bluuebunny/crossref_metadata_2025 huggingface dataset:
‘Teach Mercy to Ten Thousand Hearts’
Authors: Allpress Roshan
Published: November 2023

Between 1815 and 1840, philanthropy grew increasingly transnational, localized its activity in the United Kingdom through expanding networks of auxiliary societies, and became a cultural movement, capturing the imagination of the wider British public. The Christian Observer was pre-eminent among the journals and magazines that leveraged transnational networks to present an increasingly detailed account of global humanity to the British public, shaped by the priorities of philanthropic societies. As the number, scale, and influence of societies grew rapidly, the philanthropic nexus of directors became more diffuse, and less shaped by dense collaborative communities such as the Clapham Sect. A younger generation, such as Sir James Stephen—raised in the context of associational activism—pursued new career paths in the civil service, motivated by a philanthropic world view and humanitarian convictions. By the late 1830s, the philanthropic imagination had become a prominent part of British public life and global engagement.
Emperor John II Komnenos
Authors: Lau Maximilian C. G.
Published: November 2023

John II Komnenos was born into an empire on the brink of destruction, with his father Alexios barely preserving it in the face of civil wars and invasions. A hostage to crusaders as a child, married to a Hungarian princess to win his father an alliance as a teenager, and leading his own campaigns as his father died, it was left to John to try to rebuild the empire all but lost in the eleventh century. This book, the first English language study on John and his era, re-evaluates an emperor traditionally overlooked in favour of his father, hero of the Alexiad written by John’s sister Anna, and his son Manuel, acclaimed for reigning at the height of Komnenian power. His reign is one of contradictions, as his capital of New Rome/Constantinople was to fall to the armies of the Fourth Crusade just over sixty years after he died, and yet his descendants led vibrant successor states based in the lands that John reconquered. His reign lacks a dominant textual source, and so this history is related as much through personal letters, court literature, archaeology, and foreign accounts as much as traditional historical narratives. This study includes extensive study of the landscapes, castles, and cities that John built and campaigned through. It is also a guide to the world in which John lived. It covers the empire’s neighbours and rivals, the turning points of ecclesiastical history, the shaping of the crusader movement, and the workings of Byzantine government and administration.
Sources
Authors: Lau Maximilian C. G.
Published: November 2023

One of the central problems with John’s reign is that there is no overarching, dominant historical narrative that, however flawed, gives us at least a skeletal account of what occurred and why; instead, John’s reign must be pieces together from sources not specifically focused on him and his era. Historians have traditionally looked to the broad histories of Niketas Choniates and John Kinnamos, who both open their works with a summary of John’s reign, and so this chapter first highlights the problems with this approach, while also noting what is still to be gained from these texts. But, having freed ourselves from dependence on these two accounts, it turns out that there are actually a lot of other sources on John: notably contemporary court texts, such as occasional poetry not dissimilar from modern press releases, and letters by key figures at court. There are also underused documentary archival texts, as well as legal and administrative manuals. Beyond Byzantium, we have many significant non-Greek voices from neighbouring regions (in Syriac, Turkish, Armenian, and Arabic, in addition to Latin texts from both Western Europe and the Crusader East), in addition to more exotic texts that still provide individual crucial details, such as Norse Sagas or Rus and Georgian chronicles. Finally, of crucial importance is the growing corpus of archaeological evidence, which demonstrates the effect the events in these texts had upon the landscape. Overall, this chapter introduces the reader to all the sources on John and his reign.
The Horizons of 1118
Authors: Lau Maximilian C. G.
Published: November 2023

Where the previous chapter focused on the state of the Byzantine Empire before and at the moment John rose to sole rule in 1118, this chapter introduces the reader to the state of the empire’s neighbours, near and far, at this time, which will all impact upon the developments in John’s reign. This chapter gives the reader a tour of the horizons seen from Constantinople, following the model of the tenth-century De Administrado Imperio in describing the geography, recent political history, and rulers of each of the peoples around the empire’s core. It starts in the Balkans before looking north across the Black Sea, and then across to the Caucuses and Anatolia. The Crusader and Islamic powers of the Levant, Egypt, and central Asia are then introduced, and even the western Liao dynasts of Chinese descent beyond that. Then we look west towards Italy, the Germanic empire to the north-west, and other European powers beyond. After this tour, the foreign engagements undertaken by Alexios and John in the earlier 1110s are discussed, such as the war with the Normans in southern Italy, and how Bohemond was beaten through John’s marriage with the Hungarian Princess Piroska and Alexios’ trade concessions to Venice. Interventions in the Serb polities are also outlined, and Alexios’ last campaigns in Anatolia against the Turks. We then see how John continued these policies in his first years: advancing the imperial cause in Anatolia while maintaining alliances with the Rus and Georgia.
The Raškan Insurrection and the Hungarian War
Authors: Lau Maximilian C. G.
Published: November 2023

This chapter focuses on John’s Balkan campaigns and their diplomatic and economic context between 1126 and 1129. The countdown to war with Hungary is first outlined, and the various factors that led to it becoming entangled in the disputes between the two rival Serb courts of Raška and Diokleia, the latter of which supported the empire while the former supported greater independence. The highs and lows of King Stephen of Hungary’s invasion and the Serb campaigns are then examined from both a multi-textual and archaeological basis, highlighting the hugely divergent historical opinion on their chronology and significance. Following this, the implications for the peace treaties John signed are analysed in the context of John’s wider policies towards the west, including the Italian and Dalmatian cities. This chapter also includes discussion of the many fortresses John built in the Balkans, and what these are the texts indicate about the nature of imperial rule over these regions.
Conclusion
Authors: Lau Maximilian C. G.
Published: November 2023

This conclusion runs through medieval and modern opinions on John before bringing together the arguments of this book to establish what we should make of his reign—further, it will ask what John’s plan for his empire was, and to what extent his personal character aided or limited those plans. This conclusion will also examine whether we should see John as a crusader, and what his place should be in that movement. John’s relationships with his family and reputation with contemporaries and successors will receive an especial focus, while there will also be discussion of the iconography that John minted on his coins, and how those choices reflected his evolving designs for his empire.
Introduction
Authors: Peers Steve
Published: November 2023

Chapter 1 introduces Volume I’s main topics. This volume sets out and analyses both the institutional arrangements for EU cooperation on immigration and asylum law and the substantive law which has been adopted in the various fields that make up this area of law. The chapter outlines the contents of the rest of the volume. The four fields covered here are united by a series of four common and closely connected themes. First, a central issue in EU immigration and asylum law is the balance between protection of human rights and civil liberties on the one hand, and the State interests in public order, security, and migration control on the other. A second theme, now largely of historical importance following the entry into force of the Treaty of Lisbon, is the complex and often controversial interaction and overlap between the rules that apply to most areas of EU law (in particular, the free movement of EU citizens, and EU association agreements) and the specific issues of immigration and asylum law. The third theme is the continued dispute over the scope of the powers granted to the EU in the areas of immigration and asylum law. Finally, the fourth theme is the convoluted territorial scope of EU immigration and asylum law.
Irregular Migration
Authors: Peers Steve
Published: November 2023

Chapter 7 descsribes and analyses the EU law on irregular migration, including carrier sanctions for airlines which transport irregular migrants, criminal penalties for trafficking in persons or smuggling persons, the status and rights of victims of trafficking in persons, advance passenger information, immigration liaison officers, restriction on employment of irregular migrants, readmission to non-EU countries, and the EU’s Returns Directive—in particular that Directive’s rules (and the extensive case law) on detention, appeals, treatment of irregular migrants, procedural rights, and entry bans. This includes discussion of proposed amendments to the laws on returns, advance passenger information, and trafficking in persons. It also examines the impact of EU free movement law and EU association agreements on these issues.
Substantive Criminal Law
Authors: Peers Steve
Published: November 2023

This chapter describes and analyses the EU rules on substantive criminal law, examining which offences the EU has harmonized, in particular the laws on terrorism, organized crime, fraud against the EU budget, corruption, hate crime, environmental crimes, cybercrime, drugs, money laundering, trafficking in persons, smuggling of persons, and sexual abuse of children. It also considers the minimum penalties which must be imposed for committing these crimes and rules on limitation periods according to EU law, and the proposed EU criminal laws on violence against women/domestic violence and foreign policy sanctions, along with the proposed amendment of EU law on environmental crimes. The chapter also explores the impact of other EU laws on criminal law issues (eg the links between limits on cash movements and the free movement of capital).
Policing and Security
Authors: Peers Steve
Published: November 2023

This chapter describes and analyses the EU law on policing, in particular the police cooperation agency Europol, along with the various EU mechanisms for databases or exchanging data between policing and prosecution authorities (Schengen Information System, Prüm, Swedish Framework Decision, and the use of EU immigration databases). It also examines operational measures such as joint investigation teams and the application of data protection law in this field: both the general harmonization of EU law on data protection and policing (including aspects of the EU’s General Data Protection Regulation), and the extensive case law (including case law of both the CJEU and the European Court of Human Rights) in specific fields such as retention of telecoms data and passenger name records. The chapter also includes cooperation with non-EU countries such as the UK post-Brexit, discussing issues such as the potential limits on exchanging law enforcement data outside the EU.
Introduction
Authors: Boute Anatole
Published: November 2023

This chapter introduces the impact of the 2022 energy crisis on the European and global energy markets, and explains why, faced with the weaponization of energy, energy law can no longer be examined in isolation from energy geopolitics and economic statecraft. The chapter defines the concept of supply security, and explains how, under the existing European and international energy regimes, trade and investment instruments are expected to ensure secure energy supplies. It then introduces the literature on economic statecraft and energy geopolitics that has long warned of the security risks associated with certain types of energy dependencies, and the literature on imperialism and international law that has criticized the use of investment and trade agreements as an instrument of control and power. As states can use trade and investment instruments to achieve geopolitical benefits, it is necessary to critically reflect on how energy market regulation, and energy trade and investment agreements, can contribute to the creation of dependencies that allow for the weaponization of energy. At the same time, the international economic law scholarship on national security provides a solid theoretical basis to understand how existing energy, trade, and investment disciplines can constrain energy security strategies.
Lexical Variation and Change
Authors: Geeraerts Dirk , Speelman Dirk , Heylen Kris , Montes Mariana , De Pascale Stefano , Franco Karlien , Lang Michael
Published: November 2023

Distributional semantics embodies the idea that the context in which a word occurs reveals the meaning of that word. In contemporary corpus linguistics, that idea takes shape in various types of quantitative context analysis. This monograph explores how count-based token-level semantic vector spaces, as an advanced form of such a quantitative methodology, can be applied to the study of polysemy, lexical variation, and lectometry. What can distributional models reveal about meaning? How can they be used to analyse the semantic relationship between near-synonyms? And how can they contribute to the study of lexical variation as a sociolinguistic variable? The book details the conceptual background of lexical semantic and lexical variation research, explains the mechanism of distributional modelling, and introduces distributional workflows and corpus linguistic tools to answer the questions. Combining a cognitive linguistic interest in meaning with a sociolinguistic interest in variation, it illustrates that distributional methodology with case studies on Dutch and Spanish lexical data, focusing on the value of distributional models for semantic analysis, the interaction of semasiological and onomasiological change, and sociolinguistic issues of lexical standardization and pluricentricity.
Lexical variation and the lexeme-lection-lect triangle
Authors: Geeraerts Dirk , Speelman Dirk , Heylen Kris , Montes Mariana , De Pascale Stefano , Franco Karlien , Lang Michael
Published: November 2023

As this monograph is situated at the crossroads of lexical variation research and distributional semantics, a double background has to be described. This chapter introduces the first of these two backdrops: what model of lexical variation do we start from, where do we situate our own research within that field, and how do we relate to previous research? Specifically, we show how lexical variation research is organized on the basis of two dimensions, one linking linguistic forms to meaning, and an orthogonal one considering that association from the point of view of lectal variation. Both dimensions can be traversed in two directions. This produces a distinction between semasiology and onomasiology for the first dimension, and a distinction between lectal variation as an explanatory or as a response variable for the second dimension.
Quantifying lectal structure and change
Authors: Geeraerts Dirk , Speelman Dirk , Heylen Kris , Montes Mariana , De Pascale Stefano , Franco Karlien , Lang Michael
Published: November 2023

Instead of treating polysemy or lexical variation as a variable dependent on lectal factors (as in the preceding chapters), this chapter switches the perspective: it treats variation in form-meaning pairings as an input variable for determining lectal structure. By focusing on formal onomasiological variation, lexical variation can be analysed as a sociolinguistic variable in the Labovian sense, and aggregating over such variables allows to find out how various lects relate to each other, both synchronically and diachronically. The chapter introduces various measures that flesh out such a lectometrical approach: measures of the uniformity between lects, measures of the internal homogeneity within a lect, and measures focusing on lexical diversity and success. An example shows how such measures can be used to analyse processes of standardization and informalization.
Lectometry step by step
Authors: Geeraerts Dirk , Speelman Dirk , Heylen Kris , Montes Mariana , De Pascale Stefano , Franco Karlien , Lang Michael
Published: November 2023

The approach to lexical variation research demonstrated in this book rests crucially on the concept of an ‘onomasiological profile’, the set of synonymous names for a concept, differentiated by their relative frequency. This chapter introduces a workflow for the identification of onomasiological profiles that capitalizes on what was shown in Chapter 6: when we analyse near-synonyms in the same vector space, we can identify the areas where their sense clusters overlap, that is, where they are interchangeable. The distributional workflow for determining onomasiological profiles consists of a number of steps, involving both type-based and token-based vector representations: selecting an initial set of near-synonyms, setting the parameters that demarcate the range of models to be considered, pruning the models by removing out-of-concept clusters, and potentially also selecting models.
Steam-Engine Economy and the Heat of the Mine in Early Nineteenth-Century Cornwall
Authors: Gillin Edward J.
Published: November 2023

In the early nineteenth century, Cornwall was the centre of the world’s copper production. This extensive mining industry relied on powerful steam engines to keep the region’s deep mines pumped free of water. But Cornwall lacked its own coal reserves, which had to be imported at great cost. This problem of high energy cost sustained a rich engineering culture, focused on the pursuit of steam-engine economy. After the introduction of James Watt’s engines during the 1780s and 1790s, Cornish engineers experimented with new types of steam engine and recorded their performance through measures of ‘duty’. This chapter explores this activity and shows how, in this industrial context, local natural philosopher Robert Were Fox grew increasingly concerned with examining mines in terms of their heat. As miners dug ever deeper into the earth, they reported an increase in temperature, which Fox confirmed through a series of underground experiments. In this way, he likened the planet to a vast steam engine. Cornwall’s intense mining and steam-engine innovation shaped a rich scientific culture that was unmistakably industrial in its character.
Disquotation, Translation, and Context-Dependence
Authors: Heck Richard Kimberly
Published: November 2023

It has been known for some time that context-dependence poses a problem for disquotationalism, but the problem has largely been regarded as one of detail: one that will be solved by the right sort of cleverness. This chapter argues that the problem is one of principle and that extant attempts to solve the problem (which are based upon the notion of translation) cannot succeed. Along the way, it suggests that there are other familiar disquotationalist theses that are plausible only if we ignore context-dependence. And I argue against another way that translation is sometimes deployed, and not just by disquotationalists, but as an alternative to semantics.
On Lying, “Strictly Speaking”
Authors: Raimer Marga
Published: November 2023

What is involved in lying? This chapter focuses on the defense of three claims. First, deceptive intent is not a necessary condition for lying in general, even though deceptive intent is a defining feature of prototypical lies. Second, while ordinary folk might regard (non-logical) implying as a potential vehicle for lying in a “loose” sense, saying is required for lying in a “strict” sense. Third, the aptness of the descriptor “liar” depends, in part, on whether deceptive intent was present during the presumptive lie. Additionally, the relevance of experimental studies to philosophical accounts of lying is discussed, as is the potential philosophical importance of how we (as ordinary speakers vs. philosophical theorists) think and speak about those who lie: about those whom we think of (and refer to) as “liars,” and those whom we don’t.
À Propos de Pierre, Does He … or Doesn’t He?
Authors: Salmón Nathan
Published: November 2023

In Frege’s Puzzle (1986), Nathan Salmón analyzed ‘a withholds believing p’ in terms of a ternary relation BEL of x believing a proposition p under a guise g. The analysis is the following: There is a proposition guise g such that a grasps p by means of g but a does not stand in BEL to p and g. Sean Crawford has made a proposal for Millians to evade propositional guises through second-order belief. Specifically, in effect, Crawford proposes to analyze the crucial notion of withheld belief instead as believing that one does not believe: a believes that a does not believe p. Crawford’s clever proposal thus avoids explicit quantification over guises. However, it is shown that the proposal is inadequate to avoid guises. The resulting notion is too weak to capture the relevant notion of withheld belief.
Jewish Soldiers in Nazi Captivity
Authors: Linenberg Yorai
Published: November 2023

The book explores the extraordinary story of Jewish POWs in German captivity during the Second World War—extraordinary because of the contrast between Germany’s genocidal policy towards Jews on one hand, and its relatively non-discriminatory treatment of Jewish POWs from western countries on the other. The radicalization of Germany’s anti-Semitic policies entered its last phase in June 1941 with the invasion of the Soviet Union; during the following four years, nearly 6 million Jews were murdered. In parallel, Germany’s POW policies had gone through a radicalization process of their own, resulting in the murder of millions of Soviet POWs, of Allied commando soldiers, and of POW escapees, with Adolf Hitler eventually transferring in July 1944 the responsibility for POWs from the Wehrmacht to Heinrich Himmler, in his role as head of the Replacement Army. And yet, despite all that, Jewish POWs from western countries were usually not discriminated against and were treated, in most cases, according to the 1929 Geneva Convention. Focusing on the experience of American and British Jewish POWs, the book analyses their story from two points of view: bottom-up—from the Jewish POW’s personal experience; and top-down—from the German High Command and the German POW Office’s—and addresses the following questions: what was it like to be an American or British Jewish POW in Nazi captivity; how were these POWs treated by their captors; and why were they treated in that way? Its conclusions will help to reshape our understanding of the Holocaust and of Nazi Germany.
Conclusion
Authors: Linenberg Yorai
Published: November 2023

Summarizing the main findings of this book, this chapter suggests that when it came to non-Soviet Jewish POWs, the OKW’s POW Office, unlike most German government and non-government organizations, refused to ‘work towards the Führer’ by implementing Nazi policies even without direct instructions to do so; and that it did not suffer any consequences as a result. Furthermore, the POW Office was able to do so because there was never a direct order from Hitler to treat non-Soviet Jewish POWs in a different manner to that of their non-Jewish comrades. The chapter also discusses why the two main explanations found in literature for the treatment of the Jewish POWs—the concern about reciprocity and the ‘national conservative value system’ of the Wehrmacht—did not play a major role in the decision-making process of the German leadership. The significance of these conclusions is that they challenge the accepted perception of the Holocaust as being an indiscriminate attempt to completely eradicate a specific ethnic group by using all means available to the state.
Organizing Creativity
Authors: Schaefer Stephan M.
Published: November 2023

The book systematically unpacks the complex interdependencies of contexts, processes, and practices of organizing creativity. It draws on abundant empirical examples, case illustrations, and seminal research from sociology, social psychology, and organization studies. Departing from a systematic overview of important theoretical perspectives, the book successively illuminates the implications of context, process, and practice for different dimensions of the creative process such as generating, evaluating, and organizing ideas. In addition to its thorough analysis of these dimensions, it contains a critical reflection on dominant notions of creativity in economy and society and suggests taking a radical transformative approach to organizing creativity which seeks to address social and ecological grand challenges. Overall it contributes a novel, multidimensional perspective and provides an interpretative and critical analysis of the complex interplay of the organizational, social, and cultural contexts, processes, and practices of organizing creativity.
IBM
Authors: Brooker Paul , Hayward Margaret
Published: November 2023

Lou Gerstner carried out the tech-company ‘comeback of the century’ through his 1990s redevelopment of the IBM (International Business Machines) corporation. This venerable and huge computer corporation was in decline by the time Gerstner became CEO in 1993. He launched a cost-cutting turnaround and, after the turnaround’s success, redeveloped IBM through a cultural and structural transformation. He continued the redevelopment through a prioritizing reorientation towards IT (information technology) services, such as consultancy and outsourcing. By the time Gerstner retired in 2002, IT services were the backbone of a remedially renewed IBM. However, Gerstner had not diversified into the cloud-computing services that were emerging by 2002: a point that is discussed in Appendix 2. The chapter’s final section provides some 2010s comparisons by looking at how Yahoo’s CEO, Marissa Mayer, tried to redevelop the relatively small Yahoo corporation, which had originated as a pioneering Internet-access start-up.
QBism and the Subjective Stance
Authors: French Steven
Published: November 2023

Phenomenology has also been brought to bear on QM in the context of recent discussions over the approach known as ‘QBism’. This takes the theoretical formalism to be simply a device for predicting an agent’s future experiences, rather than as representing the world. Such a first-person perspective has been widely taken to mesh with the phenomenological stance, as usually understood. However, although advocates of QBism maintain that any slide into solipsism can be resisted, they struggle to accommodate what has been called the ‘kicks from the world’. Here it is argued that in order do so while remaining within a phenomenological framework, the correlationist feature identified by London and Bauer should be incorporated. Interestingly, one of the phenomenologist philosophers who is often cited in this specific context, Merleau-Ponty, took classes with Gurwitsch and drew on London and Bauer’s ‘little book’ in his own analysis of quantum physics.
Interpretation or Reconstruction?
Authors: French Steven
Published: November 2023

Both the ‘Many Worlds’ interpretation and Relational Quantum Mechanics are typically presented as interpretations of quantum theory, whereas QBism is understood as a reconstruction of it. The latter has been suggested as the appropriate approach for phenomenologists to adopt, particularly since this account adopts a first-person perspective. However, in Chapter 10 it is argued that such a dramatic move is not necessary as London and Bauer have already laid down the groundwork for an appropriately phenomenological understanding of the theory. This can then be supplemented with the relationist features emphasized by ‘Many Worlds’ and RQM. Husserl himself insisted that phenomenology does not require any such reshaping of scientific practice itself, theoretical or otherwise; rather it and its foundations need to be understood from the perspective afforded by the epoché. It is precisely this understanding that London and Bauer’s ‘little book’ presents, with the theory taken as not just a piece of physics but a theory of knowledge in itself. The chapter, and book, concludes with the suggestion that as a result, London and Bauer’s account sits somewhere between an interpretation and a reconstruction of the theory and by virtue of that, represents a novel advance in considerations of how we should conceive of our relationship to the world.
The British Slave Trade
Authors: Webster Jane
Published: November 2023

Chapter 2 opens with an overview of Britain’s part in the transatlantic slave trade between the first documented British slaving voyage in 1562 and 1807, when Britain’s slave trade was abolished. The primary slave trading ports on the coast of West Africa are then introduced, and the mechanics of slave trading at these sites are detailed. Archaeological work at key African sites is also briefly introduced here, as a preface to more detailed use of information from these projects later in the book. Finally, brief information is provided on the principal New World disembarkation points for captives carried on British ships.
Modern Quantum Theory
Authors: Bertlmann Reinhold , Friis Nicolai
Published: November 2023

Based on a series of courses taught by the authors, this theoretical-physics textbook takes the reader on a journey from the beginnings of quantum theory in the early twentieth century to the realm of quantum-information processing in the twenty-first. It provides an introductory text on quantum mechanics and quantum information theory for undergraduate students in physics and related subjects, but also serves as a resource for graduate students who want to engage with more advanced topics, while offering a collection of derivations, proofs, technical methods, and references for graduate students and more experienced readers engaged with teaching and active research.
Wave-Particle Duality
Authors: Bertlmann Reinhold A. , Friis Nicolai
Published: November 2023

This chapter examines some crucial experiments and basic principles of quantum mechanics that have strongly influenced the development of quantum theory in its modern form: starting from Planck’s law of black-body radiation and its derivation using the quantization of energy; Einstein’s photon hypothesis for the puzzle presented by the photoelectric effect and its test via the Millikan experiment; the Compton effect; Bohr’s theses for the structure of the hydrogen atom and the complementarity of waves and particles i.e., the wave-particle duality, culminating in de Broglie’s ideas for matter waves and their confirmation in the Davisson-Germer experiment for electron diffraction from a crystal; Heisenberg’s uncertainty principle for position and momentum as well as for energy an time; the famous double-slit experiment and Born’s probability interpretation, and finally the provocative thought experiment of Schrödinger’s cat
The Time-Dependent Schrödinger Equation
Authors: Bertlmann Reinhold A. , Friis Nicolai
Published: November 2023

The second chapter introduces the notion of wave functions and their equation of motion proposed by Erwin Schrödinger. The interpretation and normalization of the wave function are discussed, leading to the continuity equation. The chapter also introduces basic mathematical operations that can be carried out for wave functions and operators, describing e.g., how to calculate scalar products and commutators, as well as expectation values and variances of observables. With these tools at hand, Heisenberg’s uncertainty principle is re-examined, focusing on the example of a Gaussian wave packet, which is studied both in position space and momentum space. We also discuss the time evolution of general states and of the exemplary wave packet. Finally, we will see how classical physics is recovered as a limiting case of the quantum-mechanical description
Mathematical Formalism of Quantum Mechanics
Authors: Bertlmann Reinhold A. , Friis Nicolai
Published: November 2023

In this chapter we present the mathematical framework of describing wave functions as vectors in a Hilbert space and observables as Hermitian operators on such a vector space. We describe the mathematical formulation of these ideas for finite and infinite-dimensional cases via the Dirac notation, and discuss the example of the Hilbert space of photon polarization. Important classes of linear operators on Hilbert spaces are discussed, including projectors, Hermitian and self-adjoint operators, as well as unitary operators. As an important centre piece for the mathematical language of quantum mechanics we present the spectral theorem. We discuss the subtleties of this framework in infinite dimensions, giving a brief overview of the distributional aspects of quantum mechanics and the conceptually important problem of finding self-adjoint extensions via the Weyl-von Neumann theorem
The Quantum Harmonic Oscillator
Authors: Bertlmann Reinhold A. , Friis Nicolai
Published: November 2023

We consider the time-independent Schrödinger equation for the harmonic oscillator potential and determine its bound states and energy levels in one spatial dimension using two approaches: the algebraic and the analytic method. Using the former, we introduce ladder operators: the annihilation and creation operators, as well as the occupation-number operator, and determine the ground state of the harmonic oscillator to be a Gaussian wave packet, while the latter method yields the general bound state solutions in terms of the Hermite polynomials. We further discuss the zero-point energy and uncertainty relation for the quantum harmonic oscillator and make a comparison to the classical harmonic oscillator. Finally, we examine the three-dimensional harmonic oscillator, which leads us to the description of systems with multiple degrees of freedom via the tensor product
Orbital Angular Momentum
Authors: Bertlmann Reinhold A. , Friis Nicolai
Published: November 2023

In this chapter we introduce the concept of orbital angular momentum into the mathematical language of quantum mechanics. We discuss the commutation relations of the corresponding operators and their roles as generators of rotations in the context of the theory of Lie groups and Lie algebras, focusing on the three-dimensional rotation group SO(3). We further examine how scalar and vector-valued operators transform under spatial rotations. We then turn to the derivation of the eigenfunctions and eigenvalues of the angular-momentum operators, for which we follow a dual approach in analogy to that employed for the harmonic oscillator in Chapter 5. Using both the algebraic ladder-operator method and an analytical method using spherical polar coordinates we discover the relevant azimuthal and magnetic quantum numbers and their relation to the spherical harmonics and the Legendre polynomials
The Three-Dimensional Schrödinger Equation
Authors: Bertlmann Reinhold A. , Friis Nicolai
Published: November 2023

In this chapter we consider the time-independent Schrödinger equation for three spatial dimensions. Making use of the orbital angular momentum observables, including the Laplacian in spherical polar coordinates, and introducing an effective potential, we recast the three-dimensional Schrödinger as a one-dimensional differential equation for the reduced radial wave function. In this context we discuss conditions for the existence of bound states and an upper bound on the ground-state energy obtained from the Rayleigh-Ritz variational principle. As an example we then consider the bound-state solutions for the spherical potential well and discuss the conditions for it admitting a ground state. We then turn to the Coulomb potential representing the hydrogen atom and discuss methods for obtaining upper and lower bounds on the ground-state energy to explain the stability of matter. Finally, obtain the Laguerre-polynomial solutions of the radial Schrödinger equation for the hydrogen atom, determine their energies and discuss their properties
Perturbative Methods in Quantum Mechanics
Authors: Bertlmann Reinhold A. , Friis Nicolai
Published: November 2023

In this chapter we review time-independent and time-dependent perturbation theory in quantum mechanics. We begin with Rayleigh-Schrödinger perturbation theory for small corrections to the Hamiltonian for non-degenerate and degenerate spectra, which leads us to a discussion of avoided crossings. We then apply these methods to calculate the fine-structure corrections for the energy levels of the hydrogen atom, including the relativistic correction to the kinetic energy, the spin-orbit correction, and the Darwin term. We then turn to the effect of weak constant magnetic fields: for the resulting Zeeman effect we distinguish between the anomalous Zeeman effect and the Paschen-Back effect. In the context of the corresponding Stark effect for electric fields we introduce the Wigner-Eckart theorem and calculate perturbations to first and second order. We then turn to time-independent problems and discuss the Born-von Neumann series for the propagator, time-ordered integrals, the interaction picture, before explaining Fermi’s golden rule.
Density Matrices
Authors: Bertlmann Reinhold A. , Friis Nicolai
Published: November 2023

In this chapter we discuss statistical mixtures of pure quantum states, resulting in so-called mixed states, and their representation using density operators. The properties of density operators for pure and mixed states are analysed and we examine their time evolution governed by the Liouville-von Neumann equation. As particular examples of interest we consider the density operators for thermal states, focusing on harmonic oscillators and the application of this model to calculate the average photon number for the modes of the electromagnetic field at thermal equilibrium. We then turn to two-level systems, or qubits, which are of particular relevance in quantum information theory and we inspect the geometry of the state space of density operators as a convex subspace of the Hilbert-Schmidt space. Finally, we take a closer look at density operators for bipartite systems which forms the mathematical basis for considering entanglement in later chapters.
Bell Inequalities
Authors: Bertlmann Reinhold A. , Friis Nicolai
Published: November 2023

This chapter presents a detailed discussion of Bell inequalities and their experimental tests. Starting from the Aharonov-Bohm version of the Einstein-Podolsky-Rosen (EPR) paradox, we review EPR’s criteria for realism and completeness and Bell’s locality condition, before deriving the Clauser-Horne-Shimony-Holt (CHSH) inequality. This is followed by an exposition on Bell’s original inequality and other Bell inequalities by Wigner, as well as Clauser and Horne. We then discuss the milestones in the experimental violation of Bell inequalities, from the experiment of Freedman and Clauser in the 1970s, to the efforts of Aspect et al. in the 1980s, the experiments by the teams of Zeilinger and Gisin in the 1990s, and culminating the loophole-free tests in 2015. Finally we turn to a brief discussion of the interpretations of quantum mechanics, focusing on contrasting the realist views held by, e.g., Einstein and Bell, and the informational views with proponents such as Brukner and Zeilinger
Entanglement and Separability
Authors: Bertlmann Reinhold A. , Friis Nicolai
Published: November 2023

This chapter gives a detailed overview of entanglement for pure and mixed states. We begin with the Schmidt-decomposition theorem, which allows us to associate the subsystem mixedness of pure state with entanglement. We discuss the purification of mixed quantum states, the convexity of the set of separable states, and entanglement as a form of correlation. As an example we examine the Bloch decomposition for two qubits. For the detection of entanglement the Peres-Horodecki criterion is introduced, before we analyse the relation between entanglement and non-locality via the CHSH-Operator Criterion and the family of Werner states. We further consider Tsirelson’s bound and hidden non-locality. We then discuss important mathematical tools for entanglement detection, including the positive-map theorem, the Størmer-Woronowicz theorem, and the reduction criterion. In this context we examine the family of isotropic states. Finally, the Weyl states provide an example for which we study the geometry of two-qubit entanglement
High-Dimensional Quantum Systems
Authors: Bertlmann Reinhold A. , Friis Nicolai
Published: November 2023

Chapter 17 deals with the description of high-dimensional quantum systems and entanglement between them. We start with the generalized Bloch decomposition and present several useful options for the choice of operator bases, including the generalized Gell-Mann basis, the polarization-operator basis, and the Weyl-operator basis. We apply these bases for the example of isotropic two-qudit states and for the detection of bound entanglement for systems of two qutrits. We then turn to the problem of detecting entanglement in high-dimensional systems. For this purpose we review mutually unbiased bases and employ them for entanglement detection. We then discuss entanglement detection using entropic uncertainty relations, before we show how to obtain lower bounds on pure-state fidelities, on the entanglement of formation, and on the Schmidt number from measurement in pairs of mutually unbiased bases
Multipartite Entanglement
Authors: Bertlmann Reinhold A. , Friis Nicolai
Published: November 2023

This chapter takes a closer look at entanglement in multipartite systems. An examination of pure tripartite systems serves a starting point from which we discover the equivalence classes of Greenberger-Horne-Zeilinger (GHZ) states and W states. We then continue with the mixed-state case and discuss the notions of full separability, partition-separability and biseparability versus genuine tripartite entanglement, before stating the GHZ theorem in the formulation following Mermin. For systems of three or more parties we then formulate the definitions for k-separability and genuine multipartite entanglement (GME), as well as for k-producibility and entanglement depth, followed by prominent examples for GME states such as the generalized GHZ states and Dicke states. We give an overview of the problem of detecting GME using various linear and non-linear GME witnesses, lifted witnesses, PPT mixers, before discussing challenges for the characterization and quantification of multipartite entanglement. We close by analysing the phenomenon of entangled entanglement.
Quantum Measurements
Authors: Bertlmann Reinhold A. , Friis Nicolai
Published: November 2023

In this chapter we first review projective or von Neumann measurements from the point of view of the projection postulate and the Lüders rule, before turning to more general measurements modelled using positive operator-valued measures (POVMs). After examining their mathematical description, we discuss symmetric informationally complete (SIC) POVMs and Zauner’s conjecture, as well as the representation of POVMs as projective measurements on a larger Hilbert space, a result called Naimark dilation. We then a model for non-ideal projective measurements and analyse the properties of such measurements in relation to the properties unbiasedness, faithfulness, and non-invasiveness of ideal projective measurements. Finally, we consider the problem of distinguishing non-orthogonal quantum states and examine how the use of POVMs can be beneficial for this task.
Quantum Metrology
Authors: Bertlmann Reinhold A. , Friis Nicolai
Published: November 2023

Chapter 24 provides a compact introduction to the topic of quantum metrology, focusing on Hamiltonian parameter estimation in the frequentist and in the Bayesian paradigms. We first discuss how estimates of non-directly measurable quantities such as phases are obtained from measurement statistics in the frequentist approach. We then discuss the Cramér-Rao bound and the Fisher information and study single-qubit phase estimation in the light of this result. We then turn to the multi-qubit setting and discuss the quantum Cramér-Rao bound, for which the quantum Fisher information is the central quantity of interest. In this context we discuss the Uhlmann fidelity in detail. We further contrast Heisenberg scaling with the standard quantum limit in the phase-estimation scenario. Finally, we analyse phase estimation in the Bayesian-estimation approach and derive the van Trees inequality as a Bayesian version of the Cramér-Rao bound
Quantum States of Light
Authors: Bertlmann Reinhold A. , Friis Nicolai
Published: November 2023

In this chapter we collect a number of key elements of quantum optics relevant for quantum information theory. We begin by discussing the quantization of the electromagnetic field in terms of harmonic oscillators with ladder operators and the corresponding Fock space. Based on this description we introduce Glauber’s coherent states and examine their properties as proper quantum analogues of the classical harmonic oscillator. We then study the description of states of light in a quantum-mechanical phase space by employing quasi-probability distributions such as the Wigner function. With these tools at hand we then focus on the family of Gaussian states and their compact description in terms of covariance matrices and vectors of first moments. We review the formalism of Gaussian operations, symplectic operations, the Williamson normal form, and the Bloch-Messiah decomposition. Finally, we take a look at entanglement of Gaussian states.
Particle Physics—Bell Inequalities
Authors: Bertlmann Reinhold A. , Friis Nicolai
Published: November 2023

In this chapter we review the phenomenology of K mesons, or kaons, and the possibility of Bell-inequality violation in systems of K-meson pairs. To this end we first study their properties and features: strangeness represented by the strange quark, the violation of the charge-conjugation parity (CP) symmetry, strangeness oscillation, and regeneration. These interesting phenomena emerge from the fact that the strangeness eigenstates, CP eigenstates, and mass eigenstates are not the same, as well as from the interplay of the strangeness-conserving and CP-conserving strong interaction and the weak interaction which violates these conservation rules. We then examine the quasi-spin analogy of K mesons and the correlation functions for entangled K-meson pairs. After concluding that the physical measurements possible for K-mesons do not allow a direct violation of Bell inequalities such as the Uchiyama-Bell inequality we identify the CP violation as an indirect violation of Bell inequalities.
Particle Physics—Entanglement and Decoherence
Authors: Bertlmann Reinhold A. , Friis Nicolai
Published: November 2023

In this chapter we revisit the creation of an entangled kaon state where the particles comprising the relevant pair propagate in to opposite directions. Experimental tests of Bell inequalities in particle physics are difficult and feature loopholes for local realistic models. Although such Bell tests are of fundamental interest, the examination of entanglement rather than non-locality for meson-antimeson pairs might be more feasible. To examine the possibilities and challenges for such tests, it is useful to study possible mechanisms for decoherence that might influence the quality of the entanglement. We consider possible decoherence effects arising from interactions of the quantum system with its environment: strong-interaction scatterings of kaons with nucleons, weak-interaction decays, as well as experimental noise. We concentrate on a specific model of decoherence developed by Bertlmann and Grimus that allows us to quantify the strength of such possible decoherence effects by the data of existing experiments