bluuebunny/crossref_metadata_2025 huggingface dataset:
The Quantum Theory of Light
Authors: Loudon Rodney
Published: November 2023

This third edition, like its two predecessors, provides a detailed account of the basic theory needed to understand the properties of light and its interactions with atoms, in particular the many nonclassical effects that have now been observed in quantum-optical experiments. The earlier chapters describe the quantum mechanics of various optical processes, leading from the classical representation of the electromagnetic field to the quantum theory of light. The later chapters develop the theoretical descriptions of some of the key experiments in quantum optics. Over half of the material in this third edition is new. It includes topics that have come into prominence over the last two decades, such as the beamsplitter theory, squeezed light, two-photon interference, balanced homodyne detection, travelling-wave attenuation and amplification, quantum jumps, and the ranges of nonliner optical processes important in the generation of nonclassical light. The book is written as a textbook, with the treatment as a whole appropriate for graduate or postgraduate students, while earlier chapters are also suitable for final- year undergraduates. Over 100 problems help to intensify the understanding of the material presented.
Planck’s radiation law and the Einstein coefficients
Authors: Loudon Rodney
Published: November 2023

Another main stream in the initial formulation of the quantum theory was concerned with the interpretation of atomic spectral lines. The interaction of electromagnetic radiation with atoms was discussed by Einstein f4] in 1917. His theory of the absorption and emission of light by an atom depends upon simple phenomenological considerations but it leads to predictions that are reproduced by the more formal quantum mechanics developed later. The use of quantum theory is, of course, essential for even a gross description of the nature of the states of an atom and the theory is outstandingly successful in its ability to predict the finest details of atomic energy-level structures.
Optical generation, attenuation and amplification
Authors: Loudon Rodney
Published: November 2023

A typical optical experiment consists of three main components. The light is provided by a source, which may be a thermal source that emits chaotic light, but is most often a laser that emits coherent light in quantum-optical experiments. The light is processed in some interaction region of the experiment, where it may, for example, be subjected to attenuation, amplification, beam splitting, or one of the various nonlinear optical processes. The processed light beam is finally detected, for example by the direct or homodyne schemes covered in Chapter 6.
Linear transformations
Authors: Kaye Richard , Wilson Robert
Published: November 2023

In this part of the book, we will study linear transformations in the same spirit as we studied inner products and quadratic forms. In this chapter we will see how a linear transformation can be represented by a matrix, with respect to a particular basis, and in later chapters we will discuss how to find the ‘best’ basis, so that the corresponding matrix is as simple as possible, with applications to the solution of many kinds of differential and difference equations, and to quadratic forms. Our vector spaces will be over a field F. For this chapter, F can be any field whatsoever. If it helps, it is possible to think of F as either ℝ. or ℂ without much being lost. In later chapters, we will need some further properties of the field, taking the form that certain polynomials have roots; these properties are always true of the field ℂ, so it is safe to think of F as ℂ throughout the rest of the book.
The minimum polynomial
Authors: Kaye Richard , Wilson Robert
Published: November 2023

The central result of this chapter is the remarkable and important fact that for any n × n matrix A there is a polynomial p(x) of degree at most n such that p(A) is the zero matrix. This can be proved either from results in the previous chapter on upper triangular matrices, or more directly. Because of this, it turns out that we can define a special minimum polynomial m  A(x) (i.e. of least degree) such that m  A(A) = 0. The properties of this minimum polynomial will be central to all the material in the remainder of this book.
Diagonalization
Authors: Kaye Richard , Wilson Robert
Published: November 2023

Our basic aim is to find as nice a matrix as possible representing a given linear transformation. That is, given a vector space V and a linear transformation f: V → V, we want to find a basis for V with respect to which the matrix off is ‘nice’. In this chapter, ‘nice’ will mean diagonal, if possible. The process of diagonalization is where one tries to transform a matrix A to a matrix P−1 AP which is diagonal, or to find a basis with respect to which the matrix representation of a given linear transformation f is diagonal. We have already seen in examples that this process is often useful or necessary for solving certain kinds of simultaneous equations, such as the example in Section 10.1.
The Self-Made Tapestry
Authors: Ball Philip
Published: November 2023

Why do similar patterns and forms appear in nature in settings that seem to bear no relation to one another? The windblown ripples of desert sand follow a sinuous course that resembles the stripes of a zebra or a marine fish. In the trellis-like shells of microscopic sea creatures we see the same angles and intersections as for bubble walls in a foam. The forks of lightning mirror the branches of a river or a tree. This book explains why these are no coincidences. Nature commonly weaves its tapestry by self-organization, employing no master plan or blueprint but by simple, local interactions between its component parts - be they grains of sand, diffusing molecules or living cells. And the products of self- organization are typically universal patterns: spirals, spots, and stripes, branches, honeycombs. This book explains, in non-technical language, and with profuse illustrations, how nature's patterns are made.
Bubbles
Authors: Ball Philip
Published: November 2023

I am quite sure that a fascination with patterns in nature is as old as civilization. When the Egyptians began to keep bees in clay pipes 5000 years ago, they cannot have failed to notice the astonishing hexagonal pattern of the honeybee’s dwelling {Fig. 2.1). Charles Darwin declared it ‘absolutely perfect in economising labour and marvelled at the bees’ instincts for producing such a masterpiece of engineering. If you want to fill up a plane space with identical, equal-sided and equalangled cells, there are only three choices: triangles, squares or hexagons. Only these regular polygons can be packed together to fill space without leaving gaps. Pentagons, for example, will not work, and neither will octagons (Fig. 2.2). Bees making a pentagonal honeycomb would be constantly leaving gaps, and it is not hard to see why these aberrant bees would not be very successful in the Darwinian struggle for survival. The same is true for circular cells.
Waves
Authors: Ball Philip
Published: November 2023

Amongst the sprawling modern myth of Thomas Pynchon's Gravity's Rainbow is a fleeting reference to a man who tried to make patterned paint. The reference is clearly meant to document a quixotic, absurd ambition, for we all know that paint does not unmix into the separate pigments that went into its making. But life is always stranger than we think. Take a look at Plate 4. Pynchon's ill-fated entrepreneur would have done well to follow the recipe that produced these blue and yellow stripes; for this is indeed a stable pattern that emerges spontaneously from a mixture of chemical compounds. This brew of chemicals is just one of many that have been found to generate spatial patterns. Some of these, like that in Plate 4, are stationary; others are dynamic, releasing waves of colour to a pulse as regular as a clock's tick.
Branches
Authors: Ball Philip
Published: November 2023

In Mike Leigh’s film Nuts in May, a pair of gauche campers named Keith and Candice Marie discover how a kind of modern-day vitalism colours our preconceptions about complex growth and form. They take a trip to a local quarry to search for fossils in the ancient Purbeck limestone of Dorset. At the prompting of a quarryman, the unsuspecting couple find a delicate, plant-like pattern traced out in the stone. Took at that—seaweed!’ exclaims Keith. ‘Yar, well, ‘tis not seaweed, see’, drawls the quarryman, adding that it is manganese oxide—a mineral—they are looking at. Keith is not convinced. It's looks like a living organism to me.’ ‘Yar,’ the quarryman rejoins, ‘most people think that.’ You can see why Keith and Candice Marie jumped to the wrong conclusion. The structures they saw are called mineral dendrites, and they look for all the world like the kind of forms we associate with ferny plants.
Breakdowns
Authors: Ball Philip
Published: November 2023

When things break down, they tend to do so spectacularly. I don’t just mean that bridges fall down, that ships sink, that cities are levelled by earthquakes. I mean that we may be left with stunningly rich patterns, sometimes on an awesome scale (Fig. 6.2). Cracks are amongst the most familiar of branching patterns. They are also amongst the least well understood. It is only very recently, in fact, that scientists have begun to understand why it is that cracks form at all. For a long time, the science of fracture and failure of materials limped along with just a handful of basic concepts, most of which failed to provide any predictive power for what was seen in the real world. This was much more than an academic embarrassment: society wanted strong, tough materials, but scientists still had no clear concept of what it was that made a material tough. They would earnestly apply what seemed to be sensible criteria, only to end up with substances ‘about as strong as stale hard cheese’. On the other hand, their experience with materials that were genuinely strong sometimes flew so much in the face of what seemed like common sense that they had some persuading to do. The materials scientist James Gordon, to whom I owe the acerbic quote above, recalls the response of a British Air Marshall in 1943 to the idea that Lancaster bombers were to have glass-fibre domes: ‘Glass!-Glass! I won’t have you putting glass on any of my bloody aeroplanes, blast you!’.
Grains
Authors: Ball Philip
Published: November 2023

On the 17th of October 1989 the residents of the Marina district of San Francisco Bay discovered the wisdom of the advice that Jesus offered to house builders-beware of building on sand. A shudder of the San Andreas fault centred in the mountains to the north-east of Santa Cruz brought many of the houses in this district tumbling to the ground. Miraculously there was no loss of life, but hundreds of millions of dollars’ worth of damage was done by the magnitude-6.9 earthquake. Unlike most other buildings in the Bay area, those in the Marina district stood on sand-more precisely, on sand-rich landfill sites. The ground certainly felt solid enough, and under normal circumstances it was. But when the earth shook, these wet, sandy soils turned to a slurry that flowed like treacle.
The Standard Model in the Making
Authors: Bardin Dima , Passarino Giampiero
Published: November 2023

In recent years quantum field theory has been very successful, not only in the critical but also in the popular sence. However, this book is not a systematic presentation of quantum field theory from first principles. To some degree it is a celebration of the fact that the theory agrees with the data and currently the numerical agreement is unequivocal.

From this point of view this book is somewhat unusual in that we discuss the structure of the perturbative expansion by viewing the theory in its true relation with precision experiments. There is every reason to believe that the Standard Model describes elementary processes with g1eat accuracy. The sensitivity in radiative corrections allows precision tests at the level of the quantum structure and, therefore, they require the highest standards on . the theoretical side. This book may be understood as concluding a certain period of theoretical development and providing a consensus about the present situation in the calculation of precision observables and estimates of their theoretical errors. In summary, the book provides a basic documentation on the sizeable amount of theoretical work that has contributed to a steady improvement of the foundations and of the predictions of the SU(3) × SU(2) × U(l) theory that finally took shape also during recent decades.
Pure Qed Processes
Authors: Bardin Dima , Passarino Giampiero
Published: November 2023

One of the main goals of this book will be to present and discuss a multitude of realistic cross-sections based on the Standard Model (SM) for the electromagnetic, weak and strong interactions. To start a complete presentation of the perturbative expansion for gauge theories we will consider the simplest case of a gauge theory, quantum electrodynamics (QED), describing the interaction of spin-½ particles with photons.
One-Loop Neutral Current Amplitudes
Authors: Bardin Dima , Passarino Giampiero
Published: November 2023

In this_section we derive the complete one-loop expressions for the amplitude Z → ff in the GMS and OMS renormalization schemes. Using this amplitude we construct the partial widths of the Z boson, Tf, which—through some procedure— can be extracted from the experimental data. To make this statement more precise we will introduce the following definitions:
One-Loop Corrected Partial Widths Of The w Boson
Authors: Bardin Dima , Passarino Giampiero
Published: November 2023

In this chapter, we shall consider the one-loop corrections to the partial widths of the W boson. The total width is dominated by decays into fermion-antifermion pairs and in the lowest order the partial width into two fermions of masses mi and mj is given by
Mathematical Analysis During the 20th Century
Authors: Pier Jean-Paul
Published: November 2023

For several centuries, analysis has been one of the most prestigious and important subjects in mathematics. The present book sets off by tracing the evolution of mathematical analysis, and then endeavours to understand the developments of main trends, problems, and conjectures. It features chapters on general topology, 'classical' integration and measure theory, functional analysis, harmonic analysis and Lie groups, theory of functions and analytic geometry, differential and partial differential equations, topological and differential geometry. The ubiquitous presence of analysis also requires the consideration of related topics such as probability theory or algebraic geometry. Each chapter features a comprehensive first part on developments during the period 1900-1950, and then provides outlooks on representative achievements during the later part of the century. The book provides many original quotations from outstanding mathematicians as well as an extensive bibliography of the seminal publications. It will be an interesting and useful reference work for graduate students, lecturers, and all professional mathematicians and other scientists with an interest in the history of mathematics.
General Topology
Authors: Pier Jean-Paul
Published: November 2023

Limit processes are basic features of mathematical analysis; so the elaboration of convergence and continuity concepts is mandatory. By the end of the XIXth century, the study of functions represented by convergent trigonometric series led G. Cantor to prove his uniqueness theorem’. Given a function, the trigonometric series representing it is unique. He then showed the statement still holds if finite subsets, certain countable subsets, are removed and went on establishing further extensions (Ausdehnungeri).
Prehistoric Calendars
Authors: Richards E G
Published: November 2023

Our knowledge of calendars before the invention of writing is meagre and speculative; the very existence of such calendars can only be inferred from evi dence that is equivocal at best. It may be surmised that man had to take heed of the seasons and the effect of these on his food supply while he was still hunting and gathering, and the invention of agriculture can only have accen tuated this. When cities and civilizations arose, the need for keeping proper records of taxes and the logistics of building works demanded writing-and the invention of calendars. Sure enough, soon after the invention of writing, calendars begin to be mentioned.
HEV systems
Authors: Chan C C , Chau K T
Published: November 2023

When incorporating both of the ICE and electric motor, the vehicle is usually known as the hybrid EV (HEV). This HEV is actually not a new idea. A patent by Pieper in 1905 delineated that a battery-powered electric motor was used to boost the acceleration of an ICEV (Wouk, 1995; Bates, 1995). What exactly is a HEV? The definition available is so general that it anticipates future technologies of energy sources. As proposed by Technical Committee 69 (Electric Road Vehicles) of the International Electrotechnical Commission, a HEV is a vehicle in which propulsion energy is available from two or more kinds or types of energy stores, sources or converters, and at least one of them can deliver electrical energy. Based on this general definition, there are many types of HEVs, such as the petrol ICE & battery, diesel ICE & battery, battery & fuel cell, battery & capacitor, battery & flywheel, and battery & battery hybrids. However, the above definition is not well accepted. Ordinary people have already borne in mind that a HEV is simply a vehicle having both an ICE and electric motor.
Introduction
Authors: Silk Joseph
Published: November 2023

The infinite has to be a relative concept. Go any distance: an infinite space means that there is more to explore. The end is never reached. Could the universe be like that?

The notion that the universe could be infinite has excited extreme views. To some, the concept of an infinite universe is horrifying. The chances of creating intelligent life may be infinitesimal, but they are finite. It happened at least once! In an infinite universe replicas of us are inevitable. There would be identical copies of ourselves replicating every action, every word, somewhere. This seems hard to accept. But this is hardly a good scientific reason for abandoning an infinite universe. Indeed, modern astronomy tells us that the infinite universe may be more than just a metaphysical concept. Physics may even require the universe to be infinite. And if it were actually infinite, would we ever know? I shall argue that there are means of exploring both a very large but finite and conceivably even an infinite universe. If the universe is topologically small – that is, very large but finite in volume – there may be clues to be unlocked in such observables as the fossil radiation left over from the Big Bang. In contrast, exploration and verification of an infinite universe is not far from the voyages of science fiction, but arguably lies in the realm of physics.
Space Is Nearly Flat
Authors: Silk Joseph
Published: November 2023

Our understanding of cosmology appears to be converging towards the idea that the universe is infinite. The geometry of the universe is close to Euclidean. Space is three-dimensional. In Euclidean space, parallel lines always stay parallel and continue to infinity. This means that in a two-dimensional analogy, the universe is as flat as a sheet. But a sheet, mathematically, is infinite. As goes the plane, so goes the universe.

In fact, we can never prove that space is precisely Euclidean or flat. The best we can hope for is to demonstrate that space approximates flatness. The universe may be very, very large, but we could never prove that it is infinite. Rather than try to measure its size, we can measure its geometry. This is a local measurement and one might imagine that it could be easier to implement, at least in principle, than a global measurement of space curvature.
The Panacea of Cold Dark Matter
Authors: Silk Joseph
Published: November 2023

Most of the matter in the universe is dark. In contrast to dark energy, we can ‘see’ dark matter because it clumps as structure forms. Dark matter is detectable. And it amounts to about a third of the total massenergy density of the universe.

The cosmic mass budget is best expressed with respect to the critical density for a universe that is spatially flat, the Einstein–de Sitter model. This density only depends on Hubble’s constant, which is now known to reasonable precision. The critical density is 200 billion solar masses per cubic megaparsec. It is useful to compare this number with the density of starlight. We can express this in units of the luminosity of the sun, and it amounts to a hundred million solar luminosities per cubic megaparsec. If the universe were at the critical density, the ratio of mass to luminosity would be 1000 solar masses per solar luminosity. This gives a clear prediction for the closure of the universe.
The Seeds of Structure
Authors: Silk Joseph
Published: November 2023

The primeval universe was a fireball of radiation, with the odd particle occasionally interspersed. There was no structure, and no boundary, no preferred location or direction.

How did galaxies arise out of this cosmic fireball? The connection with the present-day universe can be understood by studying the structure of the universe on the largest scales. All the matter we see today was once within a sphere of radius 1 centimetre at a mere 10-43 of a second after the Big Bang. But how did it get so big? And why is it so uniform? Inflation, introduced in the previous chapter, provides the key.

Inflation, you will remember, is the name coined by cosmologists for a brief instant during the very early universe when the volume of space underwent an exponential increase. Inflation is the panacea for all, or almost all, of the puzzles that have plagued modern cosmology since the time of Georges Lemaître, the first physical cosmologist.
Drainage
Authors: Weaire Denis , Hutzler Stefan
Published: November 2023

Drainage presents itself most commonly as the process by which the equilibrium profile described in Chapter 10 is gradually established, starting from a freshly made foam. The flow of liquid out of the foam slows down as equilibrium is approached - can we understand its variation with time?
Introduction and overview
Authors: Jones R A L
Published: November 2023

Soft condensed matter (or soft matter, for brevity) is a convenient term for materials in states of matter that are neither simple liquids nor crystalline solids of the type studied in other branches of solid state physics. Many such materials are familiar from everyday life-glues, paints, and soaps, for example-while others are important in industrial processes, such as the polymer melts that are moulded and extruded to form plastics. Much of the food we eat can be classed as soft matter, and indeed the stuff of life itself shares the qualities of mutability and responsiveness to its surroundings that are characteristic of soft matter. We are ourselves soft machines, in William Burroughs’ apt phrase, and the material we are made of is soft matter. In more precise terms, the materials we are discussing include colloidal dispersions, where submicrometre particles of solid or liquid are dispersed in another liquid, polymer melts or solutions in which the size and connectivity of the molecules lead to striking new properties, such as viscoelasticity, which are very different to those of a simple liquid, and liquid crystals, where an anisotropic molecular shape leads to states with a degree of ordering intermediate between a crystalline solid and a liquid.
Polymers
Authors: Jones R A L
Published: November 2023

Polymers and polymer solutions and mixtures form a large and important class of soft condensed matter. Polymers may be synthetic in origin; plastics such as polystyrene and polyethylene are polymers, as are the components of many glues, fibres, and resins. Many materials of biological origin are also composed of polymers; examples of biologically important polymers include proteins, nucleic acids such as DNA, and polysaccharides like starch. Polymers, both natural and synthetic, are often major components in complex composite materials, both natural and artificial, such as glass-reinforced plastic, wood, and tissue. Despite the very wide variety of different properties of polymers that arise from the different chemistry that makes them up, many of their physical properties have universal characteristics: these characteristics are a result of generic properties of long, string-like, molecules. An example of such a generic property is the fact that two molecules cannot cross one another; this leads to the effect of entanglement, which produces dramatic viscoelastic effects in polymer melts and solutions. Surprisingly, it proves possible to construct remarkably simple and general theories to account
Soft matter in nature
Authors: Jones R A L
Published: November 2023

Until quite recently almost all the examples of soft matter that were of economic or practical importance were derived from living things. Foodstuffs, for example, are typically systems of colloidal or polymeric character, whose transformations by cooking processes are often best understood in terms of concepts such as those discussed in this book. Materials such as glues and paints were derived from natural products by simple processing techniques carried out on a craft scale; later industrial-scale processes, some still used, extensively modify natural polymers to produce products with less obvious relation to their natural origins. Examples include the modification of cellulose from tree pulp to produce cellophane sheets and rayon fibres, and the use of animal bones and skin to produce gelatin, which apart from its food use is still the main vehicle for photographic emulsions. In the early days of colloid science and polymer science many of the objects of study were essentially biological in origin. The second half of the twentieth century saw an increasing divergence between polymer and colloid science, on the one hand, and biology on the other. The invention of synthetic polymers and the massive growth of the plastics industry were accompanied by a parallel growth of polymer physics as a subject focused on synthetic rather than natural polymers, while the discovery of the genetic code and the development of protein crystallography led to a new discipline of molecular biology, whose research prograrnrne, pursued with spectacular success and intellectual confidence, concerned itself with rather different issues.
Renormalization
Authors: Cheng Ta-Pei , Li Ling-Fong
Published: November 2023

This gives the result that at the one-loop level (L = 1) the degree of divergence D = 4, independent of the external lines. It implies that the number of derivatives in the counterterms should be four or less. The term with two derivatives is just the term in the original Lagrangian.
Renormalization and symmetry
Authors: Cheng Ta-Pei , Li Ling-Fong
Published: November 2023

Calculate the divergence of axial vector current AJ
as generated by the axial transformation (i.e. the anomaly equation).
Quantum gauge theories
Authors: Cheng Ta-Pei , Li Ling-Fong
Published: November 2023

This means that the zero norm states in ℋ2
will not contribute to physical matrix elements and all important physics are contained in the space ℋ3. The presence of ℋ1
and ℋ2
is to maintain the Lorentz and gauge invariance. This is exactly analogous to the Gupta-Bleuer quantization formalism of QED.
Quantum chromodynamics
Authors: Cheng Ta-Pei , Li Ling-Fong
Published: November 2023

In QCD loop calculations we often encounter the some SUC(3) group theoretical factors. In this problem you will be asked to calculate such factors for the general case SU(n) rather than the n = 3 special situation of three colours.
Electroweak theory
Authors: Cheng Ta-Pei , Li Ling-Fong
Published: November 2023

Show that one can choose an appropriate biunitary transformation to diagonalize M so that all diagonal elements are non-negative. If the mass matrix is real, show that the matrices in the biunitary transformation can be chosen to be orthogonal matrices.
Magnetic monopoles
Authors: Cheng Ta-Pei , Li Ling-Fong
Published: November 2023

The first term is the familiar particle angular momentum. This again confirms the interpretation of the second term as the angular momentum of the electromagnetic (monopole) field.
Instantons
Authors: Cheng Ta-Pei , Li Ling-Fong
Published: November 2023

We will now evaluate the functional integral by summing all such configurations. Since these n objects are widely separated, the classical action is just S = nS
0, where S0 is the action for one instanton. Recall that for a single-well (harmonic oscillator) potential we have.
Introduction
Authors: Schweiger Arthur , Jeschke Gunnar
Published: November 2023

Electron paramagnetic resonance (EPR) is a spectroscopic method for determining the structure and dynamics and the spatial distribution of paramagnetic species. Such species with at least one unpaired electron are often chemically reactive. Compounds with transition metal ions feature prominently as catalysts in different branches of chemistry, and free radical intermediates are observed in many organic reactions and in one-electron transfer processes. In nature, transition metal catalysis is realized by a number of metalloproteins and free radical intermediates play a central role in photosynthesis Paramagnetic defects and impurities in crystals and glasses can influence the electrical and optical properties of a material even at low concentrations. They can also be used as spin probes, for example, to obtain insight into solid-state dynamics and phase transitions. Finally, stable free radicals such
Classical description
Authors: Schweiger Arthur , Jeschke Gunnar
Published: November 2023

In this chapter we introduce the magnetization vector picture for the description of pulse EPR experiments. The motion of magnetization vectors under the influence of static and oscillatory magnetic fields is described by the classical Bloch equations, which also consider relaxation in a phenomenological way. The behaviour of the macroscopic electron spin magnetization during and after resonant and off-resonant m.w. pulses is examined. This provides the basis for a discussion of the free induction decay FID after a single m.w. pulse.
Nuclear modulation effect II: advanced methods
Authors: Schweiger Arthur , Jeschke Gunnar
Published: November 2023

The basic nuclear modulation experiments described in Chapter 10 are easy to implement and the interpretation of the results is supported by a vast body of both general and system-specific data analysis procedures. Nevertheless, due to inherent lineshape distortions and sensitivity problems or a lack in resolution, they may not yield optimum nuclear frequency spectra for many paramagnetic species. In this chapter we introduce a number of advanced methods which were designed to eliminate these shortcomings. We start with methods that provide more faithful ESEEM lineshapes, in particular for disordered systems, by avoiding deadtime and blind-spot artifacts(§ 11.1). Sensitivity problems are addressed by experiments which can enhance modulation depths across the whole spectrum, for peaks related to a certain nuclear species, or for peaks close to the frequency of weak r.f. irradiation (§11.2). Soft ESEEM experiments based on two-frequency or field-step ELDOR approaches overcome excitation bandwidth limitations in the detection of large nuclear frequencies and may also lead to considerable modulation depth enhancements(§11.3). We then describe three ID reductions of the HYSCORE experiment which provide improved lineshapes for disordered systems or access to combination peaks with a higher resolution than two-pulse ESEEM (§11.4).
Multi-frequency EPR
Authors: Schweiger Arthur , Jeschke Gunnar
Published: November 2023

Both EPR and nuclear frequency spectra are most easily interpreted in the high-field limit where the electron or nuclear Zeeman interaction are the dominating interactions in the relevant spin Hamiltonian. On the other hand some pulse EPR experiments such as nuclear modulation techniques can only be applied if field-independent interactions have the same order of magnitude as the nuclear or electron Zeeman interaction. Due to the broad range of frequencies covered by the zero-field splittings and the hyperfine and nuclear quadrupole interactions in paramagnetic species, such situations of strong mixing between different interactions are quite common in EPR. The extent of mixing varies with the external field and for this reason the spectra obtained by pulse EPR experiments depend strongly and in a non-trivial way on the choice of the m.w. frequency. Furthermore, the m.w. frequency also determines the time scale of the dynamic processes which manifest in a change of the EPR lineshape or influence relaxation times.
Genetic approaches to the estimation of dispersal rates
Authors: Rousset Frarn;ois
Published: November 2023

This chapter reviews current methods for the estimation of dispersal rates from genetic data, based on models of neutral and selected markers. The causes of their inferred failures are discussed, with a more detailed investigation of difficulties raised by long-distance dispersal. It is emphasized that studies at a local geographical scale are more likely to yield valuable estimates. It should be possible to define more efficient and reliable methods, particularly when it is possible to sample from most subpopulations connected by dispersal at a local scale.
Inbreeding, kinship, and the evolution of natal dispersal
Authors: Perrin Nicolas , Goudet Jérôme
Published: November 2023

Using analytical tools from game theory, we investigate the relevance of a series of hypotheses concerning natal dispersal, focusing in particular on the interaction between inbreeding and kin competition, as well as on the components of mating and social systems that are likely to interfere with these phenomena. A null model of pure kin competition avoidance predicts a balanced equilibrium in which both sexes disperse equally. Inbreeding costs have the potential to destabilize this equilibrium, resulting in strongly sex-biased dispersal.
Condition-dependent dispersal
Authors: Ims Rolf A , Hjermann Dag Ø
Published: November 2023

We review conditions found to induce dispersal in animals. Condition-dependent dispersal is due to both environmental conditions (typically habitat and food quality, population density, local demographic and social structure) and internal conditions (typically fat reserves, body size, and competitive ability).
Habitat selection by dispersers: integrating proximate and ultimate approaches
Authors: Stamps Judy A
Published: November 2023

Behavioural research is shedding new light on the complex relationships between the proximate mechanisms involved in habitat selection and the selective pressures that may have contributed to the evolution of those mechanisms. Habitat selection by dispersers can be divided into three stages (search, settlement, and residency); recent studies suggest that the adaptive significance of behaviour at each of these stages may differ from the assumptions of traditional habitat selection theory.
The evolutionary consequences of gene flow and local adaptation: future approaches
Authors: Barton Nick H
Published: November 2023

Almost all natural populations are subdivided and experience spatially heterogeneous selection. This article reviews the ways in which such structuring of populations may affect evolution, and then discusses the various means by which we can find the actual role of population structure and gene flow in evolution.
Perspectives on the study of dispersal evolution
Authors: Rance Ophelie , Olivieri Isabelle , Clobert Jean , Danchin Etienne
Published: November 2023

In this chapter, we stress the gaps in our knowledge about dispersal evolution and suggest several promising research directions. (i) Both empirical and theoretical studies illustrate how different causes may result in the evolution of dispersal behaviour. Integrative approaches that study the interactions between these causes are, however, rare. Theoretical expectations must be clarified by a careful comparison of existing models and their specific assumptions.
Dispersal in theory and practice: consequences for conservation biology
Authors: Macdonald David W , Johnson Dominic D P
Published: November 2023

Dispersal is a fundamental parameter of population processes. In small and isolated populations, linked only when individuals are able to disperse between them, it becomes a particularly critical one which ultimately determines whether a species will become extinct. Predictions for these populations are limited because estimates of dispersal variables from the field are difficult to obtain and therefore scarce.
The Bedrock Problem: Why We Need Renormaliz Ation Methods
Authors: McComb W D
Published: November 2023

As we have pointed out in the Preface, the term renormalization comes from quantum field theory and is usually thought of as being the prerogative of that discipline. As a result, renormalization is seen by many as probably being difficult, esoteric, and highly mathematical. Yet, the basic concept is older than quantum theory of any kind and was first developed in classical physics.
Strong Imagination
Authors: Nettle Daniel
Published: November 2023

Madness is the central mystery of the human psyche. Our minds evolved to give us a faithful understanding of reality, to allow us to integrate into our communities, and to help us adapt our behaviour to our environment. Yet in serious mental illness, the mind does exactly the opposite of these things. The sufferer builds castles of imaginative delusion, fails to adapt, and becomes a stranger among his own people. Yet mental illness is no marginal phenomenon: it is found in all societies and all historical epochs, and the genes that underlie it are quite common. Furthermore, the traits that identify the madman are found in attenuated form in normal thinking and feeling. The persistence of madness, then, is a terrible puzzle from both an evolutionary and a human point of view. In A Midsummer Night's Dream, Shakespeare suggested a link between madness and artistic creativity: 'The lunatic, the lover, and the poet', he wrote, 'Are of imagination all compact'. Recent studies have shown that there is indeed a connection. Rates of mental illness are hugely elevated in the families of poets, writers and artists, suggesting that the same genes, the same temperaments, and the same imaginative capacities are at work in insanity and in creative ability. Thus the reason madness continues to exist is that the traits behind it have psychological benefits as well as psychological costs. In Strong Imagination, Daniel Nettle explores the nature of mental illness, the biological mechanisms that underlie it, and its link to creative genius. He goes on to consider the place of both madness and creative imagination in the evolution of our species.
Quantum Transport, Anderson Localization
Authors: Imry Yoseph
Published: November 2023

The Bloch–Boltzmann quasiclassical theory of electronic transport in lightly disordered conductors has been quite successful in describing the impurity and temperature dependences of the conductivity in ordinary relatively pure conductors. Further transport properties such as magnetoconductivity, Hall effect, thermal conductivity, and thermopower can also be handled, often with success. However, when the amount of disorder (or impurity concentration) becomes very large, novel phenomena occur which are unexplainable within the weak-scattering theory. In particular, the temperature dependence of the resistivity, ρ,becomes much weaker and eventually changes direction for high enough disorder (Wiesmann et al.1977). The Mathiessen rule, according to which the contributions to ρdue to disorder and temperature are additive, thus breaks down. An extremely interesting correlation was found by Mooij (1973), namely, that dp/dTbecomes negative when ρbecomes larger than a value ranging around 80–180 ¼ Ω cm in something like a hundred disordered dirty systems. This almost “universal” trend must have an explanation which is only weakly dependent on material properties, and we remember that dp/dT > 0 alwaysin weak-scattering theory.
Mesoscopic Effects in Equilibrium and Static Properties
Authors: Imry Yoseph
Published: November 2023

This chapter will be devoted to mesoscopic effects which are not necessarily related to nonequilibrium or transport phenomena. Most of our discussion in the rest of this chapter will be concerned with electronic effects, often with fluctuations from sample to sample. We shall start here, however, by briefly reviewing more general finite-size effects due to ordinary thermodynamic fluctuations.

Such fluctuations are usually negligible in the “thermodynamic limit,” as far as their contributions to, for example, intensive properties, or to the O(N)part of extensive ones are concerned. However, thermodynamic fluctuations may play an important role in special situations where large length scales exist in the system. We mention here two of these: the elimination of certain types of long-range order (and, therefore, phase transitions) in low-dimensional systems and the effects of finite sample sizes on regular phase transitions. There are several varieties of the former effects.
Mesoscopics With Superconductivity
Authors: Imry Yoseph
Published: November 2023

Much of what we have considered in mesoscopics has had to do with phase-coherent effects of normal electrons. Each electron retains phase coherence over the length Lϕand different electrons in the energy band of a width kB Taround the Fermi energy display a similar interference pattern over the length LT.The superconducting state is characterized by having a macroscopic wavefunction, retaining its coherence ideally over arbitrarily largelengths. It is of great interest to enquire how these two (normal and super) coherence effects couple with each other. This is not an obvious issue, since in the normal conductor the active charge carrier is a single electron or a hole, while in the superconductor the coherence is of the wavefunction of the condensed Cooper pairs. It is known, however, that superconductivity can penetrate into a normal metal over a length scale of LT(which has been referred to in this context as “the normal metal coherence length, ξN”l.2). This is the well-known proximity effect (e.g., Deutscher and de Gennes 1969). Two superconductors can quite generally be correlated with each other and exchange a supercurrent through a normal metal barrier which can be LT(or Lϕ,see section 5) long. This is called “a superconducting weak link” (e.g., Likharev 1979). It is akin to (but not exactly the same as) the usual Josephson effect, which occurs via tunneling through a thin insulating barrier.
Concluding Remarks
Authors: Imry Yoseph
Published: November 2023

Many of the interesting and novel phenomena that occur in mesoscopic systems have been reviewed and discussed in this book. After a brief discussion in chapter I of the available experimental systems and “micro–” and “nano–” fabrication possibilities, the modification of the electronic properties, especially the transport, due to Anderson localization were considered in chapter 2. This is the first example where quantum interference has important consequences even macroscopically. Chapter 3 dealt with the general question of how inelastic scattering produces an uncertainty in the relative phase of partial waves, thereby eliminating their interference. An expression was produced which helps to evaluate the inelastic rate in terms of the dissipative response function of the system, which is usually known. As an application, the very nontrivial dephasing due to electron–electron interaction in the diffusive case was considered.
Superfluid helium-4
Authors: Annett James F
Published: November 2023

There are only two superfluids which can be studied in the laboratory. These are the two isotopes of helium: He and He. Unlike all other substances they are unique because they remain in the liquid state even down to absolute zero in temperature. The combination of the light nuclear masses and the relatively weak van der Waals interactions between the particles means that at low pressure they do not freeze into a crystalline solid. All other elements and compounds eventually freeze into solid phases at low temperatures.
The BCS theory of superconductivity
Authors: Annett James F
Published: November 2023

In 1957 Bardeen Cooper and Schrieffer (BCS) published the first truly microscopic theory of superconductivity. The theory was soon recognized to be correct in all the essential aspects, and to explain a number of important experimental phenomena. For example, the theory correctly explained the isotope effect:

in which the transition temperature changes with the mass of the crystal lattice ions, M. The original BCS theory predicts that the isotope exponent α is 1/2. Most common superconductors agree very well with this prediction, as one can see in Table 6.1. However, it is also clear that there are exceptions to this prediction. Transition metals such as Molybdenum and Osmium (Mo, Os) show a reduced effect, and others such as Ruthenium, Ru, have essentially zero isotope effect.
Invitations to Geometry and Topology
Authors: Bridson Martin R , Salamon Simon M
Published: November 2023

This volume presents an array of topics that introduce the reader to key ideas in active areas in geometry and topology. The material is presented in a way that both graduate students and researchers should find accessible and enticing. The topics covered range from Morse theory and complex geometry theory to geometric group theory, and are accompanied by exercises that are designed to deepen the reader’s understanding and to guide them in exciting directions for future investigation. The editors, M.R. Bridson and S.M. Salamon, have each written an article and are accompanied by A.J. Berrick; M.C. Crabb and A.J.B Potter; M. Eastwood and J. Sawon; M.A. Guest; N.J. Hitchin and J.Seade.
The Borel-Weil theorem for complex projective space
Authors: Eastwood Michael , Sawon Justin
Published: November 2023

Our aim, in this chapter, is to give a complete classification of the irreducible finite-dimensional holomorphic representations of the complex general linear group. We shall construct them as spaces of holomorphic sections of certain vector bundles over complex projective space.
The Deformation of Metals by Sperical Identers: Ideal Plastic Metals
Authors: Tabor D
Published: November 2023

We may now consider the deformation of an ‘ideal’ plastic metal, of yield stress Y, by a hard spherical indenter of radius r (Fig. 21a). The friction between the indenter and the metal surface is again assumed to be negligibly small. When the load is applied to the indenter the metal surface and the indenter will both deform elastically according to the classical equations of Hertz (1881). The region of contact is a circle of radius a (see Fig. 21 b) as given by the equation
Dynamic or Rebound Hardness
Authors: Tabor D
Published: November 2023

The dynamic hardness of a metal may be defined, by analogy with static hardness, as the resistance of the metal to local indentation when the indentation is produced by a rapidly moving indenter. In most practical methods the indenter is allowed to fall under gravity on to the metal surface. It rebounds to a certain height and leaves an indentation in the surface. Martel showed in 1895 that, over a wide range of experimental conditions, the volume of the indentation so formed is directly proportional to the kinetic energy of the indenter and these observations have been confirmed by Vincent (1900) and other workers.