bluuebunny/crossref_metadata_2025 huggingface dataset:
Single-Particle and Shell-Model Theories of Quadrupole Moments
Authors: Castel B , Towner I S
Published: November 2023

We now turn our attention to electric quadrupole moments. These moments have traditionally been invoked as good indicators of collective effects in contrast to magnetic moments. The reason for that is simple and has to do with the difference in the nature of the two relevant operators. The magnetic dipole operator leads to opposite contributions from a state |ψ⟩ and its time-reversed conjugate |ψ˜⟩ (since both currents and spin change sign in the |ψ⟩→|ψ˜⟩ conjugation). Thus one member of the paired-off nucleon cancels the contribution from the other. Such is not the case for the quadrupole operator since its contributions are invariant under time reversal. Thus if nuclear correlations can be induced by some deformation, a coherent buildup of quadrupole moment can be expected. As we shall see, this coherence can lead to sizeable effects which will be examined in this chapter in the light of single-particle and various shell models. The next chapter will be devoted to a survey of the macroscopic models currently available for the study of quadrupole moments and nuclear deformations.
Conclusion
Authors: Castel B , Towner I S
Published: November 2023

We have now arrived, after a meandering journey through the nuclear physics of the 1980s, at our final station. Let us pause here and reflect on how nuclear moments have contributed to the elucidation of some major problems of nuclear structure and discuss also some remaining difficulties and future prospects for their solution.
Giant Resonances
Authors: Harakeh M N , van der Woude A
Published: November 2023

Giant resonances are collective excitations of the atomic nucleus, a typical quantum many-body system. The study of these fundamental modes has in many respects contributed to our understanding of the bulk behaviour of the nucleus and of the dynamics of non-equilibrium excitations. Although the phenomenon of giant resonances has been known for more than 50 years, a large amount of information has been obtained in the last 10 years. This book gives an up-to-date, comprehensive account of our present knowledge of giant resonances. It presents the experimental facts and the techniques used to obtain that information, describes how these facts fit into theoretical concepts and how this allows to determine various nuclear properties which are otherwise difficult to obtain. Included as an introduction is an overview of the main facts, a short history of how the field has developed in the course of time, and a discussion of future perspectives.
Magneto-optical and electro-optical phenomena
Authors: Balkanski M , Wallis R F
Published: November 2023

This chapter is divided into three major parts. In the first part magneto optical phenomena are discussed from a classical point of view. Optical absorption as exemplified by cyclotron resonance and dispersion as exemplified by the Faraday and Voigt effects are analyzed. In the second part a quantum mechanical treatment is presented. The theory of the Landau levels of an electron moving in a uniform magnetic field is developed and applied to optical properties. In the third part the effects of an external electric field on optical properties are discussed.
Appliication Of Semiconductor Heterostructure
Authors: Balkanski M , Wallis R F
Published: November 2023

The development of techniques such as molecular beam epitaxy has made possible the production of ultrathin semiconductor structures with precisely controlled characteristics at the atomic level. These structures have formed the basis for new electronic devices with improved performance in both standard and novel applications.
Gauge Groups
Authors: Stancu Fl
Published: November 2023

The continuous symmetries we have discussed until now are calledglobal symmetries. The parameters a ρ, Equation (5.51), of a Lie group are space-time independent. In a field theory, this implies that fields at different space-time points transform by the same amount There are theories where the symmetry transformation contains space-time-dependent parameters aρ (x). These transformations are called local or gauge (Weyl 1929) and form gauge groups. They generate the gauge interactions; electromagnetic, weak, and strong interactions are all gauge interactions. Therefore, the present theory of elementary particle physics is based on the principle of gauge symmetries.
Potential flow
Authors: Guyon Etienne , Hulin Jean-Pierre , Petit Luc , Mitescu Catalin D
Published: November 2023

The study of an ideal (perfect) fluid-’dry water’, as Richard P Feynman refers to it in the Feynman Lectures in Physics-is a crucial part of fluid dynamics. In the mechanics of solids, the laws of motion can be expressed, in the absence of friction, in terms of conservation laws. In a similar way, the absence of viscosity in fluid mechanics allowed us, in Chapter 5, to express in a simpler way the energy and momentum conservation laws, and to solve a number of problems without needing a detailed knowledge of the local motion.
Flow at low Reynolds numbers
Authors: Guyon Etienne , Hulin Jean-Pierre , Petit Luc , Mitescu Catalin D
Published: November 2023

Flows at low Reynolds number, a concept introduced in Chapter 2, are characterized by the fact that viscosity effects dominate inertial ones. The Stokes equation, which describes these flows, is linear, because the convective non-linear term (∇. ∇) ∇ can be neglected. For the case of parallel flows discussed in Chapter 4, this convective term was rigorously zero.
Magneto-Transport Phenomena
Authors: Miura Noboru
Published: November 2023

The conductivity in the presence of magnetic field is expressed by the generalized Ohm’s law as follows, where J is the current density, E is the electric field vector and σ is the conductivity tensor. In a magnetic field, the conductivity tensor σ has non-diagonal components due to the Lorentz force.
Electromagnetic radiation is produced by electrons
Authors: Duke Philip John
Published: November 2023

In the previous chapter we introduced the idea of the electromagnetic wave as the regular variation of electric and magnetic fields. We explained how these waves transport energy in the form of photons from one place to another. We also described how the photon energy is related to the wavelength and frequency of the wave. Our aim in this chapter is to begin with the experimental observation that electrons are the source of both electric and magnetic fields and to show how this observation leads to a complete description, in mathematical terms, of the fields themselves and their propagation through space and time. The mathematical description which we are aiming for is known as Maxwell’s equations for the electromagnetic field. The argument will be followed at a very elementary level and can be omitted by those who are already familiar with the subject. On the other hand, those who wish for a more detailed and rigorous treatment will need to supplement this chapter with one of the many textbooks on the theory of electromagnetism and electrodynamics.
The spectral distribution of synchrotron radiation
Authors: Duke Philip John
Published: November 2023

Properties of the modified Bessel functions Equation (5.44) is an expression for the angular distribution of the synchrotron radiation which contains the modified Bessel functions, K1/3 and K2/3. Their behaviour, as a function of the general variable x, is shown in Fig. 6.1.
Photon spectral distribution integrated over vertical angles
Authors: Duke Philip John
Published: November 2023

The fact that the radiation from the accelerated electron is emitted into a narrow forward cone means that quite often an observer is interested in the photon energy (or the total number of photons) emitted over all vertical angles. This is the case when the target being irradiated subtends a vertical angle which is significantly larger than the opening angle of the forward cone from the emission point. The energy radiated by the passage of one electron into unit solid angle, located at an angle θ above the plane of the electron orbit, and unit frequency interval is given as usual by eqn (7.1) which is identical to (5.44):
Behaviour of the electron beam in a synchrotron radiation storage ring. The concept of phase space
Authors: Duke Philip John
Published: November 2023

In this chapter, we develop a formal description of the electron beam in a storage ring. We begin by defining the magnetic field function of an elementary storage ring which includes only the dipole and quadrupole fields. This will be sufficient for a basic understanding of the subject. Next, we develop an equation which describes the motion of the electron in this field and in Chapter 11 we shall show how the solutions of this equation of motion describe the oscillatory behaviour of the electron beam in the horizontal and vertical planes.
Basic Features Of Superconductivity
Authors: Asner Fred M
Published: November 2023

The unexpected discovery of superconductivity by H.K. Onnes in 1911 in Leyden was due to research and development activities in two domains: the liquefaction of gases, leading in 1908 to the liquefaction of helium, and to the investigation of the electric conductivity of metals, which Onnes intended to explore at temperatures approaching absolute zero [1, 2].
Polymer gels
Authors: Doi M , See H
Published: November 2023

A polymer gel is a three-dimensional network of polymer chains joined together at a number of connection sites, as shown in Fig. 3.1. The connections may be due to covalent chemical bonds or physical interactions such as hydrogen bonds or electrostatic forces. The former are called chemical gels, the latter physical gels. There are basically two ways to make a chemical gel. One way is to add a cross linking agent to a system of polymer chains, causing them to form a network.
Mathematical Theory of Quantum Fields
Authors: Araki Huzihiro
Published: November 2023

This is an introduction to the mathematical foundations of quantum field theory, using operator algebraic methods and emphasizing the link between the mathematical formulations and related physical concepts. It starts with a general probabilistic description of physics, which encompasses both classical and quantum physics. The basic key physical notions are clarified at this point. It then introduces operator algebraic methods for quantum theory, and goes on to discuss the theory of special relativity, scattering theory, and sector theory in this context.
Local Observables
Authors: Araki Huzihiro
Published: November 2023

In this chapter we consider for each space-time domain the set of all those observables which can be measured there and we discuss its basic properties, especially in connection with the vacuum state.
Scattering Theory
Authors: Araki Huzihiro
Published: November 2023

In this chapter we explain how particle scattering can be described by local observables. First we introduce the concept of the S-matrix, which is an idea common to classical and quantum mechanics. We show the construction of incoming and outgoing states which have a certain asymptotic behaviour at time −∞ and +∞, and we also show that the constructed states have an acceptable physical asymptotic behaviour. Then we derive the representation of the S-matrix given by these scattering states and discuss its properties.
Magnetostatic Phenomena
Authors: Chikazumi Sōshin , Graham, Jr C D
Published: November 2023

The most direct manifestation of magnetism is the force of attraction or repulsion between two magnets. This phenomenon can be described by assuming that there are ‘free’ magnetic poles on the ends on each magnet which exert forces to one another. These are called ‘Coulomb forces’ by analogy with the Coulomb forces between electrostatically charged bodies. Consider two magnetic poles with strengths ofm1(Wb (weber)) andm2(Wb) respectively, separated by a distancer(m).
Antiferromagnetism And Ferri Magnetism
Authors: Chikazumi Sōshin , Graham, Jr C D
Published: November 2023

In antiferromagnetism, neighboring spins are aligned antiparallel to one another so that their magnetic moments cancel. Therefore an antiferromagnet produces no spontaneous magnetization and shows only a feeble magnetism. The relative magnetic susceptibility of antiferromagnetic materials, ranges from 10-5 to 1O-2, the same as for paramagnets. The only difference is the presence of an ordered spin structure, as shown in Fig. 7.1. When an external magnetic field is applied parallel to the spin axis, the spins which are parallel and antiparallel to the field experience almost notorque and so keep their ordered spin arrangement. Therefore the susceptibility in this case is smaller than for a normal paramagnet.
Magnetocrystalline Anisotropy
Authors: Chikazumi Sōshin , Graham, Jr C D
Published: November 2023

The termmagnetic anisotropyis used to describe the dependence of the internal energy on the direction of spontaneous magnetization. We call an energy term of this kind amagnetic anisotropy energy.Generally the magnetic anisotropy energy term has the same symmetry as the crystal structure of the material, and we call it amagnetocrystalline anisotropy.
Magnetostriction
Authors: Chikazumi Sōshin , Graham, Jr C D
Published: November 2023

Magnetostriction is the phenomenon whereby the shape of a ferromagnetic specimen changes during the process of magnetization. The deformationδl/ldue to magnetostriction is usually very small, in the range 10−5 to 10−6 A deformation of this magnitude can be conveniently measured by means of a strain-gauge technique, the details of which are described later. Although the deformation is small, magnetostriction is an important factor in controlling domain structure and the process of technical magnetization is an important factor in controlling domain structure and the process of technical magnetization.
Atomic Masses
Authors: Wapstra A H
Published: November 2023

Since the discovery that elements occur in various isotopes, the masses M of their atoms are known to be nearly integers A (the mass number) if expressed in suitable units. Since 1960, the unit u (or mu) used is l/12th of the mass of a 12C atom in its nuclear and atomic ground states. Mass values as given in tables (e.g. ref. 1) are those of atoms in such ground states (but for some exceptions where the nucleus is in an isomeric state). The reason for giving atomic masses rather than nuclear ones is that until very recently, measurements yielded more directly, and accurately, data on atomic masses than on nuclear ones, as will become clear from the discussions below.
Static scattering properties of colloidal suspensions
Authors: Klein Rudolf , D’Aguanno Bruno
Published: November 2023

The microstructure of colloidal suspensions is commonly studied by scattering experiments. A considerable amount of theoretical background is needed to extract information about the microstructure from the measured scattered intensity I(k) and to understand such microstructure in terms of properties of the suspended particles and the solvent. It is the purpose of this chapter to provide this background and to present and discuss results for realistic systems. The discussion will almost entirely be restricted to suspensions of spherical particles. For such systems the microstructure is mainly described by the pair distribution function g(r), which is closely related to the probability of finding a particle at the distance r from another particle.
Effective Quark Interactions
Authors: Ripka Georges
Published: November 2023

Quark models are usually expressed in terms of effective interactions, which reflect the symmetries of strong interactions. However, symmetry is not sufficient to determine them. The forms of the effective interactions are further dictated by their phenomenological fitness and by their simplicity of use. We should keep in mind that we are not discussing the effective interactions with the aim of adding them to a confining potential. Rather, we have the intention of using them in models which can account for the spontaneously broken chiral symmetry of the vacuum and, hopefully also, for the formation of hadrons. Attempts to derive effective quark interactions from QCD have followed different directions. Some attempts, sometimes referred to as the global color model, lead to an effective gluon exchange interaction, the space—time dependence of which is governed by a phenomenologically determined effective gluon propagator [17, 18, 19, 20, 21, 22] or which is based on the so-called field strength approach [23]. Other attempts, based on so-called hadronization methods, introduce auxiliary non-local fields which re-sum ladders of gluon exchange diagrams [14, 24]. Another direction, which derives a different effective interaction between quarks, stems from a study of their propagation in an instanton liquid, which describes the QCD vacuum [25, 26, 27). In this chapter we describe the various interactions which are commonly used and we do not attempt to derive them from QCD.
The Nambu Jona-Lasinio Model
Authors: Ripka Georges
Published: November 2023

Like other models which account dynamically for the spontaneous breakdown of chiral symmetry, it is unable to confine color and quarks. Hadrons appear in the model as bound (instead of confined) states of quarks. The model was conceived before the discovery of quarks. It was originally designed to be a dynamical model of spontaneous chiral symmetry breaking in the vacuum (39, 40]. References to reviews and applications are given in chapter 10 for the meson sector and in chapters 12 and 13 for the baryon sector.
Chiral Solitons
Authors: Ripka Georges
Published: November 2023

The possibility of describing baryons as chiral solitons is based on the observation that bound states can be formed when quarks interact with a chiral field. Friedberg and Lee had previously shown how bound states (called solitons) could be formed when quarks interact with scalar fields (see the reviews in [183, 184]). Chiral solitons were discovered when the scalar field was supplemented by a pion field, so as to implement chiral symmetry. This lead naturally to the calculation of soIitons using the Gell-Mann Levy model (section 11.3), also extended to include vector fields [169, 170, 171]. These, as well as solitons calculated with color dielectric models, are reviewed in [172). Quite similar solitons are obtained using the Nambu Jona-Lasinio model. They are reviewed in [185, 186].
Permanent-magnet motors
Authors: Hanitsch R
Published: November 2023

New electromechanical drive systems endowed with a combination of desirable characteristics are a considerable impetus to technological progress. Taking a robot axis drive as an example, it should combine a low moment of inertia and low torque pulsations with high power/weight ratio, high torque overload capability and high efficiency. The advent of rare-earth permanent magnets has opened up the prospect of significantly improved designs for such devices, as well as for a range of other industrial drives, small electrical machines and micromotors.
The Principles of Equilibrium Thermal Monte Carlo Simulation
Authors: Newman M E J , Barkema G T
Published: November 2023

In Section 1.3.1 we looked briefly at the general ideas behind equilibrium thermal Monte Carlo simulations. In this chapter we discuss these ideas in more detail in preparation for the discussion in the following chapters of a variety of specific algorithms for use with specific problems. The three crucial ideas that we introduce in this chapter are “importance sampling”, “detailed balance” and “acceptance ratios”. If you know what these phrases mean, you can understand most of the thermal Monte Carlo simulations that have been performed in the last thirty years.
The using n1odel and the Metropolis algorithm
Authors: Newman M E J , Barkema G T
Published: November 2023

In Section 1.2.2 we introduced the using model, which is one of the simplest and best studied of statistical mechanical models. In this chapter and the next we look in detail at the Monte Carlo methods that have been used to investigate the properties of this model. As well as demonstrating the application of the basic principles described in the last chapter, the study of the using model provides an excellent introduction to the most important Monte Carlo algorithms in use today. Along the way we will also look at some of the tricks used for implementing Monte Carlo algorithms in computer programs and at some of the standard techniques used to analyse the data those programs generate.
Other Algorithms for the Using Model
Authors: Newman M E J , Barkema G T
Published: November 2023

In the last chapter we saw that the Metropolis algorithm with single-spin-flip dynamics is an excellent Monte Carlo algorithm for simulating the using model when we are interested in temperatures well away from the critical temperature Tc However, as we approach the critical temperature, the combination of large critical fluctuations and long correlation time makes the errors on measured quantities grow enormously. As we pointed out, there is little to be done about the critical fluctuations, since these are an intrinsic property of the model near its phase transition (and are, what’s more, precisely the kind of interesting physical effect that we want to study with our simulations). On the other hand, the increase in the correlation time close to the phase transition is a function of the particular algorithm we are using-the Metropolis algorithm in this case-and it turns out that by using different algorithms we can greatly reduce this undesirable effect. In the first part of this chapter we will study one of the most widely used and successful such algorithms, the Wolff algorithm. Before introducing the algorithm however, we need to define a few terms.
Disordered Spin Models
Authors: Newman M E J , Barkema G T
Published: November 2023

In the previous few chapters of this book we have studied a variety of different Monte Carlo algorithms for simulating the using model under various conditions. In Chapter 3 we looked at the Metropolis algorithm, as it applies to the using model, and in Chapter 4 we looked at a number of other algorithms, most of which are designed to simulate the model more efficiently in the critical region, the region near the phase transition between paramagnetism and ferromagnetism. In the last chapter, we looked at a slight variation on the using model theme, the conserved-order-parameter using model, which can be used as a model of a gas, or of atoms diffusing on a surface. As we have seen, for different regimes of temperature or different variations of the model, different algorithms are appropriate. The trick is to tailor the algorithm to the type of problem we wish to tackle. However, all the algorithms we have seen so far eventually boil down to one thing: they generate a series of states, a Markov chain, in which each state is derived from the previous one in the chain, and attempt to contrive that each should appear with a probability proportional to its Boltzmann weight. In this chapter, for the first time, we will come across systems for which an approach of this kind doesn’t work. The problem, as we will see, is that for some systems, the so-called glassy systems, algorithms of this kind tend to get stuck in small regions of the state space from which they cannot escape. The reason for this is two-fold. First, the fact that each state is generated from the previous one in the chain means that there is a sense in which states are “close together”. There are states which it is easy to get to from the present one in a small number of moves, such as states which differ by the flipping of just a few spins for a single-spin-flip algorithm, and there are other states which you can only get to by making a large number of moves.
Lattices and Data Structures
Authors: Newman M E J , Barkema G T
Published: November 2023

In the preceding chapters of this book we have looked at quite a number of problems and models in statistical physics, and described a variety of different Monte Carlo methods for their study. For many of these Monte Carlo methods we have also given some details about how they can be most efficiently implemented on a typical modern computer. Many details of implementation however are common to a lot of different algorithms, and in the remaining four chapters of this book we examine some of these general implementation issues. For instance, pretty much all of the problems discussed in this book are defined on a lattice, and so we need to know how to represent such a lattice on our computer. Also, most of our algorithms require us to store a certain amount of data regarding, for example, spin clusters or other constructs, and for this we need to know about the efficient implementation of data structures. In this chapter we describe the basic techniques for handling these issues in Monte Carlo programs. If you are an experienced computer programmer, some of this material may already be familiar to you, in which case you will probably want to skip over those parts.
Monte Carlo Simulations on Parallel Computers
Authors: Newman M E J , Barkema G T
Published: November 2023

Some of the simulations we would like to perform require so much computing power that it is not possible to finish them in a reasonable length of time on any available computer. Under these circumstances we have two choices: either we can wait a few years for a more powerful computer to become available, or we can perform the calculation on several computers. Since waiting a few years for the answer to a problem is not always a practical course of action, the latter approach is becoming increasingly popular and has led to the development of hardware and software for distributed and parallel computing. In this chapter we explore the ways in which these techniques can be applied to Monte Carlo simulation.
Magnetization-Induced Second Harmonic Generation From Surfaces and Ultrathin Films
Authors: Vollmer R
Published: November 2023

Optical second harmonic generation (SHG) and nonlinear optics in general became a rapidly growing field of research soon after the invention of the laser by Maiman in 1960. In the following years it was concentrated on nonlinear light generation in bulk materials. Starting in the 1980s the potential of second harmonic and sum frequency generation was explored in the investigation of surfaces and adsorbed molecules.
Nuclear clusters
Authors: Ohkubo S , Yamaya T , Hodgson P E
Published: November 2023

Since the observation of radioactivity by Becquerel in 1896 [1], and subsequently of α-particles from heavy nuclei by Rutherford in 1903, the α-particle has continued to be of central importance in nuclear physics. The nucleus itself was discovered by Rutherford [2] using α-particles. The α-particle model is the oldest nuclear model, since Gamov showed [3,4] that α-decay in heavy nuclei can be explained by assuming that in the decay process an α-particle leaves the nucleus by tunnelling through a Coulomb barrier. The classical α-particle model, in which the compositeness of the particle, and therefore the Pauli principle, is not taken into account, was useful in understanding the structure of light nuclei [5]. However, after the success of the shell model [6] and the collective model [7], which revealed single-particle and collective (rotational and vibrational) aspects of nuclei, the α-particle model was almost forgotten for some years.
Plasma Dynamics
Authors: Dendy R O
Published: November 2023

Plasma is the physical state in which most of the visible matter in the universe is found. The properties of plasma are so distinctive that it is often referred to as the fourth state of matter. This book explains the fundamental concepts of plasma physics and provides an introduction to plasma particle dynamics, plasma waves, magnetohydrodynamics, plasma kinetic theory, two-fluid theory, and non-linear plasma physics. Emphasis is placed on the underlying physical principles, rather than on mathematical considerations. The most advanced background knowledge required consists of Maxwell's equations, and these are reviewed in the introduction. This book will be useful to undergraduates in physics and postgraduates in astrophysics, nuclear physics, and plasma physics and is short enough to be covered in a single lecture course.
Motion of an electron magnetic field
Authors: Dendy R O
Published: November 2023

Every plasma has a natural tendency to disperse. Unless there is some restraining force, the energetic particles that compose the plasma will travel away from their initial positions at high velocity and the plasma will cease to exist. Furthermore, many plasmas have low densities, and collisions are therefore so infrequent that a particle travelling outwards is unlikely to be deflected by a collision. Nevertheless, both in the laboratory and in space, diffuse collision less plasmas can be sustained. They are prevented from dispersing by magnetic fields, which act on the charged particles through the Lorentz force. The dynamics of charged particles in magnetic fields therefore form an important area of plasma physics, which we shall examine in this chapter. We start by considering the simplest possible example, which consists of an electron moving in a spatially uniform magnetic field B which does not vary in time.
Non-linear plasma physics
Authors: Dendy R O
Published: November 2023

We shall now consider the connection between the two major ways of describing plasma that have been used so far. First, we considered the dynamics of a single particle in the plasma, which leads directly to a simple model for the dielectric properties of the plasma. By including the single-particle dynamics of ions as well as of electrons, it is possible to predict the normal modes of the plasma over a wide range of frequencies. There is also the magneto hydrodynamic approach. By treating the plasma as a magnetized conducting fluid, whose inertia is provided by the mass of the ions, we can describe the bulk stability of the plasma and its lower-frequency normal modes-those modes which do not involve the movement of electrons independently of ions.
Large Gain
Authors: Luchini P , Motz H
Published: November 2023

When the radiated field intensity in an FEL is comparable to the input field, that is when gain is not small compared to unity, it is no longer possible to study the electron motion independently of the radiation process. In this chapter we shall address the situation where the gain is not small but the field itself is small, so as to permit the use of linearized equations of motion. The characteristic feature of this operating regime is that the motion of each electron does not take place in an externally imposed electromagnetic field but rather in the field generated by all the other electrons. It is then preferable to abandon the single-particle description of the previous chapters, where the motion of every single electron could be studied independently of the others, and pass to a collective approach in which the position and velocity of the electrons is described by a suitable distribution function in phase space and the linearized Boltzmann equation for this distribution function and the Maxwell equations for the electromagnetic field must be solved selfconsistently.
Tapered Undulators
Authors: Luchini P , Motz H
Published: November 2023

In a large-gain free-electron laser the effect of amplitude variations of the laser field upon electron motion cannot be neglected. If, in addition to large gain, there is a substantial power extraction, that is if the laser power is a nonnegligible fraction of the power transported by the electron beam, the effect of power extraction upon electron energy cannot be neglected. Under these conditions the laser power and the energy of the electron beam, i.e. its mean γ, can no longer be considered constant along the undulator. Since variations in γ affect the synchronism condition which is essential for FEL operation, it becomes necessary to allow the undulator parameters (period and/or field amplitude) to vary as well if synchronism is to be maintained. The undulator becomes ‘tapered’.
Physics of Interacting Electrons in Disordered Systems
Authors: Kamimura Hiroshi , Aoki Hideo
Published: November 2023

The behaviour of electrons in systems without periodicity is one of the most fascinating areas in solid-state physics, and the last 25 years have seen an enormous increase in research in this field. This has given rise to many new ideas for understanding electronic states in disordered systems, especially the study of the degenerate electron gas in which electron-electron interactions are important. This book provides a much needed survey of these advances. In the first part of the book, the authors discuss impurity bands in three dimensions. Attention is focused on the regime in which the electrons are spatially localized rather than free, so that an interesting interplay of localization and interaction arises. In the second part of the book, they look at the outstanding features of the two-dimensional systems, explaining how these make the localization problem special and interesting. The authors have provided a clear outline of the theoretical picture for the chosen materials and description heuristic. Each chapter is self-contained, allowing readers to pursue their special interests.
St a tic Distortions In a Nematic Single Crystal
Authors: Gennes P G De , Prost J
Published: November 2023

However, in most practical circumstances, this ideal conformation will not be compatible with the constraints that are imposed by the limiting surfaces of the sample (e.g. the walls of a container) and by external fields (magnetic, electric, etc.) acting on the molecules.
Dynamical Properties Of Nematics
Authors: Gennes P G De , Prost J
Published: November 2023

A nematic flows very much like a conventional organic liquid with molecules of similar size. However, the flow regimes are more complex and more difficult to study experimentally than in isotropic liquids for the following reasons. The translational motions are coupled to inner, orientational motions of the molecules; in most cases, the flow disturbs the alignment. Conversely, a change in the alignment (e.g. by application of an external field) will, in many instances, induce a flow in the nematic.
Macroscopic Behaviour Of Smectics And Columnar Phases
Authors: Gennes P G De , Prost J
Published: November 2023

In Chapter 1, after the description of smectic and columnar phases, we briefly discussed the influence of thermal fluctuations in these systems. To that end we introduced what we called a ‘poor man’s’ elastic theory. This allowed us to introduce the notions of short-, long-, and quasilong-range order. The main ingredient was the number of ‘liquid-like’ directions, but no attention was paid to the number of relevant variables. A closer contact with experiment requires a proper consideration of the symmetries involved. Because of their unique-characteristics, we consider chiral systems separately in Section 7.2.
Electron Scattering Theory for Ordered and Disordered Matter
Authors: Weinberger P
Published: November 2023

The problem of the electronic structure of solid matter is addressed in terms of multiple scattering theory, starting from a short review of local density functional theories, the properties of Schrodinger and Dirac Hamiltonians for a central field, and resolvents and Green functions. Throughout this book, both ordered and disordered systems are considered, as well as non-relativistic and relativistic schemes. Also discussed are the direct applications of multiple scattering to important aspects of modern materials science, such as band structure spectroscopy (XES, XPS, ARUPS, AES), to Fermi energy related properties (specific heat, electron-phonon enhancement, nuclear spin lattice relaxation, conductivity), and the present understanding of magnetic systems.
Local Density Functional Theories
Authors: Weinberger P
Published: November 2023

Density functional theory forms the basis of most modern solid-state calculations. What started as a phenomenological suggestion to replace the non-local operators in the Hartree-Fock method by local quantities became a formally rigorous approach to deal with the n electron problem. Density functional theory now covers quite a few new aspects of this problem, such as applications to magnetic systems, relativistic corrections, extensions to finite temperatures. Last, but not least, its own ‘formal language’ moved into the area of ‘traditional’ mathematical physics. Since density functional theory itself is a very active field of research, its discussion in the following few sections has necessarily to be somewhat incomplete and is therefore restricted to a presentation of its main concepts. In order to facilitate easy access to the original literature the notation used follows closely the notation in the literature.
Multiple Scattering Theory For Disordered Systems-The Coherent Potential Approximation
Authors: Weinberger P
Published: November 2023

The theoretical methods discussed in the previous chapter are, perhaps with the exception of real space scattering (eqns (6.39) and (6.54)), restricted to ordered matter, i.e. to systems with well defined two- or three-dimensional translational symmetry (eqns (6.59) and (6.100)). Quite frequently, however, one has to deal with the physical properties of disordered solids, in particular with those of substitutional alloys or of solid solutions. A typical binary alloy, for example, does not usually have long-range order, which is characteristic for intermetallic compounds, nor arc the components of the alloy distributed completely at random-even substitutional solid solutions show a certain degree of short-range order.
Applications Of Multiple Scattering I: Band Structure Spectroscopy
Authors: Weinberger P
Published: November 2023

It was stated in Chapter 2, on local density functional theories, that strictly speaking the Kohn-Sham eigenvalues do not have the physical meaning of excitation energies. However, in as much as this statement has to be kept in mind, there seems to be no alternative to using local density functional approaches for a ‘realistic’ description and interpretation of valence band spectra. This is particularly the case for all those spectroscopies, such as angle-resolved photocmission, which rely heavily on theoretical interpretations. Nowadays, one major application of band theory for ordered and disordered systems is band structure spectroscopy. In this chapter, therefore, some of the most important spectroscopies will be discussed in terms of the now familiar scattering approach.
Spin Waves In The Ferromagnetic Heavy Rare Earths
Authors: Jensen Jens , Mackintosh Allan R
Published: November 2023

As discussed in Section 1.5, the exchange interaction dominates the magnetic behaviour of the heavy rare earth metals, and the ordered moments at low temperatures are consequently close to the saturation values. The excitations of such a system are spin waves, which may be viewed semi-classically as coupled precessions of the moments about their equilibrium directions, with well-defined frequencies which are determined by the phase relations between the precessing moments on different sites. From the viewpoint of quantum mechanics, these modes are magnons, which are linear combinations of single-ion excitations from the ground state to the first excited molecular-field state, which is to a good approximation | Jz = J − l >, with phase factors between the coefficients for different ions which determine the dispersion relation Eq for the magnon energy. A useful review of the excitations of magnetic systems has been given by Stirling and McEwen (1987).
Instabilities and Chaos in Quantum Optics: Semi-Classical Theory
Authors: Pike frs E R , Sarkar Sarben
Published: November 2023

The theoretical description of radiation − matter interactions in terms of master equations can be approximated by a semi-classical theory when quantum fluctuations are small. This approach, the exact definition of which will emerge later, has been enormously influential in understanding instabilities and chaos in quantum optics. Although much of the theory (and experiment) has been done only in the last few years, there were already indications in the early experiments on ruby lasers of ‘spiky’ behaviour. Instabilities are often due to competition between different modes which are coupled together non-linearly. Consequently we will first describe qualitatively the modes that are important when we deal with optical systems in Fabry-Perot or ring cavities.
Fokker − Planck Equations: Quantum Fluctuations
Authors: Pike frs E R , Sarkar Sarben
Published: November 2023

In the last chapter we examined the small-fluctuation limit of the master equation. However, we were not able to be very precise about what we meant by ‘small’. Although it is clear that approximations such as (8.9) would be unacceptable if fluctuations were large, their domain of validity still needs to be understood. Intuitively reasonable approximations are easy to state. A rather different approximation, for example, from the semi-classical approach is to replace the discrete structure of ℱm (cf. Exercise 7.3) by a smooth envelope. This smoothing is equivalent to a finite truncation of the operator is an extensive variable this truncation may seem a very acceptable thing to do. However, the derivative acting on P may bring down a quantity which too has some extensive properties and so we would need to examine P before we could be sure that a certain truncation was reasonable. These concerns have been expressed clearly in some classic work by van Kampen (1981) which suggests a framework for a quantitative study of such questions. One of the major successes of the theory of quantum fluctuations is the understanding of photon statistics. Moreover, we can determine how quantum fluctuations modify the chaos and instabilities found in the last chapter.
Surface Electronic Transport Phenomena Semiconductors
Authors: Dobrovolsky V N , Litovchenko V G
Published: November 2023

Layered metal-insulator-semiconductor microstructures have become an important research area in semiconductor microelectronics. New devices utilize phenomena occuring at or near the semiconductor surface directly. This monograph provides a survey of the diverse experimental and theoretical results for electron and hole transport in surface and subsurface regions of semiconductors, with an emphasis on the mechanisms involved and special measurement procedures necessary, for example in Hall current measurements. This English edition has been substantially revised and updated from the original Russian edition.
Hall effect and magnetoresistance
Authors: Dobrovolsky V N , Litovchenko V G
Published: November 2023

The present chapter is mainly concerned with the Hall effect applied extensively in experimental studies of charge carrier scattering and transport. In the previous chapter the charge carrier mobilities at the surface were assumed to be the same as in the bulk. However, surface scattering suppresses carrier mobility.
Energy quantization and electron and hole transport in surface channels
Authors: Dobrovolsky V N , Litovchenko V G
Published: November 2023

If the thickness of a surface channel is comparable or smaller than the electron (or hole) wavelength, quantum size effects become observable there. Such effects were first studied theoretically by Lifshitz and Kosevitch (1953) and then experimentally by Ogrin et al. (1966) in thin films. Schrieffer (1957) was the first to discuss electron energy quantization in a surface SCR of a semiconductor. The beginning of intensive investigations of quantum effects in surface channels of semiconductors dates to the mid-sixties when Fowler et al. (1966) proved that a two-dimensional gas of charge carriers could be realized near a semiconductor surface.
Computer Experiments
Authors: Cloizeaux Jacques des , Jannink Gerard
Published: November 2023

Computer experiments have in the past been one of the best available sources of information concerning the experimental values of the critical exponents. Many of these computations were performed from 1955 to 1970 by English and American physicists. The polymers are simulated by chains constructed on lattices with the help of computers.
Osmotic Pressure and Density
Authors: Cloizeaux Jacques des , Jannink Gerard
Published: November 2023

In the past, the basic experiment used to study the general properties of solutions was the measurement of the vapour pressure lowering of the solvent (Raoult 1890). But this method which is, in general, efficient is not really useful when the vapour pressure reduction is small. In such situations, it has been replaced by another method which is quite similar: it consists in measuring the osmotic pressure of the solution with respect to the solvent.
Feynman diagrams
Authors: Gastmans R , Wu Tai Tsun
Published: November 2023

It’s nevertheless an endless mess before one can assess Nature’s inventiveness. A Feynman diagram [l] is a graphical representation of the amplitude for a given process. It is composed of three types of elements: external lines, internal lines and vertices. With everyone of these elements one associates a mathematical expression, and the product of these expressions, in an appropriate order (together with some overall factors), yields the amplitude.The Feynman rules tell us which mathematical expression is to be associated with a given element of the Feynman diagram.
Single Bremsstrahlung in QED
Authors: Gastmans R , Wu Tai Tsun
Published: November 2023

It’s the electron’s plight to send out light. To predict this sight is within our might. Consider the process of electron-positron annihilation into three photons, where the four-momenta of the particles are given in the parentheses.
Double Bremsstrahlung
Authors: Gastmans R , Wu Tai Tsun
Published: November 2023

Double bremsstrahlung processes in QED, such as e+e-  →  γ  γ  γ  γ, e+e-  → μ+  μ- γ  γ ande+e-  → e+e- γ γ, are of interest for several reasons. They have all been observed in experiments and provide high energy QED tests of order α4 [28]. The agreement between theory and experiment for the process e+ e-→ μ+ μ-  γ  γ has been widely used to set lower limits on the mass of the excited muon. This was done both at PEP [29] at GeV and at PETRA [30] at higher energies. It is also not inconceivable that the effects of this process have to be taken into account if the accuracy of the charge asymmetry measurements in e+ e-→ μ+ μ- continues to increase. Finally, the process e+ e-→ μ+ μ- γ γgives an a4 contribution to small angle Bhabha scattering, which is generally used to determine the beam luminosity of e+ecolliders [28].
Introduction
Authors: Rubinstein Michael , Colby Ralph H
Published: November 2023

Much of human history has been influenced by the availability of materials. In fact, history is divided into eras named after the primary materials used; the Stone Age, the Bronze Age, and the Iron Age. Similarly, we can assert that in the twentieth century we entered the Polymer Age. Humans have used naturally occurring polymers, called biopolymers, for centuries without realizing that they were dealing with macro-molecules. A prime example is caoutchouc, or natural rubber, that comes from Hevea brasiliensis, the rubber-tree plant. Natural rubber was used for many centuries before it was identified as polymeric.
Networks and gels
Authors: Rubinstein Michael , Colby Ralph H
Published: November 2023

When the crosslinking reactions of Chapter 6 are driven far beyond the gel point, nearly all species are attached to the gel in a single macroscopic network polymer. Such networks, with either chemical or strong physical bonds, are important soft solids. If the glass transition and melting temperatures are below room temperature, the material is a rubber. Rubbers are an important class of materials with many practical uses. Common examples are rubber bands, gaskets, adhesives, and automobile tires. Rubber bands can be stretched enormous amounts without breaking or even losing their elasticity. In this chapter, the physics that allow for such marvellous properties will be considered in detail. The entropic nature of elasticity in rubbers is the origin of their remarkable mechanical properties.