This book aims to deliver a concise, practical and intuitive introduction to probability and statistics for undergraduate and graduate students of physics and other natural sciences. The author attempts to provide a textbook in which mathematical complexity is reduced to a minimum, yet without sacrificing precision and clarity. To increase the appeal of the book for students, classic dice-throwing and coin-tossing examples are replaced or accompanied by real physics problems, all of which come with full solutions.
In the first part (chapters 1–6), the basics of probability and distributions are discussed. A second block of chapters is dedicated to statistics, specifically the determination of distribution parameters based on samples. More advanced topics follow, including Markov processes, the Monte Carlo method, stochastic population modelling, entropy and information.
The author also chooses to cover some subjects that, according to him, are disappearing from modern statistics courses. These include extreme-value distributions, the maximum-likelihood method and linear regressions using singular-value decomposition. A set of appendices concludes the volume.
An introduction to the novel and developing field of quantum information, this book aims to provide undergraduate and beginning graduate students with all of the basic concepts needed to understand more advanced books and current research publications in the field. No background in quantum physics is required because its essential principles are provided in the first part of the book.
After an introduction to the methods and notation of quantum mechanics, the authors explain a typical two-state system and how it is used to describe quantum information. The broader theoretical framework is also set out, starting with the rules of quantum mechanics and the language of algebra.
The book proceeds by showing how quantum properties are exploited to develop algorithms that prove more efficient in solving specific problems than their classical counterparts. Quantum computation, information content in qubits, cryptographic applications of quantum-information processing and quantum-error correction are some of the key topics covered in this book.
In addition to the many examples developed in the text, exercises are provided at the end of each chapter. References to more advanced material are also included.
This book collates information from various literature to provide students with a unified guide to contemporary developments in atomic physics. In just 400 pages it largely succeeds in achieving this aim.
The author is a professor of physics at the Indian Institute of Science in Bangalore. His research focuses on laser cooling and trapping of atoms, quantum optics, optical tweezers, quantum computation in ion traps, and tests of time-reversal symmetry using laser-cooled atoms. He received a PhD from the Massachusetts Institute of Technology under the supervision of David Pritchard, a leader in modern atomic physics and a mentor of two researchers – Eric Cornell and Wolfgang Ketterle – who went on to become Nobel laureates.
The book addresses the basis of atomic physics and state-of-the-art topics. It explains material clearly, although the arrangement of information is quite different to classical atomic-physics textbooks. This is clearly motivated by the importance of certain topics in modern quantum-optics theory and experiments. The physics content is often accompanied by the history behind concepts and by explanations of why things are named the way they are. Historical notes and personal anecdotes give the book a very appealing flair.
Chapter one covers different measurement systems and their merits, followed by universal units and fundamental constants, with a detailed explanation of which constants are truly fundamental. The next chapter is devoted to preliminary materials, starting with the harmonic oscillator and moving to concepts – namely coherent and squeezed states – that are important in quantum optics but not explicitly covered in some other books in the field. The chapter ends with a section on radiation, even including a description of the Casimir effect.
Chapter three is called Atoms. Alongside classical content such as energy levels of one-electron atoms, interactions with magnetic and electric fields, and atoms in oscillating fields, this chapter explains dressed atoms and also, unfortunately only briefly, includes a description of the permanent atomic electric dipole moment (EDM).
The following chapter is devoted to nuclear effects, the isotope shift and hyperfine structure. At this point it would have been nice to see some mention of the flourishing field of laser spectroscopy of radioactive nuclei, which exploits the two above effects to investigate the ground-state properties of nuclei far from the valley of stability.
Chapter five is about resonance, which is often scattered around in other books about atomic physics. Here, interestingly, nuclear magnetic resonance (NMR) plays a central role, and the chapter connects this topic very naturally to atomic physics. The chapter closes with a description of the density matrix formalism. After this comes a chapter devoted to interactions, including the electric dipole approximation, selection rules, transition rates and spontaneous emission. The last section is concerned with differences in saturation intensities by broadband and monochromatic radiation.
Multiphoton interactions are the topic of chapter seven, which is clearly motivated by their importance in modern quantum-optics laboratories. Two-photon absorption and de-excitation, Raman processes and the dressed atom description are all explained. Another crucial concept in modern quantum optics is coherence. Thus it is included as a full chapter, which includes coherence in a single atom and in ensembles of atoms, as well as coherent control in multilevel atoms. Spin echo appears as well, showing again how close the topics presented in the book are to NMR.
Chapter nine is devoted to lineshapes, which is clearly a subject relevant for modern atomic spectroscopists. Spectroscopy is the next chapter, which starts with alkali atoms – used extensively in laser cooling and Bose–Einstein condensates. The rest of the material is aimed at experimentalists. Uniquely for such a book, it includes a description of the key experimental tools, followed by Doppler-free techniques and nonlinear magneto-optic rotation.
The last chapter covers cooling and trapping, with so many relevant concepts already presented in the preceding chapters. The content includes different cooling approaches, principles of atom and ion traps, the cryptic and equally common Zeeman slower, and even more intriguing optical tweezers.
Each chapter ends with a problems section, in which the problems are often relevant to a real quantum-optics lab, for example concerning quantum defects, RF-induced magnetic transitions, Raman scattering cross-sections, quantum beats or the Voigt line profile. The problems are worked out in detail, allowing readers to follow how to arrive at the solution.
The appendices cover the standards and the frequency comb, which is one of the ingenious devices to come from the laboratory of Nobel laureate Theodor Hänsch and which can be now found in an ever-growing number of laser-spectroscopy and quantum-optics labs. Two other appendices are very different: they have a philosophical flair and deal with the nature of the photon and with Einstein as nature’s detective.
The presented theoretical basis leads to state-of-the art experiments, especially related to ion and atom cooling and to Bose–Einstein condensates. The selection of topics is thus clearly tailored for experimentalists working in a quantum optics lab. One small criticism is that it would be good to read more about the EDM experiments and laser spectroscopy of radioactive ions, which are currently two very active fields. Readers interested in different classic subjects, like atomic collisions, should turn to other books such as Bransden and Joachain’s Physics of Atoms and Molecules.
The level of the book makes it suitable for undergraduate level, but also for new graduate students. It can also serve as a quick reference for researchers, especially concerning the topics of general interest: metrology, what is a photon or how a frequency comb works, and how to achieve a Bose–Einstein condensate. Overall, the book is a very good guide to the topics relevant in modern atomic physics and its style makes it quite unique and personal.
Following their previous book on many-body theory, the authors have written a new volume focused on exactly solvable models, to add to the literature in this field. Several theoretical models are presented for selected systems in condensed states of matter – including solid, liquid and disordered states – and for systems of few or many bodies.
The book starts with an introduction to low-order density matrices, then discusses exactly or nearly exactly solvable models for several few-particle systems. The material is arranged according to the statistics of these particle assemblies, going from small clusters of fermions to small clusters of bosons – with specific reference to Efimov trimers in nuclear and condensed-matter assemblies – to anyon statistics.
The second group of chapters is dedicated to models for selected many-body systems in condensed matter, where particular attention is given to superconductivity and superfluidity, and to isolated impurities in a solid. Pair-potential and many-body force models for liquids are also discussed, as well as disorder and its implications for transport in solids.
The authors then deal with more general topics, in particular statistical field theory (discussing some specific models and critical exponents) and relativistic field theory. Open problems in quantum gravity are also briefly reviewed in the concluding chapter, and several appendices are included at the end of the book.
As the author himself states, the primary aim of this book is to explain why so many scientists choose to work on a theory that has no direct experimental support and is unlikely to have so anytime soon.
String theory, the origins of which date back to 1968, has developed into a major component of theoretical particle physics. It is most famous as a theory of quantum gravity and as a candidate unified theory of fundamental interactions at the smallest scales – so small that, unfortunately, we cannot directly test it with experiments.
Although string theory is built on a very solid mathematical basis and allows rigorous calculations, the author uses almost no equations. Rather than a textbook, this is a book on the history, science and philosophy lying behind a fascinating and speculative theory.
In the first part, the theory of quantum-mechanical relativistic strings is placed within the broader context of theoretical particle physics, and ultimately science in general. It is then discussed why there is still a need for ideas and paradigms that go beyond what we already know, and why string theory is a candidate for being a global theory that includes all others. Following this, the author describes the motivation driving this field and how this has evolved during the past 50 years. In particular, he dedicates various chapters to the connections of string theory with quantum field theory, mathematics, cosmology, particle physics and quantum gravity.
The last part of the book discusses the social aspects of science: the diverse ways of approaching the topic as well as various personal driving forces. A chapter is also dedicated to the most significant criticisms of string theory, to which the author provides a reply.
The book is intended to appeal to laypersons interested in fundamental physics as well as to physics students, so the author chooses to avoid mathematical formulations of the theory. However, the risk is that the book is then not sufficiently clear and explanatory to be an easy read for non-experts, nor technical and detailed enough to appeal to students.
This concise book provides a rigorous introduction to the theory of nonlinear mechanics and chaos, suitable for students across physics, mathematics and engineering.
Nonlinear dynamics treats problems that cannot be “solved”, in the sense that it is not possible to derive equations of motion that describe the positions of the various parts of a system as functions of time using standard analytic functions. If, on one side, the formulations of mechanics of Lagrange and Hamilton lead to systems that cannot be solved in the usual sense of the word, perturbation theory, in turn, fails in providing approximate solutions because of the problem of small dividers. This is the path that led originally to the discovery of chaos, and it is the one that the author pursues in the book.
The first part is dedicated to the basic concepts of the Lagrangian and Hamiltonian formulation of mechanics, and to canonical transformations. The author then deals with more advanced topics, including Liouville’s theorem and perturbation theory. In the third part of the book, the modern theory of chaos is introduced. The author describes chaotic motion using the tools of discrete maps and Poincaré sections, along with the Poincaré–Birkhoff and Kolmogorov–Arnold–Moser (KAM) theorems and their applications.
Each chapter is accompanied by a set of problems, with the last section providing more advanced projects that require some expertise in computing. As a conclusion, an appendix discusses the relevance of the KAM theorem to the ergodic hypothesis and the second law of thermodynamics.
The aim of this book is to bridge the gap between introductory quantum mechanics and the most recent advances in modern optics.
The author opts for an unconventional approach. Rather than providing an exhaustive treatment, he introduces a single analytic tool – the density matrix – to analyse complex optical phenomena and applies it to a wide range of problems. Among the many mathematical tools available to treat nonlinear and quantum optics, he chooses the density matrix because it is extremely versatile and applicable virtually to any problem. In particular, it is well suited for dealing with coherence in isolated or interactive systems, and allows researchers to ignore parts of a problem that appear irrelevant.
After covering the basics, the book quickly passes to more sophisticated topics. It starts with the simplest systems (stationary two-level atoms) and then introduces atomic motion and additional energy levels, and continues with a discussion of coherence effects effects (of first-, second- and third-order).
Finally, a section is dedicated to selected examples from recent research topics in which the use of the density matrix is profitable, including laser tweezers, laser cooling, coherent population trapping and transfer, optical magnetism, electromagnetically induced transparency, squeezed light and quantum information processing.
The text is based on two decades of lectures and is oriented to graduate students not only of traditional disciplines such as physics, chemistry, electrical engineering and materials science, but also of interdisciplinary courses such as biophysics, biomedicine and photochemistry.
In this second revised edition, new sections on quantum interference, Fano resonances, optical magnetism, quantum computation, laser cooling of solids, and irreducible representation of magnetic interactions have been included, along with more than 40 new problems.
This book addresses five selected physics topics in modern cancer radiation therapy. Examining them in more detail than can be found in standard medical-physics textbooks, the author has also formulated and solved a large number of exercises that are provided at the end of each chapter, together with a detailed bibliography.
Despite its title, the book is not a substitute for comprehensive textbooks in medical-radiation physics, rather it complements them. It is therefore of interest to experienced medical physicists who would like to better understand the physics of their daily work, as well as to young researchers approaching this discipline for the first time, often following a PhD in particle physics.
The first section deals with the main tool of modern cancer radiation therapy: the electron linear accelerator (linac). Starting from the basics of electrodynamics, travelling- and standing-wave linear accelerators are discussed together with resonating cavities. Particular care is given to mathematical formulations and to the definition of symbols. This chapter could also appeal to accelerator physicists willing to know more about electron acceleration at energies of a few MeV.
Proton therapy, which is generally considered an advanced topic in medical radiation therapy, is approached in a somewhat easier way. Starting from an historical introduction, emphasis is given to accelerators and to dose-distribution systems, with a glimpse of future developments. It is a pity that carbon-ion therapy is not mentioned and that active dose-distribution systems are not discussed in more detail.
The two topics that follow address the daily work of the medical physicist. Dose-computation algorithms are treated following a careful mathematical formulation complemented by examples and references to practical cases. Deterministic radiation transport is introduced, starting from the basic quantities used in medical radiation physics. The transport and Fermi–Eyges equations are then derived and discussed.
The last theme, tumour control and normal tissue complications, is the most relevant for the patient. Is the therapy effective? What is the quality of life after treatment? The answers to these questions may be searched for using the bridge that connects physics to medicine. To accomplish this task, models are necessary. Starting from the concepts of probability and of dose-volume histograms, empirical and mechanistic models are presented together with the serial and parallel architecture of the organs in the human body.
The application of radiation physics to medicine is an expanding multidisciplinary field based on knowledge, tools and techniques derived from nuclear and particle physics. This book will therefore appeal not only to curious medical physicists and scientists active in the field, but also to physicists in general who – as the author comments – “like understanding”.
This book’s aim, as stated in the introduction, is to provide a practical introduction to particle physics in the LHC era at the level of an advanced undergraduate or introductory graduate course. Indeed, in its almost 400 pages, it covers a wide range of topics, from instrumentation and detector technologies to some mathematical techniques and the traditional particle-physics topics that are usually included in similar textbooks. It hovers, by design, at the border between the established textbooks aimed at undergraduates and the more advanced graduate texts that often start with quantum field theory.
Following the introduction, the book commences with a three-chapter sequence with somewhat technical content. Chapter 2, dedicated to mathematical methods, covers discrete symmetries, angular momentum and rotations in space, Lorentz invariance and the calculation of phase-space factors, decay widths and cross-sections, and concludes with a brief review of group theory. Chapter 3, on accelerators, includes a concise yet clear description of the basic concepts and terminology often encountered by students starting to work on experiments but not readily available. The topics include synchronicity, beam optics, Q values and beam tunes, luminosity, and even some characteristics of past accelerators. Chapter 4 is on particle detectors. Beyond the standard topics expected in such an overview, e.g. the interaction of particles and radiation with matter, the chapter includes topics that are usually neglected, including short presentations on signal generation, triggering of experiments and the selection of a magnetic field. As would be expected, calorimetry is well covered, as are tracking detectors, to which an extensive description, including an introduction to solid-state detectors, is included. The topics and detector examples provided are too centred on the LHC and its experiments, though.
Chapter 5, on the static quark model, is the first “particle-physics-proper” section. It’s a clear and self-contained introduction to mesons and baryons, with a modern perspective. The authors have decided to include heavy quarks (with the exception of the top quark) and their mesons and baryons, and the result is a full overview for the reader. Finally, chapter 6 on relativistic quantum mechanics concludes what could be called the first part of the book on “concepts, tools and methods”. There is a modern angle in this chapter: as an example, Weyl spinors are introduced and used, along with the associated Lorentz transforms and spin matrices. This material is better absorbed by graduate students. The rest of the chapter covers the traditional Klein–Gordon and Dirac equations, and introduces the electromagnetic interaction. It concludes with a short introduction to gauge symmetry.
Chapters 7–10 constitute a second part that concentrates on particle physics. Chapter 7, on weak interactions, covers all of the material from the four-point Fermi interaction to the Standard Model (SM), although without symmetry breaking. The descriptions of V–A, parity violation and the weak interactions of quarks, the CKM matrix and hadron decays via the weak interaction are clear, as is the extended introduction of SU(2) × U(1) symmetry as the basis of the SM. Chapter 8, on experimental tests of electroweak theory, is one of the more modern presentations of the topics covered: it starts with neutrino interactions and charged and neutral currents, and moves to Z physics and then WW production at LEP. It includes some experimental aspects such as the use of resonant depolarisation for the precise determination of the LEP beam energy. Moving away from convention, the discovery of the W and Z bosons at the CERN SPS is left for after the LEP presentation. The chapter concludes with a brief presentation of the discovery of the top quark and some later results from the Tevatron.
Chapter 9, on dynamic quarks, breaks the flow slightly. It contains Rutherford scattering, the quark–parton model and neutrino interactions, and concludes its first part with electron–nucleon deep inelastic scattering. This is a departure from standard practice in most textbooks. The second part of the chapter is on the introduction of colour, QCD, parton distribution functions and hadron–hadron collisions, and the Drell–Yan process. The material, which is extensive but presented quite briefly, is more appropriate for undergraduates.
Chapters 10 (oscillations and CP violation in meson systems) and 11 (neutrino oscillations) are great introductions to physics mixing, both in the quark and the lepton sector. The discussion in chapter 10 is modern, with results from experiments at LEP, the B factories and hadron colliders. Chapter 11 has one of the best summaries on neutrino physics for this level: it starts with the first evidence of mixing in atmospheric neutrinos, and proceeds to laboratory experiments, and then the MSW effect, solar-neutrino oscillations and then three-flavour oscillations, concluding with the measurement of θ13. This chapter is a novel and useful addition to the textbook.
Chapter 12 is on the Higgs boson. It starts with a short introduction to spontaneous symmetry breaking and proceeds to a description of the discovery of the Higgs boson by the ATLAS and CMS experiments. The material, with the exception of a section on the statistical significance, which is too short and ill-placed to be useful, is at the right level for the advanced-undergraduate-to-graduate student audience.
The book concludes with chapter 13 on the LHC and BSM (physics Beyond the Standard Model). It has an interesting selection of topics, including expected ones like supersymmetry and some unexpected ones (for a textbook) like the search for new contact interactions and new resonances. The approach is quite experimental in that only the motivation for new phenomena is presented, and the theory is skipped. It is nevertheless a useful introduction to the subject, adequate for motivating students to explore further.
Overall, the book achieves its goal of bridging the gap between undergraduate and graduate textbooks. The descriptions of the various topics are mostly clear, although at times too short. In a formal course, the tutor would probably choose to cover the material in a slightly different mix to the order it is presented here, combining material from the first part (chapters 2–6) and the second part (mainly chapters 7–10). In summary, this is a welcome, useful and modern addition to the current list of textbooks in particle physics.
In this book the author offers an overview of Raman spectroscopy techniques – including Raman optical activity (ROA) and surface-enhanced Raman scattering spectroscopy (SERS) – covering their applications and their theoretical foundations.
The Raman effect is an inelastic two-photon process in which the incident (scattering) photon is absorbed by an atom or molecule (the scatterer) that immediately emits a photon of different energy and frequency than the incident one. This energy difference, which arises because the incident photon vibrationally excites the molecule, is called the Raman shift. Raman shifts provide information on the molecular motion and thus its structure and bond strength. As a consequence, this effect is used for material analysis in Raman spectroscopy.
More important than the energy difference are the Raman intensity of the scattered light, which offers insights into the dynamics of the photon-perturbed molecule, and the electronic polarisability of the molecule, which is a measure of how easily the electrons can be affected by the light.
After introducing the Raman effect and the normal mode analysis, the author discusses the bond polarisabilities, the intensity analysis and the Raman virtual states. A group of chapters then cover the extension of the bond polarisability algorithm to the ROA intensity analysis and many findings on ROA mechanism resulting from the work of the author and his collaborators. The last chapter introduces a unified classical theory for ROA and vibrational circular dichroism (another spectroscopic technique).
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