bluuebunny/crossref_metadata_2025 huggingface dataset:
The effect of air-drag on the descent of bodies
Authors: Chandrasekhar S
Published: November 2023

In Propositions XV and XVI, Newton formulates a problem on the effect of air-drag on the descent of bodies under centripetal attraction. As a prelude to Newton’s method of solution, we shall state the problem simply and provide the solution as one might today.
The kinematics of fluids
Authors: Guyon Etienne , Hulin Jean-Pierre , Petit Luc , Mitescu Catalin D
Published: November 2023

This chapter covers the study of the motion of a fluid including, in particular, the analysis of its deformations (or strains), without concerning itself with the origin of these strains, which is discussed in Chapter 4. We start by indicating the methods used to characterize the motion of the fluid (Section 3.1)-the definition of the velocity of a particle of fluid, the Eulerian and Lagrangian descriptions, the acceleration and paths characteristic of a flow-and then we analyse (in Section 3.2) the strains in the fluid.
Electronic States In High Magnetic Fields
Authors: Miura Noboru
Published: November 2023

In this chapter, we overview the electronic states in high magnetic fields for mobile electrons and bound electrons. This provides an important basis for understanding the contents of the subsequent chapters. Readers who are already familiar with these basics can skip this chapter and jump to Chapter 3.
Magneto-Optical Spectroscopy
Authors: Miura Noboru
Published: November 2023

When electromagnetic radiation is incident upon a semiconductor, the radiation is absorbed when the photon energy of the radiation exceeds the band gap, as electrons in the valence band are subjected to a transition to the conduction band. The absorption coefficient is expressed by the same formula as (4.21) based on the transition probability.
Experimental Techniques for High Magnetic Fields
Authors: Miura Noboru
Published: November 2023

In this chapter, we describe key aspects of experimental techniques, particularly those for generating pulsed high magnetic fields and for measurements of solid state physics.
General References
Authors: Miura Noboru
Published: November 2023

Many excellent books have been published on the physics of semiconductors, and the science and technology of high magnetic fields. Here, we list only typical useful books related to the topics discussed in this book. Some of them are now rather old, but still very useful.
Synchrotron radiation and electromagnetic waves
Authors: Duke Philip John
Published: November 2023

Synchrotron radiation was first observed in 1947 and began to be used as a research tool in the mid-l960s. The first synchrotron radiation sources were low energy (several hundred MeV) electron accelerators which were also used for nuclear and particle physics. It was quickly realized that the needs of the growing number of people who used synchrotron radiation for their research required dedicated sources of radiation. Many of these research programmes required X-radiation, which pointed to the need for these sources to accelerate electrons to GeV energies in order to provide a useful output of X-rays as well as lower energy radiation. The first such dedicated X-ray source was the SRS (Synchrotron Radiation Source) at the Daresbury Laboratory in the UK, which operates at 2 GeV electron energy. The SRS did not retain its unique status for long. The NSLS (National Synchrotron Light Source) at Brookhaven, USA and the Photon Factory, Tsukuba, Japan quickly followed. There were similar developments in the then USSR; initially at Akademgorodok, Novosibirsk, and later in Moscow. The most recent advances have included the construction and operation of large scale facilities at Grenoble, France (ESRE 6 GeV) Argonne, USA (APS, 7 GeV) and Nishi-Harima, Japan (SPring-8, 8 GeV).
Radiation from moving electrons
Authors: Duke Philip John
Published: November 2023

Electromagnetic waves in free space—no electric charges or currents In Chapter 2 we showed that Maxwell’s equations for the electromagnetic field could be rearranged as two equations which described the progress of an electric and a magnetic field throughout the whole of space and time at a speed which experiment showed was equal to the speed of light. We call these two waves electromagnetic radiation. Let us consider their properties.
Introduction to electron storage rings
Authors: Duke Philip John
Published: November 2023

Principles of operation The development of circular (or approximately circular) electron storage rings has been essential for the construction and utilization of synchrotron radiation sources. These machines have evolved from the first cyclotron, constructed by Ernest Orlando Lawrence (1901-58) at the Berkeley campus of the University of California in 1932, to the massive complexes operating or under construction at present-day research centres. A brief historical survey has been compiled by Wiedemann.
Synchrotron radiation from electron storage rings
Authors: Duke Philip John
Published: November 2023

Description of the electron beam At any point in the storage ring, an electron can be described in terms of its position, its direction of motion, and its energy. It is convenient to measure these quantities relative to the ideal electron orbit. If we imagine a coordinate system as shown in Fig. 9.1 then at any given instant, any individual electron will be located at a point (x, y) in an x−y plane which intersects the ideal orbit at a point P, located at a distance s measured along the ideal orbit from some arbitrary starting point s0. This coordinate frame must be imagined as moving around the ideal orbit, so that, relative to an observer in the laboratory, the coordinate axes s and x(which with y, form a set of mutually perpendicular coordinate axes) change their direction in space as the electron moves around the storage ring. The advantage of this coordinate system is that it enables us to describe the movement of the electron in position and time relative to the ideal orbit as though the ideal orbit were a straight line.
Insertion devices—wigglers
Authors: Duke Philip John
Published: November 2023

Insertion devices are a general term for a range of magnetic elements which can be added to a storage ring (or designed in from the beginning). They are designed to provide radiation whose characteristics are enhanced compared with that available from the dipole magnets. The insertion device is placed in a drift space between the existing magnets of the storage ring. There are two principal types of such devices—the multipole wiggler and the undulator which are illustrated and compared with the dipole source in Fig. 13.1. Synchrotron radiation from dipole magnets has many desirable characteristics and the aim of the insertion device is to improve on these. These improvements are best described with reference to Table 13.1.
Insertion devices—undulators
Authors: Duke Philip John
Published: November 2023

Multipole wigglers have, in general, high magnetic fields and large K values. They are used to augment or enhance the synchrotron radiation spectrum at high photon energy. Undulators represent a logical extension of the multipole wiggler towards lower magnetic fields, more magnetic poles, and shorter magnetic wavelengths (see Fig. 13.1 ). These devices are designed with K values of the order of unity and operate in a completely different way to wigglers with large K. When K≈1 the maximum deflection angle of the electrons is of the same order as the angle of production of the radiation and the photons are emitted in a narrow forward cone.
Flux-Jumping In Superconductive Filaments And Composites; Stability Criteria
Authors: Asner Fred M
Published: November 2023

The emergence of hard Type-II superconductors, once their behaviour and mechanism had been understood—see Chapter 2—raised considerable expectations as to their application in different domains. Increased performance and savings were expected from the use of high magnetic fields such as reduced energy losses in the excitation windings of electrical transformers and machines, smaller running costs and devices of reduced size, compared to ‘classical’ ones. When by the early 1960s the first technical super-conductors became available in the form of NbTi wires of 100—250 mm diameter and of Nb3Sn tapes of∼ 0.1 mm thickness, the obtained performances were disappointing; the test coils either failed at currents and magnetic fields well below the critical values or exhibited considerable training, a large number of quenches before approaching nominal performance.
The Quenching Process In Superconducting Magnets And Their Protection
Authors: Asner Fred M
Published: November 2023

The transition from the superconductive to the normal state in superconducting magnets and their protection from possible serious consequences of the quenching process have been investigated since the early development of superconducting coils. It has been demonstrated that the electromagnetic and mechanical energies stored in the magnet coils and released during a quench could seriously damage or even destroy them, unless adequate quench protection schemes and devices are implemented. With the recent development of large-size superconducting magnets wound with high jc, and high field superconductors of high energy density, the problem of protecting individual or strings of magnets has grown in complexity. With the emergence of large superconductive magnet systems in particle accelerators and colliders one had to extend the notion of quench protection of a single magnet to a string of interconnected magnets. The quenching process and the quench protection analysis comprise a large number of magnet components, which can be divided into internal and external elements.
Winding Configurations For Superconducting Accelerator Magnets
Authors: Asner Fred M
Published: November 2023

In the preceding chapter on transverse beam dynamics examples of classical 2n-pole magnets for particle accelerators have been given. The steady development and improvement of technical superconductors of high jc and B as described in Chapter 5, led to a vigorous development of superconducting magnets for accelerators and colliders; an energy increase by a factor of 4-5 could be achieved solely by increasing B. A number of successfully operating accelerators and colliders like the I GeV Tevatron in the USA and the 800 GeV HERA in Germany were built and the design and construction of the ambitious project of the 7 TeV—7 TeV hadron collider LHC of CERN is under way.
High Field Solenoids And Detector Magnets
Authors: Asner Fred M
Published: November 2023

High field solenoidal magnets or solenoids belong to the second large group of superconducting high field magnets to be treated in this book. In fact, solenoids were the first devices to be wound and tested since the emergence of technical superconductors, which started with the development of Nb3Sn wires by Kunzler et al. in 1951 [1]. Solenoids are still efficient devices for the testing of technical superconductors and for the verification of specific coil winding techniques.
Magnetic Measurements Of Superconducting Magnets
Authors: Asner Fred M
Published: November 2023

The history of magnetic measurements coincides with the discovery of electromagnetism during the first half of the nineteenth century, notably of the laws related to electromagnetic induction by M. Faraday in 1831. If the measuring methods remained to a large extent unchanged, the measuring equipment has been steadily improved due to constant progress in new and better materials, precision mechanics, fast electronics, and computers. In this chapter we shall concentrate on high precision magnetic field (or induction) measurements of superconducting accelerator and large detector magnets, on the comparison of different measuring methods, and on the requirements the measuring equipment should satisfy. Error sources and their compensation will also be discussed. Although important to the magnet design, transient magnetic field measurements will not be dealt with.
Physics of Ferromagnetism
Authors: Chikazumi Sōshin , Graham, Jr C D
Published: November 2023

This textbook offers students and researchers an overview of the physical aspects of ferromagnetism. It emphasizes the explanations of physical concepts rather than rigorous theoretical treatments that require a more advanced background than is assumed here. The book includes recent developments and techniques in magnetics, and describes magnetic phenomena and engineering applications in magnetism.
Dynamic Magnetization Processes
Authors: Chikazumi Sōshin , Graham, Jr C D
Published: November 2023

In this section we treat time-dependent magnetization processes. These processes become particularly important when the magnetization must change rapidly, as in high-frequency or pulsed fields.
Low-dimensional physics
Authors: Kelly M J
Published: November 2023

In this chapter we introduce some of the key new physics principles that have dominated semiconductor physics research in the last two decades, namely the concepts associated with low-dimensional systems, i.e. systems that exhibit properties associated with less than three spatial dimensions. However, we start with an introduction to some of the length scales that are relevant to modem solid state physics. An appreciation of these length scales is an important prerequisite to a more detailed understanding of the new physics and when it is likely to apply in practice. Figure 4.1 shows, on a logarithmic scale extending over six orders of magnitude between 0.1 nm and 0.1 mm, an indication of lengths associated with a number of phenomena that occur in physics, technology, or everyday life.
Mesoscopic phenomena and Coulomb blockade
Authors: Kelly M J
Published: November 2023

In Chapters 6 and 11 we encountered structures in which there were very few free and mobile carriers. Certainly, the usual condition for statistical averaging, namely that the number N of particles satisfies 1 < < N < < N, is violated. In this chapter, we concentrate on the physics of few-carrier systems, assuming that the fabrication and measurement techniques are those already described. The physics contains a number of new aspects, and their investigation is far from complete. Many new effects appear undesirable in terms of eventual device applications, while others are being proposed as the basis for radically new device technologies. The term mesoscopic (meso=middle) has been introduced to describe those systems that are neither microscopic (one or a few atoms) nor macroscopic. In practice, we shall always be dealing with structures whose volume might be several tens of nanometres on each side, but which contain only a few carriers taking part in the relevant transport or optical processes. Until now, our discussion has concentrated on the wave . nature of electron transport behaviour and not on its charge nature. The capacitances encountered in these small structures are so small that the energy to charge a structure with even a single electron is such that e2!2C > k T, and charge transfer into and out of the structure can be inhibited by this inequality, which is known as the Coulomb blockade.
Introduction
Authors: Ripka Georges
Published: November 2023

The hadronic structure of the vacuum is governed by low-energy non-perturbative QCD and it determines the effective interactions of quarks, propagating in the vacuum. We have but scanty knowledge of the vacuum structure. We do, however, know the symmetries of the effective interactions, because they reflect the observed symmetries of the strong interactions (chapter 2). Symmetry is not sufficient to determine the effective quark interactions and additional assumptions are required to model them. Most of the effective interactions which have been used are inspired either by gluon exchange or by an assumed instanton structure of the vacuum. In some channels the two are similar but in other channels they differ significantly. They are described and compared in chapter 3.
Symmetry Conserving Approximations
Authors: Ripka Georges
Published: November 2023

The one-loop approximation (7.34) of the effective action is but one of several symmetry conserving approximations. Other forms of symmetry conserving approximations exist which are briefly reviewed in this chapter. They were developed in the 1960s [101, 102]. For a review see [42]. Symmetry conserving approximations are conveniently be expressed in terms of Feynman graphs which have specific irreducibility properties. They proceed by expressing the partition function as a functional, either of the fields as in the effective action formalism, or of the quark propagators as explained in section 8.7. The self-energy of the quark propagator is then defined by the stationary point of the functional. When a symmetry of the action (typically chiral symmetry) is spontaneously broken by the self-energy, the correlation function acquires a pole at q2= 0 which corresponds to a zero mass Goldstone boson. Symmetry conserving approximations ensure that the existence of the Goldstone boson is maintained at any level of approximation.
Intrinsic Magnetic Properties
Authors: Franse J J M , Radwański R J
Published: November 2023

This chapter focuses on the intrinsic magnetic properties of iron-rich rare-earth intermetallics. We are concerned with rare-earth metals R where the magnetic properties of the ion cores are well defined; the 4f level lies deep below the Fermi energy, and hybridization with the conduction-band electron states is negligible. This situation is realized for most iron and cobalt-based compounds with 4f elements, with the exception of some Ce compounds that exhibit anomalies which can be ascribed to a mixed-valence state of the cerium atom. The emphasis here is on R2Fe14B compounds and on Nd2Fe14B in particular, although other RnTm series are discussed as well. The Nd2Fe14B family is rather extended. Isomorphous iron compounds exist for almost the whole rare-earth series, including Y and The, while isomorphous cobalt compounds exist for most of the light rare-earth elements and for Gd and Tb. Likewise, there are extended isomorphous series for rare-earth iron compounds with 2 : 17 and 1 : 12 structures.
Phase relations
Authors: Knoch K G
Published: November 2023

Metallurgical phase diagrams illustrate which phases coexist in equilibrium at a particular temperature and elemental composition. Knowledge of phase equilibria is important for an understanding of the processes taking place during casting, sintering and annealing of alloys for permanent magnets, and the resulting microstructures. Systems of most interest here are the binaries R-Fe, R = Pr, Nd or Sm, ternaries, especially Nd-Fe-B, and quaternary and higher systems where additional elements are incorporated in an effort to improve magnetic properties, corrosion resistance and processability.
Magnet processing
Authors: Harris I R
Published: November 2023

Unlike their predecessors based on Sm-Co, the Nd-Fe-B alloys can be processed into permanent magnets by many different routes. The most important group of processing routes consists of variants of powder metallurgy, where monocrystalline powder with grains a few microns in size is oriented and sintered to yield a uniform, fine grain structure with a high degree of c-axis orientation, where each grain is isolated from its neighbours by Nd-rich grain boundary phases. Such a microstructure is necessary to achieve the greatest energy product for a particular magnet composition. A second group of processes yield polycrystalline powder or flakes composed of many submicron crystallites which are isotropic, or at best imperfectly oriented. Melt-spinning is used to make this material industrially, and it is particularly suitable for bonded magnets. A third type of process avoids the use of powders by hot-working cast ingots to achieve an appropriate microstructure with a high degree of c-axis orientation in relatively simple shapes such as arc segments.
Magnetomechanical devices
Authors: Yonnet J –P
Published: November 2023

The forces acting between permanent magnets are exploited in magnetic bearings, magnetic couplings and holding devices. For all these applications, the effects (force, torque) depend quadratically on the polarization of the magnet J. If a coupling is designed with SmCos magnets (J = 0.9 T), then replacing the magnets by Nd-Fe-B (J = 1.3 T), the torque is more than doubled. Magnetomechanical devices need high-polarization magnets. Moreover, these devices very often use repulsion forces between the magnets. The polarization must remain constant, even in a large reverse field. The coercive field must be high. Rare-earth iron permanent magnets are frequently the most suitable.
The diffraction of light
Authors: Akhmanov S A , Nikitin S YU
Published: November 2023

Diffraction as evidence of the wave nature of light-fundamental experimental facts. Grimaldi’s experiment. The Huygens principle. The Huygens-Fresnel principle. Fresnel’s diffraction integral. Fresnel zones. Graphical construction of diffraction patterns. Edge diffraction. The diffraction length of an optical beam. Near- and far-field zones of diffraction. The diffraction divergence of a beam in the far-field zone. The focusing of light as a diffraction phenomenon. Kirchhoff’s diffraction theory.
The analysis, transformation, and synthesis of optical fields
Authors: Akhmanov S A , Nikitin S YU
Published: November 2023

The spectral description of the spatial structure of the field. The lens as an element performing Fourier’s spatial transformation. Optical image formation and Abbe’s theory. Porter’s experiments. The dark-field technique. The phase-contrast technique. The resolving power of a microscope and telescope. Holography: the recording and reconstruction of optical fields. The diffraction grating and the Fabry-Perot interferometer as spectroscopic instruments. Fourier spectroscopy. Light-beat spectroscopy.
Optics of anisotropic media
Authors: Akhmanov S A , Nikitin S YU
Published: November 2023

Anisotropic materials and the basic effects of crystal optics. The structure of an optical wave in an anisotropic crystal. The material equation of an anisotropic medium. Classification of crystals. The polarization eigenstates of an optical wave in an anisotropic crystal. Ordinary and extraordinary waves. Optical birefringence at the anisotropic medium boundary. The production and analysis of polarized light. The interference of polarized rays. Induced anisotropy.
Theoretical non-linear optics
Authors: Akhmanov S A , Nikitin S YU
Published: November 2023

Optical second-harmonic generation. Stimulated Raman scattering. Self-focusing of light. The theory of non-linear optical effects is based on Maxwell’s equations and the material equations. From Maxwell’s equations one can obtain the wave equation (see Chapter 22).
Introduction
Authors: Newman M E J , Barkema G T
Published: November 2023

This book is about the use of computers to solve problems in statistical physics. In particular, it is about Monte Carlo methods, which form the largest and most important class of numerical methods used for solving statistical physics problems. In this opening chapter of the book we look first at what we mean by statistical physics, giving a brief overview of the discipline we call statistical mechanics. Whole books have been written on statistical mechanics, and our synopsis takes only a few pages, so we must necessarily deal only with the very basics of the subject. We are assuming that these basics are actually already familiar to you, but writing them down here will give us a chance to bring back to mind some of the ideas that are most relevant to the study of Monte Carlo methods. In this chapter we also look at some of the difficulties associated with solving problems in statistical physics using a computer, and outline what Monte Carlo techniques are, and why they are useful. In the last section of the chapter, purely for fun, we give a brief synopsis of the history of computational physics and Monte Carlo methods.
Femtosecond Time-Resolved Linear and Second-Order Reflectivity of Metals
Authors: Hohlfeld J
Published: November 2023

Second harmonic generation (SHG) in reflection off surfaces is a background free technique that offers several advantages, covered by an extensive literature that cannot all he cited here. We only want to recall some features of the technique and quote a few selected examples from the literature.
Single crystal diffraction
Authors: Willis B T M , Carlile C J
Published: November 2023

In this chapter, we consider nuclear Bragg scattering from single crystals and in the next chapter the same type of scattering from poly- crystalline materials. If the sample contains unpaired electrons, as in the elements of the first transition series with incomplete 3d electronic shells, then there is also magnetic scattering. We shall consider magnetic neutron diffraction in Chapter 9.
Dielectric description of cold plasma
Authors: Dendy R O
Published: November 2023

The macroscopic response of any medium to an applied electric field is determined by the sum of the microscopic responses of the individual particles that make up the medium. In a conducting medium, the macroscopic response is determined at a microscopic level by the separation between positive and negative charges that is produced by the applied electric field. If the applied field varies with time, so too will the microscopic state of the medium: the separation between the positive and negative charges will change with time, as will the electric field that is produced by their separation. Thus, particle currents and displacement currents are produced.
Kinetic description of plasma
Authors: Dendy R O
Published: November 2023

Let us first look back at the different approaches that we have used for describing plasmas. After emphasizing the collective nature of plasma behaviour in Chapter 1, we considered the dynamics of single particles in Chapter 2. In order to achieve a collective description, we needed to sum the effects of single-particle dynamics for all the particles in the plasma. This summation was carried out in a simplistic, but nevertheless successful, way at eqn (3.21). By considering the current created by the sum of the individual electron velocities, we constructed the dielectric tensor of the plasma. This tensor was then employed in Maxwell's equations to yield the normal modes of the plasma. By including the contribution of the ions, this approach was extended to low frequencies.
Undulators and Free-electron Lasers
Authors: Luchini P , Motz H
Published: November 2023

This book is a reference text for all those working in free-electron laser research as well as being a learning aid for physicists and graduate students who wish an introduction to this field. Only a basic understanding of relativistic mechanics and electromagnetism is presupposed. After an overview of early developments and general principles of operation, the different models that can be used to describe free-electron lasers are presented, organized according to their range of applicability. The relevent conceptual and mathematical constructs are built up from first principles with attention to obtaining the practically important results in a simple but rigorous way. Interaction of the undulator with the driving electron accelerator and the laser cavity and design of undulator magnets are treated and an overview is given of some typical experiments.
Introduction
Authors: Kamimura Hiroshi , Aoki Hideo
Published: November 2023

The last 10 years have witnessed a remarkable development in the physics of disordered systems and, although the field is still in the process of rapid growth, it is worthwhile giving a theoretical overview of the field. In this book we have tried to describe what makes the physics of disordered systems so special in the realm of solid-state physics.
Cluster Calculations For Interacting Electron Systems
Authors: Kamimura Hiroshi , Aoki Hideo
Published: November 2023

To examine the interplay between disorder and electron-electron interactions, we can either formulate an approximate theory for infinite systems or perform a numerical simulation for finite systems. The advantage of the latter approach is that the method, although limited to systems of small sizes, can be derived from first principles. From this viewpoint, a computer simulation has been performed by Takemori and Kamimura (1983a,b) for finite clusters of donors. The calculation is performed for clusters, each of which contains six donors located randomly in space, with electron-electron interactions taken fully into account. The calculation for each donor concentration is carried out for an ensemble of samples with different geometrical configurations of donors. Although the cluster size is quite small, this does not cause serious limitations because, for the concentrations considered here, the localization length is of the order of the average donor separation and does not exceed the sample diameter. By examining electron configurations and wavefunctions, the validity of the picture presented in Chapter 4 can be confirmed. The electronic specific heat and spin susceptibility have also been obtained for comparison with the experimental results for Si: P.
Renormalization Approach For Disordered Electron Systems
Authors: Kamimura Hiroshi , Aoki Hideo
Published: November 2023

We have seen that disordered systems give rise to a host of interesting effects related to the localization of states. Thus, from the outset we have explicitly to take account of the localization in the theoretical framework, which makes computer experiments on finite systems an important first-principles method. This situation immediately poses several essential questions, such as: (i) how can the properties of macroscopic systems be deduced from the results for finite systems; and (ii) how can the concept of Anderson localization be extended to disordered systems with electron-electron interactions in a numerical model in which disorder and electron correlation are treated on an equal footing? In this chapter we address these questions. In this section we introduce the concept of renormalization for disordered systems. Specifically, we examine real-space renormalization schemes.
Two-Dimensional Disordered Systems
Authors: Kamimura Hiroshi , Aoki Hideo
Published: November 2023

In the physics of disordered systems, two-dimensional (2D) systems have attracted very special interest. The reasons for this include:
Defects And Textures In Nematics
Authors: Gennes P G De , Prost J
Published: November 2023

In Chapter 3 we restricted our attention to distortions of the nematic arrangement that involved continuous variations of the director n(r). But there are other, important, physical situations where n(r) is not a smooth function of r at all points. Two current examples are described below.
Cholesterics
Authors: Gennes P G De , Prost J
Published: November 2023

The helical arrangement characteristic of the cholesteric phase has been presented in Chapter 1. In this ideal state the director n(r) varies in space according to the law where we have taken the helical axis along z. A cholesteric single crystal, described by eqns (6.1) and (6.2), can often be obtained in thin slabs (thickness d in the 100 µm range) provided that the boundary conditions on both sides of the slab are tangential. The configuration is represented in Fig. 6.1; it is usually called the ‘planar texture’ or ‘Grandjean texture’. Typical examples include the following.
Phase Transitions In Smectics
Authors: Gennes P G De , Prost J
Published: November 2023

Over the last 20 years there has been a considerable effort put into understanding the physics of phase transitions in liquid crystals. The main reason is probably that statistical mechanics has seemed ready to provide a comprehensive view of the successive phase changes that lead from liquids to crystals. This goal is almost reached, but not quite.
Introduction And Relationships Of The Group
Authors: Weinberger P
Published: November 2023

There are quite a few in the solid-state community who would call all those performing electronic structure calculations ‘quantum engineers’. On the other hand, there are also many who claim that, with the arrival of the age of fast computers, the traditional structure of solid-state physics has changed substantially. They claim that 'computational physics' nowadays is an increasingly important part of solid-state physics. Irrespective of whether one uses the expression ‘quantum engineering’ or ‘computational physics', there is no doubt that the emphasis of theoretical investigations concerning electronic properties of solid matter has shifted considerably towards direct calculations of physical observables and problems of materials science. Although perhaps ab initio calculations of phase diagrams in a routine manner are yet to come, the incorporation of surfaces, non-stoichiometry, and disorder is no longer a severe computational obstacle.
Resolvents And Green Functions
Authors: Weinberger P
Published: November 2023

In this chapter the basic properties of resolvents and of Green functions are briefly reviewed. These properties are the formal basis of scattering theory to be discussed in the following chapters. Since no use will be made of time-dependent schemes later on, only time-independent (stationary) properties are considered here. For a treatment of timedependent schemes the reader is referred to Economou (1979) or Taylor (1972).
Spectral Densities
Authors: Weinberger P
Published: November 2023

The previous two chapters were devoted entirely to the concept of multiple scattering, the concept of structure constants, and approximations dealing with the problem of disorder. Since the same formal language was used for both ordered and disordered systems, it is now comparatively easy to discuss spectral densities quite generally. A spectral density is defined in terms of the imaginary part of a representation of a given resolvent. The configuration space representation of the resolvent of the (one-electron) Hamiltonian (see also Chapter 4), for example, yields the (second-order) Dirac density matrix γ(r, r′, ϵ).
Some Illustrations
Authors: Weinberger P
Published: November 2023

This chapter will illustrate the various theoretical concepts discussed in the previous three chapters. Here, results mostly for disordered systems will be presented. mainly because over the past two decades the solid state community has become very familiar with bands, densities of states, charge density contour maps, etc. for ordered systems. whereas the special features of disordered systems are perhaps not so well known.
Magnetic Structures
Authors: Jensen Jens , Mackintosh Allan R
Published: November 2023

The mean-field theory introduced in the previous section is used in this chapter as a basis for examining some of the magnetic structures assumed by the rare earth metals. The theory is presented at length in the first section. Beginning with the expression for the free energy, some general results are established for the magnetization, and applied analytically to the calculation of the susceptibility in the high-temperature limit. The mean-field approximation is then developed, and a numerical method for solving the resulting equations self-consistently, for magnetic structures which are commensurable with the lattice, is described. The Landau expansion of the free energy in terms of the order parameters of the magnetic system provides the starting point for a discussion of a number of the periodic magnetic structures which arise as a result of the long range of the indirect-exchange interaction. The ordering temperatures are calculated by analytical means, and the relative stability of different structures compared. In the following section, the important extension by Callen and Callen of the Zener power-law for the temperature dependence of the magnetic anisotropy is derived.
Linear Response Theory
Authors: Jensen Jens , Mackintosh Allan R
Published: November 2023

This chapter is devoted to a concise presentation of linear response theory, which provides a general framework for analysing the dynamical properties of a condensed-matter system close to thermal equilibrium. The dynamical processes may either be spontaneous fluctuations, or due to external perturbations, and these two kinds of phenomena are interrelated. Accounts of linear response theory may be found in many books, for example, des Cloizeaux (1968), Marshall and Lovesey (1971), and Lovesey (1986), but because of its importance in our treatment of magnetic excitations in rare earth systems and their detection by inelastic neutron scattering, the theory is presented below in adequate detail to form a basis for our later discussion.
The Quantum Theory of Radiation
Authors: Pike frs E R , Sarkar Sarben
Published: November 2023

This book is unique in covering phenomena in photon- matter interactions in a unified way over a range of many orders in energy. The quantum field theoretic approach to the fully relativistic theory of quantum electrodynamics (QED) is presented together with the non- relativistic theory in both confined and unconfined geometries. The predictions of QED have been verified to a greater accuracy than any other physical theory. Moreover QED is a paradigm for other gauge theories and is presented in such a way that the generalisation to other gauge theories is natural. Gauge and Poincare symmetry properties and the non-existence of a photon wave function are thoroughly discussed. Starting from the Dirac equation the non-relativistic interaction of the electron with the electromagnetic field is derived as an effective Hamiltonian of multipole expansions. Much of quantum optics is based on the lowest order dipole approximation. From this point on the treatment of fully relativistic QED and quantum optics is done in parallel. Applications of perturbation theory such as Compton and Moller scattering and the theory photdetection are given. After the impressive successes of QED, the limitation of the theory and the necessity of electroweak theory and quantumchromodynamics are discussed. The remaining chapters are devoted to quantum optics inside cavaties. Various approaches to open systems such as master equations are discussed within the context of active systems (e.g. the laser) and passive systems. Semi- classical approximarions are shown to imply a rich non- linear dynamics including chaos for certain parameter regimes. The effect of fluctuations on such non-linear dynamics is also studied. The final chapter is devoted to highly non- classical states of the light field such as photon number, squeezed and two photon entangled states. The latter are studied for the important system of parametric down conversion and the localisation properties of photons are characterised in terms of asympotic tails in photodetection probabilities as a function of time delay. The range of the book has wider benefits. Workers in quantum optics will gain a deeper understanding of the foundations of their subject and field theorists will see concrete examples of open systems, which are beginning to impinge on fundamental theories.
Quantization of the Free Maxwell Field, Canonical and Functional Approaches
Authors: Pike frs E R , Sarkar Sarben
Published: November 2023

The quantum theory of radiation describes the interaction of light with matter. Over the last 60 years our understanding, both experimental and theoretical, has deepened considerably. Experimentally the phenomena have been studied at energy scales which span many orders of magnitude. In the early days it was atomic physics and, in particular, spectroscopy which dominated. Since then we have had the advent of particle accelerators which routinely accelerate matter to energies of billions of electron volts. Atomic physics itself has been revolutionized by the invention, over 25 years ago, of the laser. Thanks to modern technology experiments of great accuracy are now feasible. The coherence of laser light has also allowed the study of cooperative behaviour among many atoms. Is there a simple underlying theory of all these rich phenomena or do we have to invent ad hoc theories for different energy scales? One’s belief is that any such fundamental theory has to be compatible with quantum mechanics and special relativity. It is also necessary to remember that a fundamental theory may involve in an essential way incorporation of some other matter-matter forces. In this book we will describe such a theory of electromagnetic radiation and examine its validity at different energy scales.
The Photon as a Particle: The General One-Photon State
Authors: Pike frs E R , Sarkar Sarben
Published: November 2023

Through the classic work of Planck, Einstein, and others the particle nature of the photon has been established. In the previous chapter we considered the wave field of the photon. In this chapter we will emphasize more its particle nature and discuss the extent to which a wave function with a probabilistic interpretation is an appropriate description. Once we have the concept of a particle it is natural to ask how localized the state can be. The degree of localizability of photons is of concern in the interpretation of experiments in quantum optics involving weak light sources and non-linear electromagnetic media. If a photon is not to have the structure of a composite particle its quantum states should be describable by translations, rotations, and Lorentz boosts of a particular state and possibly super positions of such states. This is equivalent to a photon being associated with an irreducible representation of the Poincaré group. A brief overview of the general theory of group representations is given in Appendix 3. We will be able to give a complete discussion of the representations of the Poincaré group pertinent to the photon. Our discussion of localizability will be quite rigorous but we will gloss over measure-theoretic niceties. For more mathematical discussions the reader can refer to the works of Mackey (1978) and Wightman (1962). We will finish the chapter by examining the implication of Poincaré invariance for the metric on the space of quantum states of the photon.
Electron − Photon and Matter − Photon Interactions: Relativistic and Non-Relativistic Cases
Authors: Pike frs E R , Sarkar Sarben
Published: November 2023

Without the interaction of light with matter the world would not exist. There would be no chemistry and no biology. With recent advances at the particle accelerators throughout the world, our knowledge of what constitutes matter has increased. Matter is characterized as leptons, the electron and neutrino being prime examples, and hadrons (made up of quarks), the proton and neutron being prime examples. Hadrons are more complicated than leptons in the sense that they interact via strong nuclear forces. There are weak nuclear forces as well and the leptons also feel such forces. (Everything does feel gravity of course, but for elementary particles at current terrestrial energies such effects are unimportant.
Quantum Electrodynamic Processes
Authors: Pike frs E R , Sarkar Sarben
Published: November 2023

We will consider now the consequences of the theory that we have developed for situations in which the geometry is essentially unbounded. The simplest scattering of a photon by an electron is described by the Feynman diagram shown in Fig. 5.1. The matrix element M for the process (on using the momentum-space Feynman rules of Chapter 4) is given by The transition probability | M |2 involves the square of a 8-function which needs to be suitably interpreted.
Extensions of Quantum Electrodynamics
Authors: Pike frs E R , Sarkar Sarben
Published: November 2023

So far we have accumulated an impressive set of successful predictions of QED. However, the fact that it is not an ultimate theory appears even in low-energy experiments for stable atoms. From the discussions in Chapters 1 and 3 it is clear that the theory is invariant under parity. Since QED is rotationally invariant and the parity transformation can be made up of a mirror reflection and a rotation, parity violation is equivalent to a breakdown of mirror reflection symmetry. In experiments in bismuth and lead vapour it has been shown that the effective refractive index of light passing through the vapour is different for left and right circularly polarized light. This can be deduced from the rotation of the plane of polarization of linearly polarized light passing through the vapour. The effect is very small, the rotation angle being approximately 10 −7 radians for 1 metre of dense vapour. Other types of experiment may also be devised. Some involve an explicit handedness in the experimental configuration. An important example is provided by the breaking of parity symmetry in the configuration shown in Fig. 6.1
Non-Classical Light
Authors: Pike frs E R , Sarkar Sarben
Published: November 2023

The processes that we have already described in quantum optics undoubtedly produce effects which are specifically quantum or ‘non-classical’ in nature. In this chapter we will first give more precise criteria for our notion of nonclassical light and then consider specific examples of non-classical experiments in optics. We conclude with a detailed discussion of parametric down-conversion as an example of a practical source of non-classical light.
Effects caused by the Lorentz force acting along the surface’s normal
Authors: Dobrovolsky V N , Litovchenko V G
Published: November 2023

Subsurface SCR is formed if there exists a force acting on electrons and holes along a normal to the surface. The most thoroughly studied case is that seen when this force is induced by electric field (see Chapter 1 and 2). However, SCR may arise and change under the action of forces of other nature, for example, the Lorentz force. Under Hall effect conditions, this situation is realized near the surface of a sample parallel to the magnetic field, when charge carriers are being deflected towards this surface. This is discussed in the present chapter.
Polymers and Polymer Solutions
Authors: Cloizeaux Jacques des , Jannink Gerard
Published: November 2023

The observation of polymers and the work devoted to their synthesis goes back to the beginning of the nineteenth century. However, the definitions given to them varied until 1920. Flory has shown that the many incidents which occurred during the formation of the basic notions are of great interest even now, and a few notable facts are mentioned below.
Radiation Scattering
Authors: Cloizeaux Jacques des , Jannink Gerard
Published: November 2023

The interaction between radiation and condensed matter produces multiple effects, which have been the subject of many observations and of very different studies. Scattering has been one of the first observed effects. Originally, scattering was studied in order to know more about the nature of light and the interaction of light with matter. The discovery of the Tyndall effect (1863) is a typical example. When white light encounters a material, the scattered light often appears as coloured, the reason being that for shorter wavelengths the scattering is stronger.
Renormalization and Criticality
Authors: Cloizeaux Jacques des , Jannink Gerard
Published: November 2023

Theconcept of renormalization covers several different processes. Its origins are old and, for instance, dielectric constants and effective masses can be considered as renormalized quantities. In Quantum Electrodynamics, renormalization was developed around 1950, especially by Schwinger, Feynman, and Dyson, in order to eliminate non¬ physical ultraviolet divergences.