apparatus of quantum conform theory of gauge fields. Audience: This book will be of interest to graduate students andresearchers whose work involves quantum field theory.

Quantum and chaos, key concepts in contemporary science, are incompatible by nature. This volume presents an investigation into quantum transport in mesoscopic or nanoscale systems which are classically chaotic and shows the success and failure of quantal, semiclassical, and random matrix theories in dealing with questions emerging from the mesoscopic cosmos. These traditional theories are critically analysed, and this leads to a new direction. To reconcile quantum with chaos and to restore genuine temporal chaos in quantum systems, a time-discrete variant of quantum dynamics is proposed. Audience: This book will be of interest to graduate students and researchers in physics, chemistry and mathematics, whose work involves fundamental questions of quantum mechanics in chaotic systems.

"Fundamental Tests of Physics with Optically Trapped Microspheres "details experiments on studying the Brownian motion of an optically trapped microsphere with ultrahigh resolution and the cooling of its motion towards the quantum ground state.
Glass microspheres were trapped in water, air, and vacuum with optical tweezers; and a detection system that can monitor the position of a trapped microsphere with Angstrom spatial resolution and microsecond temporal resolution was developed to study the Brownian motion of a trapped microsphere in air over a wide range of pressures. The instantaneous velocity of a Brownian particle, in particular, was studied for the very first time, and the results provide direct verification of the Maxwell-Boltzmann velocity distribution and the energy equipartition theorem for a Brownian particle. For short time scales, the ballistic regime of Brownian motion is observed, in contrast to the usual diffusive regime.
In vacuum, active feedback is used to cool the center-of-mass motion of an optically trapped microsphere from room temperature to a minimum temperature of about 1.5 mK. This is an important step toward studying the quantum behaviors of a macroscopic particle trapped in vacuum.

This monograph identifies the essential characteristics of the objects described by current quantum theory and considers their relationship to space-time. In the process, it explicates the senses in which quantum objects may be consistently considered to have parts of which they may be composed or into which they may be decomposed. The book also demonstrates the degree to which reduction is possible in quantum mechanics, showing it to be related to the objective indefiniteness of quantum properties and the strong non-local correlations that can occur between the physical quantities of quantum subsystems. Careful attention is paid to the relationships among such property correlations, physical causation, probability, and symmetry in quantum theory. In this way, the text identifies and clarifies the conceptual grounds underlying the unique nature of many quantum phenomena.