bluuebunny/crossref_metadata_2025_split huggingface dataset:
Potential energy surfaces
Authors: Henriksen Niels E. , Hansen Flemming Y. 
Published: January 2010

Abstract
This chapter discusses potential energy surfaces, that is, the electronic energy as a function of the internuclear coordinates as obtained from the electronic Schrödinger equation. It focuses on the general topology of such energy surfaces for unimolecular and bimolecular reactions. To that end, concepts like saddle point, barrier height, minimum-energy path, and early and late barriers are discussed. It concludes with a discussion of approximate analytical solutions to the electronic Schrödinger equation, in particular, the interaction of three hydrogen atoms expressed in terms of Coulomb and exchange integrals, as described by the so-called London equation. From this equation it is concluded that the total electronic energy is not equal to the sum of H-H pair energies. Finally, a semi-empirical extension of the London equation — the LEPS method — allows for a simple but somewhat crude construction of potential energy surfaces.
Unimolecular reactions
Authors: Henriksen Niels E. , Hansen Flemming Y. 
Published: January 2010

Abstract
This chapter considers unimolecular reactions; photo-induced reactions, i.e. true unimolecular reactions; and reactions initiated by collisional activation, i.e. apparent unimolecular reactions where it is assumed that the time scales for activation and subsequent reaction are well separated. Elements of classical and quantum dynamical descriptions are discussed, including Slater theory and the quantum mechanical description of photo-induced reactions. Statistical theories aiming at the calculation of micro-canonical as well as canonical rate constants are discussed, including a detailed discussion of RRKM theory. It concludes with a discussion of femtochemistry, i.e. the observation and control of chemical dynamics using femtosecond pulses of electromagnetic radiation, focusing on the control of unimolecular reactions via the interaction with coherent light, that is, laser control.
Microscopic interpretation of Arrhenius parameters
Authors: Henriksen Niels E. , Hansen Flemming Y. 
Published: January 2010

Abstract
This chapter reviews the microscopic interpretation of the pre-exponential factor and the activation energy in rate constant expressions of the Arrhenius form. The pre-exponential factor of apparent unimolecular reactions is, roughly, expected to be of the order of a vibrational frequency, whereas the pre-exponential factor of bimolecular reactions, roughly, is related to the number of collisions per unit time and per unit volume. The activation energy of an elementary reaction can be interpreted as the average energy of the molecules that react minus the average energy of the reactants. Specializing to conventional transition-state theory, the activation energy is related to the classical barrier height of the potential energy surface plus the difference in zero-point energies and average internal energies between the activated complex and the reactants. When quantum tunnelling is included in transition-state theory, the activation energy is reduced, compared to the interpretation given in conventional transition-state theory.
Introduction to condensed-phase dynamics
Authors: Henriksen Niels E. , Hansen Flemming Y. 
Published: January 2010

Abstract
This chapter discusses chemical reactions in solution; first, how solvents modify the potential energy surface of the reacting molecules, and second the role of diffusion. As a first approximation, solvent effects are described by models where the solvent is represented by a dielectric continuum, focusing on the Onsager reaction-field model for solvation of polar molecules. The reactants of bimolecular reactions are brought into contact by diffusion, and the interplay between diffusion and chemical reaction that determines the overall reaction rate is described. The solution to Fick's second law of diffusion, including a term describing bimolecular reaction, is discussed. The limits of diffusion control and activation control, respectively, are identified. It concludes with a stochastic description of diffusion and chemical reaction based on the Fokker–Planck equation, which includes the diffusion of particles interacting via a potential U(r).
Dynamic solvent effects, Kramers theory
Authors: Henriksen Niels E. , Hansen Flemming Y. 
Published: January 2010

Abstract
This chapter discusses dynamical solvent effects on the rate constants for chemical reactions in solution. The effect is described by stochastic dynamics, where the influence of the solvent on the reaction dynamics is included by describing the motion along the reaction coordinate as Brownian motion. Two theoretical approaches are discussed: Kramers theory with a constant time-independent solvent friction coefficient and Grote-Hynes theory, a generalization of Kramers theory, based on the generalized Langevin equation with a time-dependent solvent friction coefficient. The expressions for the rate constants have the same form as in transition-state theory, but are multiplied by transmission coefficients that incorporate the dynamical solvent effect. In the limit of fast motion along the reaction coordinate, the solvent molecules can be considered as ‘frozen’, and the predictions of the Grote–Hynes theory can differ from the Kramers theory by several orders of magnitude.
Simple Future and Future Perfect in Archaic Latin
Authors: DE MELO WOLFGANG DAVID CIRILO 
Published: January 2010

Abstract
It is often claimed that the contrast between simple future and future perfect is one of aspect in the early period. The simple future is said to be imperfective, the future perfect, perfective. In reality there are many simple futures that have to be interpreted as perfective as well. Since the future perfect is very rare in main clauses and relatively frequent in subordinate ones, it makes more sense to regard it as a future anterior. The simple future, which is not restricted in any way, is its non-anterior counterpart. There is only a limited overlap of usage in that, in certain contexts, either tense is possible.
Prohibitions with fēcerīs and faciās in Archaic Latin
Authors: DE MELO WOLFGANG DAVID CIRILO 
Published: January 2010

Abstract
There are many ways of forming prohibitive clauses in Latin. This chapter looks at those containing perfect and present subjunctives. Various possible contrasts are examined, for instance that between inhibitive prohibitions (‘stop doing’) and preventive ones (‘do not do’). Prohibitions introduced by nē (‘not’) are often indistinguishable from subordinate negative clauses; since the latter are historically derived from the former, this fuzziness of categories comes as no surprise. Prohibitions can also be introduced by caue, an original imperative (‘beware’) that underwent a grammaticalization process and turned into a simple prohibition marker. The use of perfect subjunctives in prohibitions does not fit into the synchronic tense system; we are dealing with old aorist uses that were eventually restricted to the second person, in contrast to the present subjunctive.
The Sigmatic Future in Archaic Latin
Authors: DE MELO WOLFGANG DAVID CIRILO 
Published: January 2010

Abstract
The sigmatic future has a remarkable pattern of distribution. In main clauses only the fossilized faxō occurs, while in subordinate clauses we find forms belonging to different verbs and persons. In main clauses the meaning is that of a simple future (‘I shall do’), whereas in subordinate clauses the forms could be replaced by future perfects (‘I shall have done’). The perfective, but non-anterior meaning in main clauses is original. The anterior meaning in subordinate clauses is the result of reanalysis.
The Type duim in Archaic Latin
Authors: DE MELO WOLFGANG DAVID CIRILO 
Published: January 2010

Abstract
Subjunctives of the type duim ‘I may give’ contain the same optative morpheme as the sigmatic faxim ‘I may do’. Similarly, they always have non-past meaning, but have peculiar restrictions of use in that they are absent in commands and ut-clauses, but frequent in prohibitions and subordinate nē-clauses. These forms also belong to an elevated register.
Some Problems of Reconstruction
Authors: DE MELO WOLFGANG DAVID CIRILO 
Published: January 2010

Abstract
In theory the sigmatic forms could go back to Proto-Indo-European desideratives or aorists. While diachronic morphology on its own remains inconclusive, the perfective meaning of the forms and their prevalence in prohibitions point strongly to aoristic origin. Even though some of the forms are undoubtedly old, the frequent faxō ‘I shall do’ must be relatively recent. Both duim and dem ‘I may give’ go back to aorist forms, but only dem was reanalysed as a present subjunctive. The -u- in duim is of Proto-Italic age.
Introduction
Authors: Jenkins Alice 
Published: January 2010

Abstract
This introductory chapter begins with a brief discussion of the purpose of the book, which is an interdisciplinary study of British literary and scientific culture in the first half of the 19th century, focusing on the development in those decades of a new spatial imagination. Its central concern reflects the increasing importance of space in critical enquiry over recent decades. The book steps back from the lived spaces of social geography to view the abstract space with and within which early 19th century writers organized knowledge, and which affected literature and the literary imagination in ways which have not yet been fully investigated by literary critics. An overview of the subsequent chapters is presented.
Culture as Nature: Landscape Metaphors and Access to the World of Learning
Authors: Jenkins Alice 
Published: January 2010

Abstract
This chapter discusses the landscape metaphors that were very frequently used to regulate and describe access to knowledge. By imaging knowledge as a series of outdoor spaces, subject to a greater or lesser degree of human intervention, and accessible to a greater or lesser range of human characters, these metaphors of gardens, wildernesses, pastoral, and picturesque landscapes staged debates about who should be able to learn what in early 19th-century Britain as a tussle between nature and culture. The chapter asks how spatial rhetorics were mobilized to manage access to knowledge in the face of strong pressures at once to enlarge and to control popular engagement in education. Using evidence from both popular and elite texts, it explores the political implications of the particular kinds of spatial metaphor most widely deployed, focusing especially on arguments and anxieties about individualism, conquest, and exploration.
Bodies in Space: Ether, Light, and the Beginnings of the Field
Authors: Jenkins Alice 
Published: January 2010

Abstract
This chapter argues that physics in the early 19th century was radically changing the nature of conceptions of space, essentially by dematerializing it. Contrary to the accepted account of Victorian culture as increasingly rooted in the material, the story of Victorian physics is one of jettisoning material explanations for phenomena. The contemporary success of the theory that light is a wave rather than a particle is one indication of the rise of dematerializing explanations in the period; another is the development of field theory. Field theory, particularly in its early form as propounded by Michael Faraday, collapses the distinction between matter and space, describing them instead as greater and lesser intensities of lines of electromagnetic and other forces. Field theory thus dramatically undermined all previous conceptions of space as passive container for material objects and paved the way for the energy physics of the late 19th century.
Scale-Free Networks
Authors: Caldarelli Guido 
Published: January 2010

Abstract
A variety of different social, natural and technological systems can be described by the same mathematical framework. This holds from the Internet to food webs and to boards of company directors. In all these situations, a graph of the elements of the system and their interconnections displays a universal feature. There are only a few elements with many connections and many elements with few connections. This book reports the experimental evidence of these ‘Scale-free networks’ and provides students and researchers with a corpus of theoretical results and algorithms to analyse and understand these features. The content of this book and the exposition makes it a clear textbook for beginners and a reference book for experts.
The Theory of Open Quantum Systems
Authors: Breuer Heinz-Peter , Petruccione Francesco 
Published: January 2010

Abstract
This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation, the text begins with a survey of classical probability theory and with an introduction to the foundations of quantum mechanics, with particular emphasis on its statistical interpretation and on the formulation of generalized measurement theory through quantum operations and effects. The fundamentals of density matrix theory, quantum Markov processes, and completely positive dynamical semigroups are developed. The most important master equations used in quantum optics and condensed matter theory are derived and applied to the study of many examples. Special attention is paid to the Markovian and non-Markovian theory of environment induced decoherence, its role in the dynamical description of the measurement process, and to the experimental observation of decohering electromagnetic field states. The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics. The fundamentals of the treatment of non-Markovian quantum processes in open systems are developed on the basis of various mathematical techniques, such as projection superoperator methods and influence functional techniques. In addition, the book expounds the relativistic theory of quantum measurements and the density matrix theory of relativistic quantum electrodynamics.
Classical Probability Theory and Stochastic Processes
Authors: Breuer Heinz-Peter , Petruccione Francesco 
Published: January 2010

Abstract
This chapter contains a survey of classical probability theory and stochastic processes. It starts with a description of the fundamental concepts of probability space and Kolmogorov axioms. These concepts are then used to define random variables and stochastic processes. The mathematical formulation of the special class of Markov processes through classical master equations is given, including deterministic processes (Liouville equation), jump processes (Pauli master equation), and diffusion processes (Fokker–Planck equation). Special stochastic processes which play an important role in the developments of the following chapters, such as piecewise deterministic processes and Lévy processes, are described in detail together with their basic physical properties and various mathematical formulations in terms of master equations, path integral representation, and stochastic differential equations.
Decoherence
Authors: Breuer Heinz-Peter , Petruccione Francesco 
Published: January 2010

Abstract
This chapter deals with the important field of environment-induced decoherence and the transition to the classical behaviour of open quantum systems. A number of techniques is developed that allows the determination of decoherence time scales. The decoherence behaviour in several Markovian models is investigated in detail, such as vacuum and thermal decoherence, decoherence in quantum Brownian motion, and the destruction of coherence through internal degrees of freedom and through the scattering of environmental particles. Moreover, experiments on the decoherence of Schrödinger cat states of the electromagnetic field are discussed, as well as the non-Markovian destruction of quantum coherence in the Caldeira–Leggett model, and the environment-induced selection of a pointer basis in the quantum theory of measurement.
Probability Distributions on Hilbert Space
Authors: Breuer Heinz-Peter , Petruccione Francesco 
Published: January 2010

Abstract
This chapter characterizes the statistical properties of a quantum mechanical ensemble in terms of a density matrix. However, if selective measurements of one or several observables are carried out on the ensemble, it will split into a number of sub-ensembles, each sub-ensemble being conditioned on a particular outcome of the measurements. The mathematical description of the collection of sub-ensembles thus created leads to probability distributions on projective Hilbert space. The chapter develops an appropriate mathematical framework which enables the general formulation of such a distribution, and leads to the concepts of stochastic state vectors and stochastic density matrices. These concepts are required in later chapters to construct appropriate stochastic differential equations describing the continuous monitoring of open quantum systems.
The Stochastic Simulation Method
Authors: Breuer Heinz-Peter , Petruccione Francesco 
Published: January 2010

Abstract
The formulation of the dynamics of open quantum systems by means of stochastic processes in Hilbert space leads to efficient Monte–Carlo simulation techniques which are introduced and examined in this chapter. Depending on whether the stochastic process is a piecewise deterministic process or a diffusion process, the corresponding individual realizations consist of intervals of deterministic evolution periods interrupted by instantaneous quantum jumps, or of continuous, nowhere differentiable paths. Various Monte Carlo algorithms for both types of processes are described in detail, and their convergence behaviour and their numerical performance is investigated for a number of applications, such as the damped harmonic oscillator, the driven two-level system, and the damped driven Morse oscillator.
Projection Operator Techniques
Authors: Breuer Heinz-Peter , Petruccione Francesco 
Published: January 2010

Abstract
This chapter is devoted to the foundations and to the basic mathematical structure of the non-Markovian quantum dynamics of open systems. It gives a survey of the Nakajima–Zwanzig projection operator methods with the help of which one derives so-called generalized master equations for the reduced system dynamics. In the non-Markovian regime, these master equations involve a retarded memory kernel, i.e. a time-convolution integral taken over the history of the reduced system. The chapter also describes an alternative method of particular relevance in many applications, which is based on a time-local quantum master equation, and which is known as the time-convolutionless projection operator method. This method serves as a starting point for a systematic expansion in terms of ordered cumulants and forms the basis for a non-Markovian stochastic unravelling of the reduced system dynamics.
Non-Markovian Dynamics in Physical Systems
Authors: Breuer Heinz-Peter , Petruccione Francesco 
Published: January 2010

Abstract
This chapter applies the time-convolutionless projection operator technique to some typical systems featuring strong non-Markovian behaviour. The first example models the decay of a two-level system into a reservoir with arbitrary spectral density. For this problem the expansion of the master equation is carried out to all orders in the system-reservoir coupling. As specific cases the damped Jaynes–Cummings model and the spontaneous decay into a photonic band gap are studied. The model is used to exemplify the breakdown of the expansion in the strong coupling regime, and to illustrate the emergence of completely positive master equations which are not in Lindblad form and involve negative decay rates. The chapter also treats the non-Markovian dynamics in quantum Brownian motion and in the spin-boson model, and illustrates the stochastic unravelling of non-Markovian quantum processes.
Introduction: The Plain Man in Characters and Court Books
Authors: HAIGH CHRISTOPHER 
Published: January 2010

Abstract
This introductory chapter begins with a description of The Plain Man's Pathway to Heaven published in 1601 by Arthur Dent, which was an instant hit and became one of the biggest sellers of the early 17th century. This popularity suggests that it has something to tell us about the nature of English. It considers the subsequent books spawned by the The Plain Man and the similarities between them. The chapter then presents an overview of the themes and analyses in the book, which asks how ordinary people saw and practised their own religion, and what they thought about those who saw and practised religion differently.
The Preacher and his People
Authors: HAIGH CHRISTOPHER 
Published: January 2010

Abstract
This chapter focuses on preachers and sermons. Arthur Dent's Theologus believed that preaching and cathechising were the means to feed Christ's sheep and save souls. Effective preachers are those who expound a ‘doctrine’ and then discuss its ‘use’, its application to his own congregation: ‘others only inform but reform not, because they speak too generally and preach as if they meant other persons and not their present auditory’.
Theologus: Pastor of a Flock
Authors: HAIGH CHRISTOPHER 
Published: January 2010

Abstract
This chapter focuses on how parishioners viewed the clergy's responsibilities. It describes the particular characteristics that parishioners commended. Parishioners had strong ideas of what a minister of the Word should be like — what was fit, and what was not. They also expected dignified behaviour from their minister, and objected to drunkenness and sexual laxity.
Philagathus: The Godly and the Rest
Authors: HAIGH CHRISTOPHER 
Published: January 2010

Abstract
This chapter focuses on the relationship between the profane and the godly. Philagathus knew well that the profane hated the godly. Theologus knew it too — ‘many of them despise the word of God, and hate all the zealous professors of it’. As he told Antilegon the caviller, ‘if a man give himself to the word and prayer, reformeth his family and abstaineth from the gross sins of the world, you will by and by say he is an hypocrite’ . At the Kettering lecture, Robert Bolton warned that the unregenerate would despise the true professors — ‘You see these fellows, which make such a show of forwardness and purity, what they are? none so covetous, none so uncharitable, none so unmerciful and cruel in their dealings as they’.
Antilegon: Attitudes to Authority
Authors: HAIGH CHRISTOPHER 
Published: January 2010

Abstract
This chapter explores parishioners' attitudes to church authority. Good fellowship among the less-godly was bestial sin to the godly, and the ceremony of ‘good and faithful drunkards’ became notorious, featuring in Samuel Ward's 1622 sermon ‘Woe to Drunkards’ — where Ward claimed that the participants all ‘died thereof within a few weeks, some sooner, some later’. But men and women could not be kept out of the alehouse — even when they should have been at church. When in 1571 Thomas Harmer of Stonehouse, Gloucestershire, was rebuked by the minister for playing cards in the alehouse in service time, he gave him an earful of abuse and called him ‘knave’. John Gay of Childerditch, Essex, was presented in 1584 for keeping evil rule in his house on a Sunday, ‘in so much that the minister could not say service for the great noise of the people’.