Cold atomic gases trapped and manipulated on atom chips allow the realization of seminal one-dimensional (1d) quantum many-body problems in an isolated and well controlled environment. In this context, this thesis presents an extensive experimental study of non-equilibrium dynamics in 1d Bose gases, with a focus on processes that go beyond simple dephasing dynamics. It reports on the observation of recurrences of coherence in the post-quench dynamics of a pair of 1d Bose gases and presents a detailed study of their decay. The latter represents the first observation of phonon-phonon scattering in these systems. Furthermore, the thesis investigates a novel cooling mechanism occurring in Bose gases subjected to a uniform loss of particles. Together, the results presented show a wide range of non-equilibrium phenomena occurring in 1d Bose gases and establish them as an ideal testbed for many-body physics beyond equilibrium.

This thesis presents a theoretical investigation into the creation and exploitation of quantum correlations and entanglement among ultracold atoms. Specifically, it focuses on these non-classical effects in two contexts: (i) tests of local realism with massive particles, e.g., violations of a Bell inequality and the EPR paradox, and (ii) realization of quantum technology by exploitation of entanglement, for example quantum-enhanced metrology. In particular, the work presented in this thesis emphasizes the possibility of demonstrating and characterizing entanglement in realistic experiments, beyond the simple "toy-models" often discussed in the literature. The importance and relevance of this thesis are reflected in a spate of recent publications regarding experimental demonstrations of the atomic Hong-Ou-Mandel effect, observation of EPR entanglement with massive particles and a demonstration of an atomic SU(1,1) interferometer. With a separate chapter on each of these systems, this thesis is at the forefront of current research in ultracold atomic physics.

Coherence, entanglement, and interference arise from quantum superposition, the most distinctive and puzzling feature of quantum physics. Silverman, whose extensive experimental and theoretical work has helped elucidate these processes, presents a clear and engaging discussion of the role of quantum superposition in diverse quantum phenomena such as the wavelike nature of particle propagation, indistinguishability of identical particles, nonlocal interactions of correlated particles, topological effects of magnetic fields, and chiral asymmetry in nature. He also examines how macroscopic quantum coherence may be able to extricate physics from its most challenging quandary, the collapse of a massive degenerate star to a singularity in space in which the laws of physics break down.

Explained by a physicist with a concern for clarity and experimental achievability, the extraordinary nature of quantum superposition will fascinate the reader not only for its apparent strangeness, but also for its comprehensibility.

This thesis investigates ultracold molecules as a resource for novel quantum many-body physics, in particular by utilizing their rich internal structure and strong, long-range dipole-dipole interactions. In addition, numerical methods based on matrix product states are analyzed in detail, and general algorithms for investigating the static and dynamic properties of essentially arbitrary one-dimensional quantum many-body systems are put forth. Finally, this thesis covers open-source implementations of matrix product state algorithms, as well as educational material designed to aid in the use of understanding such methods.

This book gives a theoretical description of linear and nonlinear optical responses of matter with special emphasis on the microscopic and "nonlocal" nature of resonant response. The response field and induced polarization are determined self-consistently in terms of simultaneous linear or nonlinear polynomial equations. This scheme is a general one situated between QED and macroscopic response theory, but is most appropriate for determining the dependence of optical signals on the size, shape, and internal structure of a nanostructure sample. As a highlight of the scheme, the multi-resonant enhancement of the DFWM signal is described together with its experimental verification.

This text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques. The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory.

But all the clocks in the city Began to whirr and chime: 'O let not Time deceive you, You cannot conquer Time. W. H. Auden It is hard to think of a subject as rich, complex, and important as time. From the practical point of view it governs and organizes our lives (most of us are after all attached to a wrist watch) or it helps us to wonderfully ?nd our way in unknown territory with the global positioning system (GPS). More generally it constitutes the heartbeat of modern technology. Time is the most precisely measured quantity, so the second de?nes the meter or the volt and yet, nobody knows for sure what it is, puzzling philosophers, artists, priests, and scientists for centuries as one of the enduring enigmas of all cultures. Indeed time is full of contrasts: taken for granted in daily life, it requires sophisticated experimental and theoretical treatments to be accurately "produced. " We are trapped in its web, and it actually kills us all, but it also constitutes the stuff we need to progress and realize our objectives. There is nothing more boring and monotonous than the tick-tock of a clock, but how many fascinating challenges have physicists met to realize that monotony: Quite a number of Nobel Prize winners have been directly motivated by them or have contributed 1 signi?cantly to time measurement.

The work presented in this thesis spans a wide range of experimental particle physics subjects, starting from level-1 trigger electronics to the final results of the search for Higgs boson decay and to tau lepton pairs. The thesis describes an innovative reconstruction algorithm for tau decays and details how it was instrumental in providing a measurement of Z decay to tau lepton pairs. The reliability of the analysis is fully established by this measurement before the Higgs boson decay to tau lepton pairs is considered. The work described here continues to serve as a model for analysing CMS Higgs to tau leptons measurements.

This monograph provides a mathematical foundation to the theory of quantum information and computation, with applications to various open systems including nano and bio systems. It includes introductory material on algorithm, functional analysis, probability theory, information theory, quantum mechanics and quantum field theory. Apart from standard material on quantum information like quantum algorithm and teleportation, the authors discuss findings on the theory of entropy in C*-dynamical systems, space-time dependence of quantum entangled states, entangling operators, adaptive dynamics, relativistic quantum information, and a new paradigm for quantum computation beyond the usual quantum Turing machine. Also, some important applications of information theory to genetics and life sciences, as well as recent experimental and theoretical discoveries in quantum photosynthesis are described.

This thesis describes the thorough analysis of the rare B meson decay into K* on data taken by the Belle Collaboration at the B-meson-factory KEKB over 10 years. This reaction is very interesting, because it in principle allows the observation of CP-violation effects. In the Standard Model however, no CP violation in this reaction is expected. An observation of CP asymmetries thus immediately implies new physics. This thesis presents an amplitude analysis of this decay and the search for CP violation in detail and discusses methods to solve related problems: The quantification of multivariate dependence and the improvement of numeric evaluation speed of normalization integrals in amplitude analysis. In addition it provides an overview of the theory, experimental setup, (blind) statistical data analysis and estimation of systematic uncertainties.

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.

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.