bluuebunny/crossref_metadata_2025_split huggingface dataset:
Simple generalizations
Authors: Molisch Andreas F , Oehry Bernhard P 
Published: November 2023

Abstract
In this chapter, we will deal only with rather straightforward generalizations, which still cause enormous mathematical problems. For the cases treated here, the solutions still take the form of a modal expansion-so no change in this respect: This class of problems includes multi-level atoms, reflecting cell walls, particle diffusion, and inhomogeneous distributions of absorbers. Added conceptual difficulties arise when CFR is not valid, or when non-linear effects come into play. These problems are relegated to Chapters 11-13.
Partial frequency redistribution
Authors: Molisch Andreas F , Oehry Bernhard P 
Published: November 2023

Abstract
Up to now, we have generously assumed that the emission frequency of a photon is completely independent of the frequency of the absorbed photon, so that there is complete frequency redistribution, CFR. This assumption is often, but not always fulfilled in practical situations. In this chapter, we analyse under what conditions CFR is valid, and what effects we have to expect when the emitted photon at least partly ‘remembers’, on which frequency it was absorbed-partial frequency redistribution, PFR. In the first subsection, we will deal with general considerations and show under which conditions PFR comes into play. In the subsequent sections, we will look at the mathematical formalism to solve trapping problems with PFR. The last section deals with the influence of large-scale particle flow.
Polarization
Authors: Molisch Andreas F , Oehry Bernhard P 
Published: November 2023

Abstract
In theory, all radiation trapping problems must be treated under consideration of the polarization state of the radiation. Even with an unpolarized excitation source, the geometry of the problem can introduce some degree of polarization to the fluorescence radiation. Of course, when the excitation source itself is polarized, as is usually the case for a laser, polarization can become even more important. One should not forget, however, that incorporation of polarization makes for a very complicated problem. The Holstein equation will become a Fredholm integral equation for a four-component vector instead of the usual scalar function (the excited-state density). Having seen the difficulties in solving the comparatively simple ‘usual’ trapping problem, we see that polarization should only be included when it is not to be avoided.
Measurements in chemical physics
Authors: Molisch Andreas F , Oehry Bernhard P 
Published: November 2023

Abstract
In the present chapter we describe some aspects of the interpretation of measurements in chemical physics. The examples will show the difficulties that can occur in the in corporation of radiation trapping. We can also deduce some general guidelines for such experiments that should help to reduce some of the occurring errors. One of the most important points is choosing an appropriate geometry for the experimental vessel. We know that the incorporation of a genuinely three-dimensional geometry is exceedingly difficult. Appropriate mirroring of the cell walls allows one to find an ‘equivalent’ cell that can often be treated more easily than the actual ceH.
Atomic line filters
Authors: Molisch Andreas F , Oehry Bernhard P 
Published: November 2023

Abstract
In free-space optical information transmission and in LIDAR systems, very narrow band filtering is often needed to eliminate broad-band solar background noise. Ideally, such filters should have a bandwidth on the order of a few hundred MHz to a few GHz. It is very difficult to produce such narrow-band filters by conventional means, but we know that atomic absorption lines have just that bandwidth. An atomic vapour cell actually is an excellent band-block filter. In order to convert it to a bandpass filter, we just have to find a way to determine whether absorption has taken place.
Introductory Nuclear Magnetic Resonance
Authors: Callaghan Paul T 
Published: November 2023

Abstract
Atomic nuclei are characterized by states which are inherently quantum mechanical in their behaviour. This means in effect that the properties we observe for a single nucleus belong to one of a discrete set of possibilities. When performing nuclear magnetic resonance, however, we deal with exceedingly large numbers of nuclei acting largely independently, so that at the macroscopic level the collection of particles appears continuous, the so-called ‘ensemble’ behaviour. We shall be mainly concerned with spin-½ nuclei. For these, all states of the ensemble may be characterized by a simple vector quantity which is referred to as the nuclear magnetization. Having established this point we may embark on a classical explanation of the nuclear magnetic resonance phenomenon.
Elements of the NMR Microscope
Authors: Callaghan Paul T 
Published: November 2023

Abstract
NMR microscopy has now become a standard option on several commercial spectrometers although few manufacturers offer magnetic field gradients of sufficient magnitude or stability to perform effective PGSE experiments with q in excess of (1 µm)-1. In keeping with the emphasis on principles adopted in this monograph, this chapter contains only a brief review of salient elements of the microscope, avoiding standard aspects of NMR spectrometer design and dealing principally with the most troublesome feature, the field gradients. Readers wishing to learn more about practical aspects of general NMR spectroscopy are referred to the excellent book by Fukushima and Roeder, and, for information on imaging system hardware, to the comprehensive text by Chen and Hoult. In addition, individual NM R companies supply a variety of useful technical and applications notes.
Operator Methods in Quantuin Mechanics
Authors: De Lange O L , Raab R E 
Published: November 2023

Abstract
Quantum mechanical problems capable of exact solution are traditionally solved in a few instances only (such as the harmonic oscillator and angular momentum) by operator methods, but mainly by means of Schrodinger's wave mechanics. The present volume shows that a large range of one- and three-dimensional problems, including certain relativistic ones, are solvable by algebraic, representation-independent methods using commutation relations, shift operators, the virial, hypervirial, and Hellman-Feyman theorems. Applications of these operator methods to the calculation of eigenvalues, matrix elements, and wavefunctions are discussed in detail. This book is an introduction to the use of operator methods in quantum mechanics and also a reference work with numerous problmes solved. It is suitable for use by students of intermediate quantum mechanics and also more advanced postgraduate students who wish to study the algebraic method of solving quantum mechanical problems.
Factorizations With Application To The Momentum Representation
Authors: De Lange O L , Raab R E 
Published: November 2023

Abstract
In Chapter 5 we considered the factorization of a radial Hamiltonian for a particle in a spherically symmetric potential which is independent of angular momentum. This factorization provides shift operators for energy and angular momentum in the eigenkets of the radial Hamiltonian for the oscillator and Coulomb potentials. These operators are linear functions of the momentum operator *p and they are also nonlinear functions of the position operator r: in the coordinate representation of wave mechanics they yield first-order differential operators. In this chapter we show that for the three-dimensional isotropic harmonic oscillator and the Coulomb potential, one can also construct shift operators for energy and angular momentum that are linear functions* of r and nonlinear functions of p. In the momentum representation of wave mechanics the shift operators yield first-order differential operators. Applications to the calculation of energy eigenvalues, matrix elements, and radial momentum-space wavefunctions are considered.
The Coulomb Problem In The Basis |H 𝒜z Lz &gt;
Authors: De Lange O L , Raab R E 
Published: November 2023

Abstract
The discussion presented below illustrates the application of operator methods in a coordinate system that is not Cartesian. The analysis is based on shift operators for n, λ, and μ. The shift operators for λ and μ are easily constructed (Section 10.1) and their properties determine in a simple manner the possible values of n, λ, and μ (Section 10.2). In Section 10.3 operators are expressed in terms of parabolic coordinates, and shift operators for n are derived in Section 10.4. The hypervirial and Hellmann-Feynman theorems are used to obtain expectation values in Section 10.5. The shift operators generate all excited bound states from the ground state (Section 10.6) and this property is used to construct normalized coordinate-space wavefunctions in parabolic coordinates (Section 10.7).
Relativistic Quantum Mechanics
Authors: De Lange O L , Raab R E 
Published: November 2023

Abstract
In this chapter we give a brief introduction to the relativistic equations for spin 0 and spin ½ particles (the Klein-Gordon and Dirac equations), and we solve these equations for two simple problems. Throughout we consider only single-particle theory: thus we do not discuss ‘second quantization’ of the relativistic equations (i.e. the use of quantized fields that create and annihilate particles and antiparticles).
Spin echoes and the dynamic properties of membranes
Authors: Bloom M , Morrison C , Sternin E , Thewalt J L 
Published: November 2023

Abstract
The discovery of spin echoes by Erwin Hahn in 1950 [ 19] has provided seminal ideas for many of the important concepts of modern NMR. For example, the observation of transient ‘free induction decay’ (FID) signals, following one or more short r.f. pulses applied at a frequency close to the average nuclear Larmor frequencyw0,led ultimately to Fourier transform NMR spectroscopy. Also, today it is impossible to conceive of preparing complex spin systems in well defined, ‘interesting’, non-equilibrium states without using pulse sequences of one sort or another. Biological and model membranes are two systems for which NMR, and especially deuterium (2H) NMR, has provided special insights in recent years. The2H NMR techniques that have proved to be fruitful up to now in elucidating the properties of membranes are very close to those described in Hahn’s original work, so that this is a particularly suitable place to discuss recent work in this area. We shall discuss several studies in our laboratory of membrane dynamics using2H NMR and shall try to place this within the perspective of current developments in membrane biophysics, which is a vibrant and dynamic field at the present time. Membrane biophysics is in the process of generating an enormous literature, so that our selection of background material is necessarily personal, being severely limited by space considerations to questions that we deem to be of potential interest to a general audience and, at the same time, amenable to study in our own laboratory.
From Nonlinearity to Coherence
Authors: Dixon J M , Tuszynski J A , Clarkson P A 
Published: November 2023

Abstract
Nonlinear physics has grown from a collection of exotic examples of nonstandard behavior to an all-embracing scientific methodology. Many examples come from condensed matter physics. This book presents a unified view of many-body condensed matter systems as essentially nonlinear structures capable of exhibiting such features as chaos, coherence, solution formation and phase transitions. The book provides an overview of nonlinear phenomena in science, introduces phase transitions and criticality, and includes a comprehensive exposition of methods and results in the analysis of nonlinear differential equations. To equip the reader with concrete skills in tackling nonlinear problems in physics, the authors also analyze important applications such as metamagnetism, superconductivity, the Hubbard Hamiltonian and the multielectron atom. The book can serve as both a compendium of facts and references related to nonlinear condensed matter physics and a practical introduction to current research methods and the field in general.
introductory concepts: a nonlinear analysis primer
Authors: Dixon J M , Tuszynski J A , Clarkson P A 
Published: November 2023

Abstract
A very small cause which escapes us determines a considerable effect which we cannot fail to see, and then we say that the effect is due to chance. If we could know exactly the laws of nature and the situation of the universe at the initial instant, we could predict exactly the situation of that same universe at a subsequent moment. But even if the natural laws had no longer any secret for us, we would know the initial situation only approximately. If that enables us to predict the subsequent situation with the same approximation, that is all we require, we say that the phenomenon has been predicted that it is governed by laws. But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the phenomenon of change.
Elementary excitations in solids
Authors: Dixon J M , Tuszynski J A , Clarkson P A 
Published: November 2023

Abstract
In this section we review what quantum excitations actually are and how we describe them in solids. This will enable us to introduce the idea of second quantization in a simple way, and how it may be used to great advantage to study a variety of different types of excitation in condensed matter. We shall later use second quantization when we develop the Method of Coherent Structures (MCS), so it is important that the reader thoroughly understands what is being done. The technique will be described at two different levels. In this part of the book we concentrate on physical ideas and how they may be employed to provide simple rules for the setting up of operators and quantum states in second quantization. We may consider this to be the simplest level. At a more advanced level, ideas such as completeness, what a representative is, how the occupation formalism follows from a configuration or momentum picture, and so on, can readily be described in more detail. The interested reader may also find in the literature how second quantized operators, within a given configuration, may be written in terms of orbital angular momentum and spin operators, which are perhaps more familiar to spectroscopists and those interested in magnetic resonance or magnetism generally.
Physical applications of MCS
Authors: Dixon J M , Tuszynski J A , Clarkson P A 
Published: November 2023

Abstract
In the education of a physicist, we recount the bold voyages of great explorers-Newton and Einstein, Faraday and Bohr-in search of new laws of nature. They found and charted the continents on which we have built our cities of the mind and of art. Does anyone really suppose that similar vast and fertile territories are still waiting to be discovered and colonized? The unaccustomed rules that govern black holes and quasars in the cosmic deeps affect our lives no more than the icy crags of the Himalayas or the conjunctions of the planets ... Think of physics simply as the ‘fundamental’ science and it is oversubscribed almost to bankruptcy. But define it as the science whose aim is to describe natural phenomena in the most mathematical or numerical language, and you will understand its past and have confidence in its future ... The task of the modern physicist is to determine the mathematically comprehensible characteristics of the natural world and of human artifacts ...
Conclusions
Authors: Dixon J M , Tuszynski J A , Clarkson P A 
Published: November 2023

Abstract
The motivation for this book was to emphasize the importance of nonlinearity in many-body systems, especially in condensed-matter physics. This approach is based on the belief that interactions between particles play a dominant role in solid state phenomena and that the constituent particles, in most cases, may not be treated as nearly independent entities. While the introduction of quasi-particles, representing collective modes of behaviour of the solid, goes a long way towards understanding the physics of such systems, there are always limitations to this approach. The first limitation is the stability of the underlying structure, e.g. the crystal lattice, which cannot be recovered using independent particle approaches. A related limitation is that, in most cases, collective modes interact, which may lead to the emergence of localized excitation modes that cannot be derived from a perturbative approach. Our strategy or philosophy, therefore, has been to complement the traditional methods of linearizing physical problems and instead explore new possibilities that nonlinear physics affords.
A multiple bifurcation point as an organizing centre for chaos
Authors: Mullin Tom 
Published: November 2023

Abstract
In this chapter we will show how qualitatively different types of bifurcations in a nonlinear system can interact with each other to produce an organizing centre for more complicated phenomena such as chaos. First, we will introduce static and time-dependent bifurcations and describe their practical features in terms of physical examples. Then we will discuss the details of an interaction between the two types of bifurcation and show how it produces a multiple bifurcation point in the specific example of a nonlinear electronic oscillator. Finally, we discuss how the ‘global dynamics’ of the system are controlled by this local bifurcation structure.
Chaos in fluid dynamics
Authors: Mullin Tom 
Published: November 2023

Abstract
The application of the ideas which have been developed in the study of low-dimensional chaos to fluid dynamics has become a rapidly increasing research area in recent years. Some of the reasons for this are that fluid turbulence still remains one of the greatest challenges of classical physics and it is of immense practical importance. In fact, it is often written in popular accounts of the subject that chaos lies at the heart of an explanation for turbulence. We will discuss this possibility using an example which has been thoroughly studied both theoretically and experimentally, to see how much confidence we can have in this assertion.
Applications of chaos to meteorology and climate
Authors: Read Peter L 
Published: November 2023

Abstract
Chaos and meteorology have had a close relationship for a number of years. The Lorenz attractor is well known as a very influential mathematical model whose properties were first studied in detail in the 1960s by the meteorologist/mathematician Ed Lorenz, working at MIT. It became a prototype for chaotic dynamics in Lorenz’s celebrated paper [l], published in 1963 in the Journal of Atmospheric Sciences. The most significant point in the present context is that it was originally motivated by a meteorological problem.
The Casimir Effect and its Applications
Authors: Mostepanenko V M , Trunov N N , Znajek R L 
Published: November 2023

Abstract
The Casimir effect arises when the zero-point vacuum oscillation spectrum is distorted by boundedness of the field quantization domain or by non-trivial spatial topology. As such, it is a widely used and intensely discussed phenomenon. This is the first book devoted to the Casimir effect. It will be valued by workers in a number of fields, including elementary particle physics, statistical physics, quantum field theory, gravitation and cosmology. Methods of calculating Casimir energies and forces are considered, and results given for bounded domains, dispersive media, and topologically non-trivial spaces. All these applications are outlined in this work covering a widely known, used and intensively discussed effect by specialists.
The Casimir effect for various fields and spatial domains
Authors: Mostepanenko V M , Trunov N N , Znajek R L 
Published: November 2023

Abstract
The most obvious regularization method, which has already been applied in the preceding chapter, is subtracting away from the vacuum expectations of the quantized field Hamiltonian in the presence of boundaries the corresponding expression for unbounded space. A more complicated local version of this approach is the determination of the EMT by summing over a countable set of eigenfunctions of the problem under consideration, with the subtraction of the empty space contribution. (The appropriate summation formulae are discussed in Section 2.2.) A whole class of regularization methods is based on using information contained in the Green function of the problem or an object similar to it. Here the method of finding the Green function itself can be arbitrary (whether or not it is associated with summation over modes).
Vacuum polarization in topologically non-trivial spaces and cosmology
Authors: Mostepanenko V M , Trunov N N , Znajek R L 
Published: November 2023

Abstract
As has been previously noted, when considering a quantized field in a topologically non-trivial space additional conditions are imposed that are similar to conditions at material boundaries. As a result, in comparison with Minkowski space, the zero-point fluctuation spectrum changes, (for example, from being continuous to being discrete), which leads to the appearance of a non-zero vacuum EMT for the quantized field in that space.
Effective temperature of the vacuum
Authors: Mostepanenko V M , Trunov N N , Znajek R L 
Published: November 2023

Abstract
In a number of problems the spectral density describing vacuum polarization of quantum fields on a manifold differing from Minkowski space formally coincides with the spectral density of equilibrium thermal radiation with some effective temperature Teff governed by the parameters of the problem. Here we first consider problems in which the volumes are bounded in one of the spatial coordinates.
Re-introductions: to what extent are they needed?
Authors: Stuart Simon N 
Published: November 2023

Abstract
The 14 Action Plans so far produced by the Specialist Groups of the IUCN Species Survival Commission (SSC) are analysed to determine how frequently re¬ introductions are recommended in relation to other conservation activities. Re¬ introductions are recommended only 24 times (compared with 401 recommendations for protected area management). Of the 418 threatened species covered by the Action Plans, just 19 (4.5%) are recommended for re-introduction programmes. The reason for so few recommendations being made is that re-introductions are only feasible when two preconditions are satisfied: adequate areas of unoccupied former habitat remain; and the causes of decline have been removed. Since most species are decreasing because of threats to their habitats, rather than directly against the species themselves, the first precondition is only met in a small minority of cases. Various factors that are commonly associated with species that might become suitable for re-introduction programmes are identified.
The role of ecological theory in planning re-introduction of endangered species
Authors: May Robert 
Published: November 2023

Abstract
This chapter focuses on populations rather than individuals, reviewing ways in which the dynamics or genetics of populations can influence the long-term success of re-introduction programmes. Among other things, it discusses minimum viable population sizes, the dynamics of ‘metapopulations’ and the role that infectious diseases can play. It is emphasized that the geographical ranges required for self maintaining populations may be much greater than suggested by intuitive estimates based on the movement patterns of individual animals.