This biography of the famous Soviet physicist Leonid Isaakovich Mandelstam (1889-1944), who became a Professor at Moscow State University in 1925 and an Academician (the highest scientific title in the USSR) in 1929, describes his contributions to both physics and technology. It also discusses the scientific community that formed around him, commonly known as the Mandelstam School. By doing so, it places Mandelstam's life story in its cultural context: the context of German University (until 1914), the First World War, the Civil War, and the development of the Socialist Revolution (until 1925) and the young socialist country. The book considers various general issues, such as the impact of German scientific culture on Russian science; the problems and fates of Russian intellectuals during the revolutionary and post-revolutionary years; the formation of the Soviet Academy of Science, the State Academy; and the transformation of the system of higher education in the USSR during the 1920s and 1930s. Further, it reconstructs Mandelstam's philosophy of science and his approach to the social and ethical function of science and science education based on his fundamental writings and lecture notes. This reconstruction is enhanced by extensive use of previously unpublished archive material as well as the transcripts of personal interviews conducted by the author. The book also discusses the biographies of Mandelstam's friends and collaborators: German mathematician and philosopher Richard von Mises, Soviet Communist Party official and philosopher B.M.Hessen, Russian specialist in radio engineering N.D.Papalexy, the specialists in non-linear dynamics A.A.Andronov, S.E. Chaikin, A.A.Vitt and the plasma physicist M.A.Leontovich. This second, extended edition reconstructs the social and economic backgrounds of Mandelstam and his colleagues, describing their positions at the universities and the institutes belonging to the Academy of Science. Additionally, Mandelstam's philosophy of science is investigated in connection with the ideological attacks that occurred after Mandelstam's death, particularly the great mathematician A.D.Alexandrov's criticism of Mandelstam's operationalism.

^ 74 GeV and |y| < 2.4; the b jets must contain a B hadron. The measurement has significant statistics up to p T O(TeV). Advanced methods of unfolding are performed to extract the signal. It is found that fixed-order calculations with underlying event describe the measurement well.

Statistical Mechanics is the study of systems where the number of interacting particles becomes infinite. In the last fifty years tremendous advances have been made which have required the invention of entirely new fields of mathematics such as quantum groups and affine Lie algebras. They have engendered remarkable discoveries concerning non-linear differential equations and algebraic geometry, and have produced profound insights in both condensed matter physics and quantum field theory. Unfortunately, none of these advances are taught in graduate courses in statistical mechanics.
This book is an attempt to correct this problem. It begins with theorems on the existence (and lack) of order for crystals and magnets and with the theory of critical phenomena, and continues by presenting the methods and results of fifty years of analytic and computer computations of phase transitions. It concludes with an extensive presentation of four of the most important of exactly solved problems: the Ising, 8 vertex, hard hexagon and chiral Potts models.

This thesis describes the controlled immobilization of molecules between two cuboidal metal nanoparticles by means of a self-assembly method to control the quantum plasmon resonances. It demonstrates that quantum-plasmonics is possible at length scales that are useful for real applications. Light can interact with certain metals and can be captured in the form of plasmons, which are collective, ultra-fast oscillations of electrons that can be manipulated at the nano-scale. Surface plasmons are considered as a promising phenomenon for potentially bridging the gap between fast-operating-speed optics and nano-scale electronics. Quantum tunneling has been predicted to occur across two closely separated plasmonic resonators at length scales (<0.3 nm) that are not accessible using present-day nanofabrication techniques. Unlike top-down nanofabrication, the molecules between the closely-spaced metal nanoparticles could control the gap sizes down to sub-nanometer scales and act as the frequency controllers in the terahertz regime, providing a new control parameter in the fabrication of electrical circuits facilitated by quantum plasmon tunneling.

'Et moi .... si favait su comment en revenir. One service mathematics bllS rendered the je n'y serais point aile.' human race. It hal put common sense back Jules Verne where it bdongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense', able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thOUght. A highly necessary tool in a world where both feedback and non Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series."

This Open Access book gives a comprehensive account of both the history and current achievements of molecular beam research. In 1919, Otto Stern launched the revolutionary molecular beam technique. This technique made it possible to send atoms and molecules with well-defined momentum through vacuum and to measure with high accuracy the deflections they underwent when acted upon by transversal forces. These measurements revealed unforeseen quantum properties of nuclei, atoms, and molecules that became the basis for our current understanding of quantum matter. This volume shows that many key areas of modern physics and chemistry owe their beginnings to the seminal molecular beam work of Otto Stern and his school. Written by internationally recognized experts, the contributions in this volume will help experienced researchers and incoming graduate students alike to keep abreast of current developments in molecular beam research as well as to appreciate the history and evolution of this powerful method and the knowledge it reveals.

Canonical commutation relations (CCR) and canonical anti-commutation relations (CAR) are basic principles in quantum physics including both quantum mechanics with finite degrees of freedom and quantum field theory. From a structural viewpoint, quantum physics can be primarily understood as Hilbert space representations of CCR or CAR. There are many interesting physical phenomena which can be more clearly understood from a representation-theoretical viewpoint with CCR or CAR. This book provides an introduction to representation theories of CCR and CAR in view of quantum physics. Particular emphases are put on the importance of inequivalent representations of CCR or CAR, which may be related to characteristic physical phenomena. The topics presented include general theories of representations of CCR and CAR with finite and infinite degrees of freedom, the Aharonov-Bohm effect, time operators, quantum field theories based on Fock spaces, Bogoliubov transformations, and relations of infinite renormalizations with inequivalent representations of CCR. This book can be used as a text for an advanced topics course in mathematical physics or mathematics.

This is the first scientic book devoted to the Pauli exclusion principle, which is a fundamental principle of quantum mechanics and is permanently applied in chemistry, physics, and molecular biology. However, while the principle has been studied for more than 90 years, rigorous theoretical foundations still have not been established and many unsolved problems remain. Following a historical survey in Chapter 1, the book discusses the still unresolved questions around this fundamental principle. For instance, why, according to the Pauli exclusion principle, are only symmetric and antisymmetric permutation symmetries for identical particles realized, while the Schrodinger equation is satisfied by functions with any permutation symmetry? Chapter 3 covers possible answers to this question. The construction of function with a given permutation symmetry is described in the previous Chapter 2, while Chapter 4 presents effective and elegant methods for finding the Pauli-allowed states in atomic, molecular, and nuclear spectroscopy. Chapter 5 discusses parastatistics and fractional statistics, demonstrating that the quasiparticles in a periodical lattice, including excitons and magnons, are obeying modified parafermi statistics. With detailed appendices, The Pauli Exclusion Principle: Origin, Verifications, and Applications is intended as a self-sufficient guide for graduate students and academic researchers in the fields of chemistry, physics, molecular biology and applied mathematics. It will be a valuable resource for any reader interested in the foundations of quantum mechanics and its applications, including areas such as atomic and molecular spectroscopy, spintronics, theoretical chemistry, and applied fields of quantum information.

This book provides extensive and novel insights into transport phenomena in MnSi, paving the way for applying the topology and chirality of spin textures to the development of spintronics devices. In particular, it describes in detail the key measurements, e.g. magnetoresistance and nonlinear electronic transport, and multiple material-fabrication techniques based on molecular beam epitaxy, ion-beam microfabrication and micromagnetic simulation. The book also reviews key aspects of B20-type MnSi chiral magnets, which host magnetic skyrmions, nanoscale objects formed by helical spatial spin structures. Readers are then introduced to cutting-edge findings on the material. Furthermore, by reviewing the author's successful experiments, the book provides readers with a valuable update on the latest achievements in the measurement and fabrication of magnetic materials in spintronics.

This thesis demonstrates the potential of two platforms to explore experimentally the emerging field of quantum thermodynamics that has remained mostly theoretical so far. It proposes methods to define and measure work in the quantum regime. The most important part of the thesis focuses on hybrid optomechanical devices, evidencing that they are proper candidates to measure directly the fluctuations of work and the corresponding fluctuation theorem. Such devices could also give rise to the observation of mechanical lasing and cooling, based on mechanisms similar to a heat engine. The final part of the thesis studies how quantum coherence can improve work extraction in superconducting circuits. All the proposals greatly clarify the concept of work since they are based on measurable quantities in state of the art devices.

This book studies the vulnerability of wireless communications under line-of-sight (LoS) and non-LoS correlated fading environments. The authors theoretically and practically provide physical layer security analyses for several technologies and networks such as Fifth-Generation (5G) networks, Internet of Things (IoT) applications, and Non-orthogonal multiple access (NOMA). The authors have provided these under various practical scenarios, and developed theoretical aspects to validate their proposed applications. Presents physical layer security (PLS) under correlated fading environments, 5G wireless networks, and NOMA networks; Provides end-to-end analyses, combination of channel correlation and outdated CSI and their effects on PL; Includes contributions of PLS research written by global experts in academia and industry.

This book studies the fundamental aspects of many-body physics in quantum systems open to an external world. Recent remarkable developments in the observation and manipulation of quantum matter at the single-quantum level point to a new research area of open many-body systems, where interactions with an external observer and the environment play a major role. The first part of the book elucidates the influence of measurement backaction from an external observer, revealing new types of quantum critical phenomena and out-of-equilibrium dynamics beyond the conventional paradigm of closed systems. In turn, the second part develops a powerful theoretical approach to study the in- and out-of-equilibrium physics of an open quantum system strongly correlated with an external environment, where the entanglement between the system and the environment plays an essential role. The results obtained here offer essential theoretical results for understanding the many-body physics of quantum systems open to an external world, and can be applied to experimental systems in atomic, molecular and optical physics, quantum information science and condensed matter physics.

The third edition of the by now classic reference on rigorous analysis of symmetry breaking in both classical and quantum field theories adds new topics of relevance, in particular the effect of dynamical Coulomb delocalization, by which boundary conditions give rise to volume effects and to energy/mass gap in the Goldstone spectrum (plasmon spectrum, Anderson superconductivity, Higgs phenomenon). The book closes with a discussion of the physical meaning of global and local gauge symmetries and their breaking, with attention to the effect of gauge group topology in QCD. From the reviews of the first edition: It is remarkable to see how much material can actually be presented in a rigorous way (incidentally, many of the results presented are due to Strocchi himself), yet this is largely ignored, the original heuristic derivations being, as a rule, more popular. - At each step he strongly emphasizes the physical meaning and motivation of the various notions introduced [...] a book that fills a conspicuous gap in the literature, and does it rather well. It could also be a good basis for a graduate course in mathematical physics. J.-P. Antoine, Physicalia 28/2, 2006 Despite many accounts in popular textbooks and a widespread belief, the phenomenon is rather subtle, requires an infinite set of degrees of freedom and an advanced mathematical setting of the system under investigation. [...] The mathematically oriented graduate student will certainly benefit from this thorough, rigorous and detailed investigation. G. Roepstorff, Zentralblatt MATH, Vol. 1075, 2006 From the reviews of the second edition: This second edition of Strocchi's Symmetry Breaking presents a complete, generalized and highly rigorous discussion of the subject, based on a formal analysis of conditions necessary for the mechanism of spontaneous symmetry breaking to occur in classical systems, as well as in quantum systems. [...] This book is specifically recommended for mathematical physicists interested in a deeper and rigorous understanding of the subject, and it should be mandatory for researchers studying the mechanism of spontaneous symmetry breaking. S. Hajjawi, Mathematical Reviews, 2008

This textbook, now in an expanded third edition, emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. Advanced Quantum Mechanics: Materials and Photons can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible, introductions to Lagrangian mechanics and the covariant formulation of electrodynamics are provided in appendices. This third edition includes 60 new exercises, new and improved illustrations, and new material on interpretations of quantum mechanics. Other special features include an introduction to Lagrangian field theory and an integrated discussion of transition amplitudes with discrete or continuous initial or final states. Once students have acquired an understanding of basic quantum mechanics and classical field theory, canonical field quantization is easy. Furthermore, the integrated discussion of transition amplitudes naturally leads to the notions of transition probabilities, decay rates, absorption cross sections and scattering cross sections, which are important for all experimental techniques that use photon probes.

This thesis makes significant advances in the quantitative understanding of two intrinsically linked yet technically very different phenomena in quantum chromodynamics (QCD). Firstly, the thesis investigates the soft probe of strong interaction topological fluctuations in the quark-gluon plasma (QGP) which is made possible via the anomalous chiral transport effects induced by such fluctuations. Here, the author makes contributions towards establishing the first comprehensive tool for quantitative prediction of the chiral magnetic effect in the QGP that is produced in heavy ion collision experiments. Secondly, the thesis deals with the hard probe of strongly coupled QGP created in heavy-ion collisions. In particular, this study addresses the basic question related to the nonperturbative color structure in the QGP via jet energy loss observables. The author further develops the CUJET computational model for jet quenching and uses it to analyze the topological degrees of freedom in quark-gluon plasma. The contributions this thesis makes towards these highly-challenging problems have already generated widespread impacts in the field of quark-gluon plasma and high-energy nuclear collisions.

This monograph aims to fill the gap between the mathematical literature which significantly contributed during the last decade to the understanding of the collapse phenomenon, and applications to domains like plasma physics and nonlinear optics where this process provides a fundamental mechanism for small scale formation and wave dissipation. This results in a localized heating of the medium and in the case of propagation in a dielectric to possible degradation of the material. For this purpose, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal asymptotic expansions and numerical simulations.

This book explains the evolution of techniques and strategies in quantum computing, discussing the digital transition towards the quantum computing application in various sectors. The book provides a comprehensive insight into the quantum mechanics and quantum computing techniques and tools and how they have evolved and the impacted in supporting and flourishing business during the quantum computing era. This book includes chapters that discuss the most primitive quantum schemes to the most recent use of Internet, finance and radar technology, thus leveraging greater use of new technologies like security and Internet and others. The content is relevant for an audience that is involved in the research and development of advanced quantum systems. It gives the industry, researchers, and students interested in learning the various quantum computing sectors with the necessary information and tools that can be used to research, design and develop advanced quantum computing systems and techniques.

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This fifth volume collects authoritative chapters covering several applications of fractional calculus in physics, including electrodynamics, statistical physics and physical kinetics, and quantum theory.

Advancing the experimental study of superfluids relies on increasingly sophisticated techniques. We develop and demonstrate the loading of Bose-Einstein condensates (BECs) into nearly arbitrary trapping potentials, with a resolution improved by a factor of seven when compared to reported systems. These advanced control techniques have since been adopted by several cold atoms labs around the world. How this BEC system was used to study 2D superfluid dynamics is described. In particular, negative temperature vortex states in a two-dimensional quantum fluid were observed. These states were first predicted by Lars Onsager 70 years ago and have significance to 2D turbulence in quantum and classical fluids, long-range interacting systems, and defect dynamics in high-energy physics. These experiments have established dilute-gas BECs as the prototypical system for the experimental study of point vortices and their nonequilibrium dynamics. We also developed a new approach to superfluid circuitry based on classical acoustic circuits, demonstrating its conceptual and quantitative superiority over previous lumped-element models. This has established foundational principles of superfluid circuitry that will impact the design of future transport experiments and new generation quantum devices, such as atomtronics circuits and superfluid sensors.

The aim of this book is to give graduate students an overview of quantum gravity but it also covers related topics from astrophysics. Some well-written contributions can serve as an introduction into basic conceptual concepts like time in quantum gravity or the emergence of a classical world from quantum cosmology. This makes the volume attractive to philosophers of science, too. Other topics are black holes, gravitational waves and non-commutative extensions of physical theories.

Quantum optics, i.e. the interaction of individual photons with matter, began with the discoveries of Planck and Einstein, but in recent years, it has expanded beyond pure physics to become an important driving force for technological innovation. This book serves the broader readership growing out of this development by starting with an elementary description of the underlying physics and then building up a more advanced treatment. The reader is led from the quantum theory of the simple harmonic oscillator to the application of entangled states to quantum information processing.
An equally important feature of the text is a strong emphasis on experimental methods. Primary photon detection, heterodyne and homodyne techniques, spontaneous down-conversion, and quantum tomography are discussed, together with important experiments. These experimental and theoretical considerations come together in the chapters describing quantum cryptography, quantum communications, and quantum computing.

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 lecture that can be followed 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'.... 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."

This book investigates two possibilities for describing classical-mechanical physical systems along with their Hamiltonian dynamics in the framework of quantum mechanics.The first possibility consists in exploiting the geometrical properties of the set of quantum pure states of "microsystems" and of the Lie groups characterizing the specific classical system. The second approach is to consider quantal systems of a large number of interacting subsystems - i.e. macrosystems, so as to study the quantum mechanics of an infinite number of degrees of freedom and to look for the behaviour of their collective variables. The final chapter contains some solvable models of "quantum measurement" describing dynamical transitions from "microsystems" to "macrosystems".

But to admit things not visible to the gross creatures that we are is, in my opinion, to show a decent humility, and not just a lamentable addiction to metaphysics. J. S. Bell, Are There Quantum Jumps? ON CANADIAN THANKSGIVING WEEKEND in the autumn of 1994, a lively conference was held at The University of Western Ontario under the title "Conceptual Problems of Relativistic Quantum Mechanics." Most of the eighteen papers in this volume are directly connected with that conference. Articles by both theoretical physicists and philosophers of science are included, and many authors will be recognized immediately for their already substantive work in the foundations of physics. A quarter century ago Howard Stein suggested that relativistic quantum field theory should be 'the contemporary locus of metaphysical research', but there were few takers. Only fairly recently has that changed, with the result that the bulk of the papers here pursue issues that go beyond nonrelativistic quantum mechanics (or at least have serious implications for its relativistic generalization). Nevertheless, problems interpreting the nonrelativistic theory remain a persistent thorn in the side of any such endeavor, and so some of the papers develop innovative approaches to those issues as well.

This book introduces the reader to the field of jet substructure, starting from the basic considerations for capturing decays of boosted particles in individual jets, to explaining state-of-the-art techniques. Jet substructure methods have become ubiquitous in data analyses at the LHC, with diverse applications stemming from the abundance of jets in proton-proton collisions, the presence of pileup and multiple interactions, and the need to reconstruct and identify decays of highly-Lorentz boosted particles. The last decade has seen a vast increase in our knowledge of all aspects of the field, with a proliferation of new jet substructure algorithms, calculations and measurements which are presented in this book. Recent developments and algorithms are described and put into the larger experimental context. Their usefulness and application are shown in many demonstrative examples and the phenomenological and experimental effects influencing their performance are discussed. A comprehensive overview is given of measurements and searches for new phenomena performed by the ATLAS and CMS Collaborations. This book shows the impressive versatility of jet substructure methods at the LHC.