This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master's-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schroedinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.

This thesis presents several related advances in the field of nonequilibrium quantum thermodynamics. The central result is an ingenious proof that the local temperature and voltage measurement in a nonequilibrium system of fermions exists and is unique, placing the concept of local temperature on a rigorous mathematical footing for the first time. As an intermediate step, a proof of the positivity of the Onsager matrix of linear response theory is given -- a statement of the second law of thermodynamics that had lacked an independent proof for 85 years. A new experimental method to measure the local temperature of an electron system using purely electrical techniques is also proposed, which could enable improvements to the spatial resolution of thermometry by several orders of magnitude. Finally, a new mathematically-exact definition for the local entropy of a quantum system in a nonequilibrium steady state is derived. Several different measures of the local entropy are discussed, relating to the thermodynamics of processes that a local observer with varying degrees of information about the microstates of the system could carry out, and it is shown that they satisfy a hierarchy of inequalities. Proofs of the third law of thermodynamics for generic open quantum systems are presented, taking into account the entropic contribution due to localized states. Appropriately normalized (per-state) local entropies are defined and are used to quantify the departure from local equilibrium.

Superfluid helium is a quantum liquid that exhibits a range of counter-intuitive phenomena such as frictionless flow. Quantized vortices are a particularly important feature of superfluid helium, and all superfluids, characterized by a circulation that can only take prescribed integer values. However, the strong interactions between atoms in superfluid helium prohibit quantitative theory of vortex behaviour. Experiments have similarly not been able to observe coherent vortex dynamics. This thesis resolves this challenge, bringing microphotonic techniques to bear on two-dimensional superfluid helium, observing coherent vortex dynamics for the first time, and achieving this on a silicon chip. This represents a major scientific contribution, as it opens the door not only to providing a better understanding of this esoteric quantum state of matter, but also to building new quantum technologies based upon it, and to understanding the dynamics of astrophysical superfluids such as those thought to exist in the core of neutron stars.

This book presents a basic introduction to quantum mechanics. Depending on the choice of topics, it can be used for a one-semester or two-semester course. An attempt has been made to anticipate the conceptual problems students encounter when they first study quantum mechanics. Wherever possible, examples are given to illustrate the underlying physics associated with the mathematical equations of quantum mechanics. To this end, connections are made with corresponding phenomena in classical mechanics and electromagnetism. The problems at the end of each chapter are intended to help students master the course material and to explore more advanced topics. Many calculations exploit the extraordinary capabilities of computer programs such as Mathematica, MatLab, and Maple. Students are urged to use these programs, just as they had been urged to use calculators in the past. The treatment of various topics is rather complete, in that most steps in derivations are included. Several of the chapters go beyond what is traditionally covered in an introductory course. The goal of the presentation is to provide the students with a solid background in quantum mechanics.

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.

A gentle introduction to the physics of quantized fields and many-body physics. Based on courses taught at the University of Illinois, it concentrates on the basic conceptual issues that many students find difficult, and emphasizes the physical and visualizable aspects of the subject. While the text is intended for students with a wide range of interests, many of the examples are drawn from condensed matter physics because of the tangible character of such systems. The first part of the book uses the Hamiltonian operator language of traditional quantum mechanics to treat simple field theories and related topics, while the Feynman path integral is introduced in the second half where it is seen as indispensable for understanding the connection between renormalization and critical as well as non-perturbative phenomena.

The lecture notes of Julian Schwinger's UCLA course consist of three parts corresponding to the three quarters of teaching. The first part begins with an analysis of Stern--Gerlach-type experiments which accomplishes a self-contained physical and mathematical development of the general structure of quantum kinematics. The second part proceeds from there. The response to infinitesimal time displacements yields the equations of motion. Then the Quantum Action Principle (QAP) is derived, and accepted as a fundamental principle. In a sense, the rest of part two and all of part three consist of instructive applications of the QAP.

This thesis summarizes the original analysis work performed by the author on data from XENON1T, a search for dark matter with a ton-size noble liquid detector operated at Gran Sasso Underground Laboratory in Italy. The nature of dark matter is one of the most open and pressing questions of modern physics, and the unique data acquired with this detector allows the exploration and investigation of several potential scenarios. The analysis of Dr. Shockley searches for a class of elusive elementary particles that interact with the electrons of ordinary atoms, instead of the nucleus. Results of the analysis present, with high confidence, an excess with respect to the expected background. Beyond more mundane explanations, this additional rate of electron-mediated interactions might be a first hint of physics beyond the standard model. This accessible thesis provides details on the detector, the data, and the theory, delivering to the reader an in-depth and coherent picture of the search for physics beyond the standard model.

It is hard to interpret quantum mechanics. The most surprising, but also most parsimonious, interpretation is the many-worlds, or quantum-multiverse interpretation, implying a permanent coexistence of parallel realities. Could this perhaps be the appropriate interpretation of quantum mechanics? This book collects evidence for this interpretation, both from physics and from other fields, and proposes a subjectivist version of it, the clustered-minds multiverse. The author explores its implications through the lens of decision making and derives consequences for free will and consciousness. For example, free will can be implemented in the form of vectorial choices, as introduced in the book. He furthermore derives consequences for research in the social sciences, especially in psychology and economics.

This book presents more than 300 exercises, with guided solutions, on topics that span both the experimental and the theoretical aspects of particle physics. The exercises are organized by subject, covering kinematics, interactions of particles with matter, particle detectors, hadrons and resonances, electroweak interactions and flavor physics, statistics and data analysis, and accelerators and beam dynamics. Some 200 of the exercises, including 50 in multiple-choice format, derive from exams set by the Italian National Institute for Nuclear Research (INFN) over the past decade to select its scientific staff of experimental researchers. The remainder comprise problems taken from the undergraduate classes at ETH Zurich or inspired by classic textbooks. Whenever appropriate, in-depth information is provided on the source of the problem, and readers will also benefit from the inclusion of bibliographic details and short dissertations on particular topics. This book is an ideal complement to textbooks on experimental and theoretical particle physics and will enable students to evaluate their knowledge and preparedness for exams.

In this volume we have collected some of the contributions made to the Twelfth European Workshop on Quantum Systems in Chemistry and Physics (QSCP-XII) in 2007. The workshop was held at Royal Holloway College, the most westerly campusof the University of London,and situated just a stone's throw from Windsor Great Park. The workshop, which ran from 30 August to 5 September, continued the series that was established by Roy McWeeny in April 1996 with a meeting held at San Miniato, near Pisa. The purpose of the QSCP workshops is to bring together, in an informal atmosphere and with the aim of fostering collaboration, those chemists and physicists who share a common ?eld of interest in the theory of the quantum many-body problem. Quantum mechanics provides a theoretical foundation for our understandingof the structure,propertiesanddynamicsof atoms, moleculesandthe solid state, in terms of their component particles: electrons and nuclei. The study of 'Quantum Systems in Chemistry and Physics' therefore underpins many of the emerging?elds in twenty-?rstcenturyscience andtechnology:nanostructure,smart materials, drug design - to name but a few. Members of the workshop were keen to discuss their research and engage in collaboration centred upon the development of fundamental and innovative theory which would lead to the exploration of new concepts. The proceedings of all of the workshops, which have been held annually since 1996, have been published both to disseminate the latest developments within the wider community and to stimulate further collaboration.

In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this step for statistical mechanics--a field rooted in physics and chemistry whose ideas and methods< br> are now central to information theory, complexity, and modern biology. Aimed at advanced undergraduates and early graduate students in all of these fields, Sethna limits his main presentation to the topics that future mathematicians and biologists, as well as physicists and chemists, will find< br> fascinating and central to their work. The amazing breadth of the field is reflected in the author's large supply of carefully crafted exercises, each an introduction to a whole field of study: everything from chaos through information theory to life at the end of the universe.

This volume contains contributions based on the lectures delivered and posters presented at the Fifth International Conference on Quantum Communication, Measurement and Computing (QCM&C-Y2K). This Conference is the fifth of a successful series hosted this time in Italy, was held in Capri, 3-7 July, 2000. The conference was attended by more than 200 participants from all over the world. There was also a high level of participation from graduate students, who greatly benefited from the opportunity to attend world-class conferences. The Conference Hall was hosted in La Residenza Hotel in Capri, where part of p- ticipants where housed, while others where housed in various cozy nearby - tels. All enjoyed the pleasant atmosphere offered by the island of Capri. There were 59 invited lectures given as oral presentations of 30 minutes and 94 poster papers. The major topics covered at the Conference where new experimental and theoretical results in quantum information. They were divided in five parts; i) Quantum Information and Communication, ii) Quantum Measurement, - coherence, and Tomography, iii) Quantum Computing, iv) Cryptography, v) Entanglement and Teleportation. We were lucky in that almost all major - perimental groups in the world working in this area were represented, as were the major theoreticians. There was very active audience participation. A n- ber of graduate students and post-docs were able to present their contributions in four after dinner poster sessions.

This textbook presents a concise yet detailed introduction to quantum physics. Concise, because it condenses the essentials to a few principles. Detailed, because these few principles - necessarily rather abstract - are illustrated by several telling examples. A fairly complete overview of the conventional quantum mechanics curriculum is the primary focus, but the huge field of statistical thermodynamics is covered as well. The text explains why a few key discoveries shattered the prevailing broadly accepted classical view of physics. First, matter appears to consist of particles which, when propagating, resemble waves. Consequently, some observable properties cannot be measured simultaneously with arbitrary precision. Second, events with single particles are not determined, but are more or less probable. The essence of this is that the observable properties of a physical system are to be represented by non-commuting mathematical objects instead of real numbers. Chapters on exceptionally simple, but highly instructive examples illustrate this abstract formulation of quantum physics. The simplest atoms, ions, and molecules are explained, describing their interaction with electromagnetic radiation as well as the scattering of particles. A short introduction to many particle physics with an outlook on quantum fields follows. There is a chapter on maximally mixed states of very large systems, that is statistical thermodynamics. The following chapter on the linear response to perturbations provides a link to the material equations of continuum physics. Mathematical details which would hinder the flow of the main text have been deferred to an appendix. The book addresses university students of physics and related fields. It will attract graduate students and professionals in particular who wish to systematize or refresh their knowledge of quantum physics when studying specialized texts on solid state and materials physics, advanced optics, and other modern fields.

The associated production of a W boson and a single charm quark (W+c) is the only process in proton-proton collisions that directly probes the strange quark content of the proton. In this thesis, W+charm production is measured in proton-proton collisions at the LHC at 13 TeV, as recorded by the Compact Muon Solenoid (CMS) experiment. The analysis focuses on the identification of W bosons in their leptonic decay to a muon and a neutrino and charm quarks are tagged via the full reconstruction of D*-Mesons. The measured cross sections of W+c production are used, in combination with other relevant CMS results and the most precise HERA DIS data, in a QCD analysis to determine the strange quark content of the proton. The resulting strange quark distribution and suppression, with respect to the other light sea quarks, are in good agreement with those obtained in neutrino scattering experiments and extend their kinematic reach.

Rising concerns about the security of our data have made quantum cryptography a very active research field in recent years. Quantum cryptographic protocols promise everlasting security by exploiting distinctive quantum properties of nature. The most extensively implemented protocol is quantum key distribution (QKD), which enables secure communication between two users. The aim of this book is to introduce the reader to state-of-the-art QKD and illustrate its recent multi-user generalization: quantum conference key agreement. With its pedagogical approach that doesn't disdain going into details, the book enables the reader to join in cutting-edge research on quantum cryptography.

This book offers a didactic introduction to light-matter interactions at both the classical and semi-classical levels. Pursuing an approach that describes the essential physics behind the functionality of any optical element, it acquaints students with the broad areas of optics and photonics. Its rigorous, bottom-up approach to the subject, using model systems ranging from individual atoms and simple molecules to crystalline and amorphous solids, gradually builds up the reader's familiarity and confidence with the subject matter. Throughout the book, the detailed mathematical treatment and examples of practical applications are accompanied by problems with worked-out solutions. In short, the book provides the most essential information for any graduate or advanced undergraduate student wishing to begin their course of study in the field of photonics, or to brush up on important concepts prior to an examination.

Systems of trapped ions and systems of ultracold Rydberg atoms are used at the forefront of quantum physics research and they make strong contenders as platforms for quantum technologies. Trapped Rydberg ions are a new hybrid technology envisaged to have both the exquisite control of trapped ion systems and the strong interactions of Rydberg atoms. In this work a single trapped Rydberg ion is experimentally investigated. A trapped strontium ion is excited to Rydberg states using two ultraviolet lasers. Effects of the strong trapping electric fields on the highly-sensitive Rydberg ion are studied. After mitigating unwanted trap effects, the ion is coherently excited to Rydberg states and a quantum gate is demonstrated. This thesis lays much of the experimental groundwork for research using this novel system.

This volume contains two major articles, one providing a historical retrosp- tive of one of the great triumphs of nuclear physics in the twentieth century and the other providing a didactic introduction to one of the quantitative tools for understanding strong interactions in the twenty-first century. The article by Igal Talmi on "Fifty Years of the Shell Model - the Quest for the Effective Interaction," pertains to a model that has dominated nuclear physics since its infancy and that developed with astonishing results over the next five decades. Talmi is uniquely positioned to trace the history of the Shell Model. He was active in developing the ideas at the shell model's inception, he has been central in most of the subsequent initiatives which expanded, cl- ified and applied the shell model and he has remained active in the field to the present time. Wisely, he has chosen to restrict his review to the domin- ing issue: the choice of the effective interactions among valence nucleons that determine the properties of low lying nuclear energy levels. The treatment of the subject is both bold and novel for our series. The ideas pertaining to the effective interaction for the shell model are elucidated in a historical sequence.

This thesis lays the groundwork for producing a new class of ultracold molecule by associating an alkali-metal atom and a closed-shell alkaline-earth-like atom, specifically Cs and Yb. Such molecules exhibit both a magnetic dipole moment and an electric dipole moment in their ground state. This extra degree of freedom opens up new avenues of research including the study of exotic states of matter, the shielding of molecular collisions and the simulation of lattice spin models. In detail, the thesis reports the first and only ultracold mixture of Cs and Yb in the world, giving details of the methods used to cool such contrasting atomic species together. Using sensitive two-colour photoassociation measurements to measure the binding energies of the near-threshold CsYb molecular levels in the electronic ground state has allowed the previously unknown scattering lengths to be accurately determined for all the Cs-Yb isotopic combinations. As part of this work, the one-photon photoassociation of ultracold Cs*Yb is also studied, yielding useful information on the excited-state potential. Knowledge of the scattering lengths enables a strategy to be devised to cool both species to quantum degeneracy and, crucially, determines the positions of interspecies Feshbach resonances required for efficient association of ground-state CsYb molecules. With these results, the prospect of bringing a new molecule into the ultracold regime has become considerably closer.

This book discusses the elementary ideas and tools needed for open quantum systems in a comprehensive manner. The emphasis is given to both the traditional master equation as well as the functional (path) integral approaches. It discusses the basic paradigm of open systems, the harmonic oscillator and the two-level system in detail. The traditional topics of dissipation and tunneling, as well as the modern field of quantum information, find a prominent place in the book. Assuming a basic background of quantum and statistical mechanics, this book will help readers familiarize with the basic tools of open quantum systems. Open quantum systems is the study of quantum dynamics of the system of interest, taking into account the effects of the ambient environment. It is ubiquitous in the sense that any system could be envisaged to be surrounded by its environment which could naturally exert its influence on it. Open quantum systems allows for a systematic understanding of irreversible processes such as decoherence and dissipation, of the essence in order to have a correct understanding of realistic quantum dynamics and also for possible implementations. This would be essential for a possible development of quantum technologies.

The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.

The nature of dark matter remains one of the preeminent mysteries in physics and cosmology. It appears to require the existence of new particles whose interactions with ordinary matter are extraordinarily feeble. One well-motivated candidate is the axion, an extraordinarily light neutral particle that may possibly be detected by looking for their conversion to detectable microwaves in the presence of a strong magnetic field. This has led to a number of experimental searches that are beginning to probe plausible axion model space and may reveal the axion in the near future. These proceedings discuss the challenges of designing and operating tunable resonant cavities and detectors at ultralow temperatures. The topics discussed here have potential application far beyond the field of dark matter detection and may be applied to resonant cavities for accelerators as well as designing superconducting detectors for quantum information and computing applications. This work is intended for graduate students and researchers interested in learning the unique requirements for designing and operating microwave cavities and detectors for direct axion searches and to introduce several proposed experimental concepts that are still in the prototype stage.

This book comprises selected peer-reviewed papers presented at the 7th Topical Conference of the Indian Society of Atomic and Molecular Physics, jointly held at IISER Tirupati and IIT Tirupati, India. The contributions address current topics of interest in atomic and molecular physics, both from the theoretical and experimental perspective. The major focus areas include quantum collisions, spectroscopy of atomic and molecular clusters, photoionization, Wigner time delay in collisions, laser cooling, Bose-Einstein condensates, atomic clocks, quantum computing, and trapping and manipulation of quantum systems. The book also discusses emerging topics such as ultrafast quantum processes including those at the attosecond time-scale. This book will prove to be a valuable reference for students and researchers working in the field of atomic and molecular physics.