This thesis provides a detailed introduction to quantum oscillation measurement and analysis and offers a connection between Fermi surface properties and superconductivity in high-temperature superconductors. It also discusses the field of iron-based superconductors and tests the models for the appearance of nodes in the superconducting gap of a 111-type pnictide using quantum oscillation measurements combined with band structure calculation. The same measurements were carried out to determine the quasiparticle mass in BaFe2(As1-xPx)2, which is strongly enhanced at the expected quantum critical point. While the lower superconducting critical field shows evidence of quantum criticality, the upper superconducting critical field is not influenced by the quantum critical point. These findings contradict conventional theories, demonstrating the need for a theoretical treatment of quantum critical superconductors, which has not been addressed to date. The quest to discover similar evidence in the cuprates calls for the application of extreme conditions. As such, quantum oscillation measurements were performed under high pressure in a high magnetic field, revealing a negative correlation between quasiparticle mass and superconducting critical temperature.

Quantum annealing employs quantum fluctuations in frustrated systems or networks to anneal the system down to its ground state, or more generally to its so-called minimum cost state. Often this procedure turns out to be more effective, in multivariable optimization problems, than its classical counterpart utilizing tunable thermal fluctuations. This volume is divided into three parts. Part I is an extensive tutorial introduction familiarizing the reader with the background material necessary to follow the core of the book. Part II gives a comprehensive account of the fundamentals and applications of the quantum annealing method, and Part III compares quantum annealing with other related optimization methods. This is the first book entirely devoted to quantum annealing and will be both an invaluable primer and guidebook for all advanced students and researchers in this important field.

This volume is the result of two international workshops; "Infinite Analysis 11 Frontier of Integrability" held at University of Tokyo, Japan in July 25th to 29th, 2011, and "Symmetries, Integrable Systems and Representations" held at Universite Claude Bernard Lyon 1, France in December 13th to 16th, 2011.

Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions.

Through these topics, the readerwill find some recent developments in the field of mathematical physics and their interactions with several other domains.
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This volume provides a detailed discussion of the mathematical aspects and the physical applications of a new geometrical structure of space-time, based on a generalization ("deformation") of the usual Minkowski space, as supposed to be endowed with a metric whose coefficients depend on the energy.

Such a formalism (Deformed Special Relativity, DSR) allows one

• to account for breakdown of local Lorentz invariance in the usual, special-relativistic meaning (however, Lorentz invariance is recovered in a generalized sense)
• to provide an effective geometrical description of the four fundamental interactions (electromagnetic, weak, strong and gravitational)

Moreover, the four-dimensional energy-dependent space-time is just a manifestation of a larger, five-dimensional space in which energy plays the role of a fifth (non-compactified) dimension. This new five-dimensional scheme (Deformed Relativity in Five Dimensions, DR5) represents a true generalization of the usual Kaluza-Klein (KK) formalism.

The mathematical properties of such a generalized KK scheme are illustrated. They include the solutions of the five-dimensional Einstein equations in vacuum in most cases of physical relevance, the infinitesimal symmetries of the theory for the phenomenological metrics of the four interactions, and the study of the five-dimensional geodesics.

The mathematical results concerning the geometry of the deformed five-dimensional spacetime (like its Killing symmetries) can be applied also to other multidimensional theories with infinite extra dimensions. Some experiments providing preliminary evidence for the hypothesized deformation of space-time for all thefour fundamental interactions are discussed.

Mesoscopic physics deals with effects at submicron and nanoscales where the conventional wisdom of macroscopic averaging is no longer applicable. A wide variety of new devices have recently evolved, all extremely promising for major novel directions in technology, including carbon nanotubes, ballistic quantum dots, hybrid mesoscopic junctions made of different type of normal, superconducting and ferromagnetic materials. This, in turn, demands a profound understanding of fundamental physical phenomena on mesoscopic scales. As a result, the forefront of fundamental research in condensed matter has been moved to the areas where the interplay between electron-electron interactions and quantum interference of phase-coherent electrons scattered by impurities and/or boundaries is the key to such understanding. An understanding of decoherence as well as other effects of the interactions is crucial for developing future electronic, photonic and spintronic devices, including the element base for quantum computation.

Quantum coherence is a phenomenon that plays a crucial role in various forms of matter. The thriving field of quantum information as well as unconventional approaches to use mesoscopic systems in future optoelectronic devices provide the exciting background for this set of lectures.

The lectures originate from the well-known Schladming Winter Schools and are carefully edited so as to address a broad readership ranging from the beginning graduate student up to the senior scientist wanting to keep up with or to enter newly emerging fields of research.

Each contribution is an article in itself, and great effort has been made by the authors to be lucid and not too technical. A few brief highlights of the round-table discussions are given between the chapters.

Topics include: Quantum non-locality, the measurement problem, quantum insights into relativity, cosmology and thermodynamics, and possible bearings of quantum mechanics to biology and consciousness. Authors include Yakir Aharanov and Anton Zeilinger, plus Nobel laureates Anthony J. Leggett (2003) and Gerardus t Hooft (1999).

Foreword written by Sir Roger Penrose, best-selling author (The Emperor's New Mind) and world-renowned mathematical physicist.

This thesis has two parts, each based on an application of the renormalization-group (RG). The first part is an analysis of the d-dimensional Coulomb gas. The goal was to determine if the Wilson RG could provide input into particle-in-cell simulations in plasma physics, which are the main family of simulation methods used in this field. The role of the RG was to identify the effect of coarse-graining on the coupling constants as a function of the cut-offs. The RG calculation reproduced established results, but in a more concise form, and showed the effect of the cut-offs on the Debye screening length.
The main part of the thesis is the application of the dynamic RG to turbulence in magnetohydrodynamics. After transformation to Elsasser variables, which is a symmetrisation of the original equations, the solution is presented as a functional integral, which includes stirring forces, their conjugates and functional Jacobian. The coarse-graining of the functional integral is represented as a diagrammatic expansion, followed by rescaling, and casting the results into differential equations for the analysis of RG trajectories. Detailed comparisons are made with the Navier-Stokes limit and with previous calculations for MHD.

Classical Mechanics teaches readers how to solve physics problems; in other words, how to put math and physics together to obtain a numerical or algebraic result and then interpret these results physically. These skills are important and will be needed in more advanced science and engineering courses. However, more important than developing problem-solving skills and physical-interpretation skills, the main purpose of this multi-volume series is to survey the basic concepts of classical mechanics and to provide the reader with a solid understanding of the foundational content knowledge of classical mechanics. Classical Mechanics: The Universal Law of Gravitation focuses on the notion that forces act through their associated fields, which is first introduced when discussing Newton's universal law of gravitation. A huge conceptual leap is required from the reader: an object can cause another object to move without even touching it. This is a difficult concept to reconcile with our everyday experiences but it makes perfect sense when we realize that is exactly how the Earth acts on us. Gravity is able to pull on us even though we are not in direct contact with the Earth. Also, the concept of super-position (and when it is applicable) is introduced. Super-position is crucial to the development of problem-solving skills so it will be illustrated in a number of example problems.

Quantum information may sound like science fiction but is, in fact, an active and extremely promising area of research, with a big dream: to build a quantum computer capable of solving problems that a classical computer could not even begin to handle. Research in quantum information science is now at an advanced enough stage for this dream to be credible and well-worth pursuing. It is, at the same time, too early to predict how quantum computers will be built, and what potential technologies will eventually strike gold in their ability to manipulate and process quantum information.

One direction that has reaped many successes in quantum information processing relies on continuous variables. This area is bustling with theoretical and experimental achievements, from continuous-variable teleportation, to in-principle demonstrations of universal computation and efficient error correction. Now the time has come to compile some of the major results into one volume. In this book the leading researchers of the field present up-to-date developments of continuous-variable quantum information. This book is organized to suit many reader levels with introductions to every topic and in-depth discussions of theoretical and experimental results.

This thesis reports on the first studies of Standard Model photon production at the Large Hadron Collider (LHC) using the ATLAS detector. Standard Model photon production is a large background in the search for Higgs bosons decaying into photon pairs, and is thus critical to understand. The thesis explains the techniques used to reconstruct and identify photon candidates using the ATLAS detector, and describes a measurement of the production cross section for isolated prompt photons. The thesis also describes a search for the Higgs boson in which the analysis techniques used in the measurement are exploited to reduce and estimate non-prompt backgrounds in diphoton events.

Most textbooks explain quantum mechanics as a story where each step follows naturally from the one preceding it. However, the development of quantum mechanics was exactly the opposite. It was a zigzag route, full of personal disputes where scientists were forced to abandon well-established classical concepts and to explore new and imaginative pathways. Some of the explored routes were successful in providing new mathematical formalisms capable of predicting experiments at the atomic scale. However, even such successful routes were painful enough, so that relevant scientists like Albert Einstein and Erwin Schroedinger decided not to support them. In this book, the authors demonstrate the huge practical utility of another of these routes in explaining quantum phenomena in many different research fields. Bohmian mechanics, the formulation of the quantum theory pioneered by Louis de Broglie and David Bohm, offers an alternative mathematical formulation of quantum phenomena in terms of quantum trajectories. Novel computational tools to explore physical scenarios that are currently computationally inaccessible, such as many-particle solutions of the Schroedinger equation, can be developed from it.

This is a collection of essays based on lectures that author has given on various occasions on foundation of quantum theory, symmetries and representation theory, and the quantum theory of the superworld created by physicists. The lectures are linked by a unifying theme: how the quantum world and superworld appear under the lens of symmetry and supersymmetry.

In the world of ultra-small times and distances such as the Planck length and Planck time, physicists believe no measurements are possible and so the structure of spacetime itself is an unkown that has to be first understood. There have been suggestions (Volovich hypothesis) that world geometry at such energy regimes is non-archimedian and some of the lectures explore the consequences of such a hypothesis.

Ultimately, symmetries and supersymmetries are described by the representation of groups and supergroups. The author's interest in representation is a lifelong one and evolved slowly, and owes a great deal to conversations and discussions he had with George Mackey and Harish-Chandra. The book concludes with a retrospective look at these conversations.

In this book, the problem of electron and hole transport is approached from the point of view that a coherent and consistent physical theory can be constructed for transport phenomena. Along the road readers will visit some exciting citadels in theoretical physics as the authors guide them through the strong and weak aspects of the various theoretical constructions. Our goal is to make clear the mutual coherence and to put each theoretical model in an appropriate perspective. The mere fact that so many partial solutions have been proposed to describe transport, be it in condensed matter, fluids, or gases, illustrates that we are entering a world of physics with a rich variety of phenomena. Theoretical physics always seeks to provide a unifying picture. By presenting this tour of many very inventive attempts to build such a picture, it is hoped that the reader will be inspired and encouraged to help find the unifying principle behind the many faces of transport.

How much knowledge can we gain about a physical system and to what degree can we control it? In quantum optical systems, such as ion traps or neutral atoms in cavities, single particles and their correlations can now be probed in a way that is fundamentally limited only by the laws of quantum mechanics. In contrast, quantum many-body systems pose entirely new challenges due to the enormous number of microscopic parameters and their small length- and short time-scales.
This thesis describes a new approach to probing quantum many-body systems at the level of individual particles: Using high-resolution, single-particle-resolved imaging and manipulation of strongly correlated atoms, single atoms can be detected and manipulated due to the large length and time-scales and the precise control of internal degrees of freedom. Such techniques lay stepping stones for the experimental exploration of new quantum many-body phenomena and applications thereof, such as quantum simulation and quantum information, through the design of systems at the microscopic scale and the measurement of previously inaccessible observables.

This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics-one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.

This book presents an up-to-date formalism of non-equilibrium Green's functions covering different applications ranging from solid state physics, plasma physics, cold atoms in optical lattices up to relativistic transport and heavy ion collisions. Within the Green's function formalism, the basic sets of equations for these diverse systems are similar, and approximations developed in one field can be adapted to another field. The central object is the self-energy which includes all non-trivial aspects of the system dynamics. The focus is therefore on microscopic processes starting from elementary principles for classical gases and the complementary picture of a single quantum particle in a random potential. This provides an intuitive picture of the interaction of a particle with the medium formed by other particles, on which the Green's function is built on.

Quantum field theory, which started with Paul Diraca (TM)s work shortly after the discovery of quantum mechanics, has produced an impressive and important array of results. Quantum electrodynamics, with its extremely accurate and well-tested predictions, and the standard model of electroweak and chromodynamic (nuclear) forces are examples of successful theories. Field theory has also been applied to a variety of phenomena in condensed matter physics, including superconductivity, superfluidity and the quantum Hall effect. The concept of the renormalization group has given us a new perspective on field theory in general and on critical phenomena in particular. At this stage, a strong case can be made that quantum field theory is the mathematical and intellectual framework for describing and understanding all physical phenomena, except possibly for a quantum theory of gravity.

Quantum Field Theory: A Modern Perspective presents Professor Naira (TM)s view of certain topics in field theory loosely knit together as it grew out of courses on field theory and particle physics taught at Columbia University and the City College of CUNY. The first few chapters, up to Chapter 12, contain material that generally goes into any course on quantum field theory, although there are a few nuances of presentation which readers may find to be different from other books. This first part of the book can be used for a general course on field theory, omitting, perhaps, the last three sections in Chapter 3, the last two in Chapter 8 and sections 6 and 7 in Chapter 10. The remaining chapters cover some of the more modern developments over the last three decades, involving topological and geometricalfeatures. The introduction given to the mathematical basis of this part of the discussion is necessarily brief and should be accompanied by books on the relevant mathematical topics as indicated in the bibliography. Professor Nair also concentrates on developments pertinent to a better understanding of the standard model. There is no discussion of supersymmetry, supergravity, developments in field theory inspired by string theory, etc. There is also no detailed discussion of the renormalization group. Each of these topics would require a book in its own right to do justice to the topic. Quantum Field Theory: A Modern Perspective serves as a portal to so many more topics of detailed and ongoing research, referring readers to more detailed treatments for many specific topics. The book also contains extensive references, providing readers a more comprehensive perspective on the literature and the historical development of the subject.

V. Parameswaran Nair is Professor of Physics at City College of The City University of New York (CUNY). Professor Nair has held Visiting Professorships at The Abdus Salam International Center for Theoretical Physics, Rockefeller University, Institute for Advanced Study at Princeton, and Massachusetts Institute of Technology.

This thesis reports on major steps towards the realization of scalable quantum networks. It addresses the experimental implementation of a deterministic interaction mechanism between flying optical photons and a single trapped atom. In particular, it demonstrates the nondestructive detection of an optical photon. To this end, single rubidium atoms are trapped in a three-dimensional optical lattice at the center of an optical cavity in the strong coupling regime. Full control over the atomic state - its position, its motion, and its electronic state - is achieved with laser beams applied along the resonator and from the side. When faint laser pulses are reflected from the resonator, the combined atom-photon state acquires a state-dependent phase shift. In a first series of experiments, this is employed to nondestructively detect optical photons by measuring the atomic state after the reflection process. Then, quantum bits are encoded in the polarization of the laser pulse and in the Zeeman state of the atom. The state-dependent phase shift mediates a deterministic universal quantum gate between the atom and one or two successively reflected photons, which is used to generate entangled atom-photon, atom-photon-photon, and photon-photon states out of separable input states.