Context: Large-scale poloidal flow cells as formed by turbulent convection in stars are an integral part of stellar interior dynamics. Since large-scale flows reside predominantly in the deeper layers of the convection zones of stars, they are difficult to detect and characterize. Asteroseismology, the study of stellar oscillations, represents a unique method with which the stellar interior can be probed and information about different layers of a star as well as the general stellar structure can be obtained. We evaluate if large-scale poloidal flow cells lead to signatures in seismic data that can be used to measure such flows.
Aims: The effects of flows on oscillation modes of stars are investigated by means of forward calculations, with a particular focus on non-axisymmetric cell formations, also referred to as giant cells. For stars other than the Sun, such a description has not been undertaken to date. For the Sun, the characterization of giant cells from observations still remains inconclusive. In particular, observations seem to disagree with current numerical models, calling for further investigation with new or refined measurement techniques. By solving the forward problem, this work provides the basis for the development of techniques to detect or characterize large-scale non-axisymmetric flow formations through global stellar oscillations.
Methods: To describe the influence of flows on stellar oscillations, we employ perturbation theory; specifically in the form proposed by Lavely and Ritzwoller (1992), who formulated an analytical framework on this matter. The presence of a flow leads to a coupling of the stellar oscillation modes, which results in frequency shifts and a mixing of the mode eigenfunctions. These effects are investigated in forward calculations for a subgiant stellar model and a solar model, in both the non-rotating and the rotating case.
Results and Conclusions: Our calculations show that resulting frequency shifts are predominantly symmetric for modes of opposite azimuthal order ±m, in contrast to previous authors, who reported asymmetric shifts. This implies that rotation inversions for stars are not affected by poloidal flows. In general, the magnitude of the obtained frequency shifts lies below current frequency errors for the subgiant as well as for the Sun, rendering the shifts inaccessible as diagnostic quantities. However, we expect that the perturbation of the eigenfunctions (mode mixing) will lead to ancillary signal components of different frequencies in observations, from which, if detected, information about the flow can be inferred. If the ancillary signal components are not detected, we expect that upper limits on flow velocities could be derived.
Quantum many-body systems present a formidable challenge to tackle either analytically or numerically. As such any extra tools we can get to treat such systems are of utmost importance for practical applications. In the first part of this thesis, we address the pure univariate quantum marginal problem, whose full solution has been found recently (Klyachko 2004). Such problem asks for the possible eigenvalues of the one-particle reduced density matrices (1-RDMs) of a globally pure state. It presents a deep insight into the local properties of many-body systems and a possible tool for the simplification of the analysis of such systems.
We present a simple solution of the fact that whenever the spectrum of the 1-RDMs of a state, which are one particle objects, is extremal, it leads to significant structural simplifications of the states that can give rise to such 1 RDMs.
We address as well the marginal problem for Fermions Fock space and characterized the mode and particle marginals. We show that for the particle reduction there are no constraints in Fock space, unlike in the case of a fixed number of particles. We consider also the mode marginals for free Fermions and fully characterize it. Resorting to the Jordan-Wigner transformation the obtained characterization corresponds exactly to the one known for a system of qubits.
Finally we examine the computational complexity of deciding from local spectral information whether many-body states are entangled or not. We show that while it is true that few easily obtainable physical measurements may be sufficient to witness many-body entanglement, the classical post processing of the obtained data is, in principle, intractable in the sense that the problem is NP-complete.
In the second part of this thesis we study the electronic transport properties of geometrically frustrated systems, with special emphasis on the AB2 chain. We begin by studying it in the non interacting case and proceed to give an exact solution in the strong coupling limit when considering interacting spinless Fermions.
We propose, as well, a method for constructing localized states in non-interacting geometrically frustrated systems which leads to states which are highly localized.
We then study the conductance through the AB2 chain and show that localized states in geometrically frustrated systems lead to rather interesting behavior in the two terminal electronic conductance through such systems. In particular in the absence of magnetic flux these localized states act as filters of the zero frequency conductance peak (where we refer to the frequency of an incident electron). The addition of magnetic flux changes the behavior of the localized states in the conductance: some still filter the zero frequency peak while others contribute to the appearance of a zero frequency peak, and as such the conductance profile exhibits a zero frequency peak with a dip, which is a distinct fingerprint of the existence of localized states.
We finally propose a new method for calculating the conductance through interacting clusters, and shown that it is in agreement with already well known methods. We use it to calculate the conductance through interacting spinless AB2 chains. We show that the non-interaction conductance profiles persist for small values of the interaction and that some possibly expected conductance peaks are actually experimentally non-accessible due to the flat band of the AB2 chain.
The quantum vacuum is subject to a spontaneous creation and annihilation of virtual photons. Electromagnetic sources (charges, permanent dipoles, fluctuating dipoles) can hence interact with one other by virtue of an exchange of virtual photons. It is the aim of this thesis to study different photon-mediated interactions in complex magnetodielectric environments: Coulomb interactions between charges, interactions between permanent dipoles, Casimir–Polder interactions between a polarizable atom and a surface, van derWaals interactions between two excited or chiral molecules. Material environments influence the interaction since the photons can be reflected from the surface of the body. In all these scenarios we fully account for the influence of macroscopic media, bodies or surfaces on the interaction and demonstrate that the latter will enhance or reduce the photon-mediated interaction via many-body interactions. Typically, time-independent perturbation theory can be applied to evaluate the interaction potential as an energy shift due to atom–field coupling. However, we will see that time-independent models cannot suitable describe van der Waals interaction between excited atoms. More elaborated dynamical approaches will be used to capture the dynamics of the coupling.
As a first example we evaluate the Coulomb interaction between charges in the presence of macroscopic media. This problem is often treated with the method of images. However, there are several examples where it not possible to construct an image: for example the interaction between a charge and a hole must be considered with another approaches. We show that the Coulomb interaction is proportional to the scalar Green’s function, which represents the propagator of the interaction. We find the tunable interaction can be controlled by changing the geometric parameters of the environment. Material environments can also screen the interaction.
Secondly, we have considered dynamical approaches to capture the dynamics of excited atoms near macroscopic bodies. When considering two atoms, one excited and the other in the ground-state, we find the remarkable and surprising result that for large distances the van der Waals force acting on the ground-state atom is monotonic, while the force acting in the excited atom is spatially oscillating, answering a long-standing controversy. This would imply an apparent violation of the action–reaction principle in excited systems in free space. However, the momentum balance is restored when taking the photon emitted by the excited atom into account. The difference between forces on the excited vs ground-state atoms can be interpreted as a photon recoil force. If in a molecule made up of two atoms we can selectively excite ome atom, and observe the center-of-mass acceleration. This is an important example where the violation of action-reaction could be achieved and measured. The mean velocity acquired by the molecule can be incremented to several cycles of excitation and thermalisation and seen by trajectory imaging of the moving molecule. Similarly we have studied another non-equilibrium situation: the thermal van der Waals interaction between ground-state molecules. Polar molecules are ideal candidates for studying the thermal vdW (van der Waals) interaction, since their heating time can be of the order of several seconds, and they have few rotational excited energy levels populated at room temperature. We find that the force acting on one molecule is different on the force acting on the other molecule due to the momentum contributed by the absorbed or emitted photon. Only for large times where both atoms have been thermalized the action-reaction principle is restored. Hence there is a connection between the violation of action-reaction symmetry and non equilibrium molecular states.
The presence of macroscopic bodies is of fundamental importance in another important example: the van der Waals interaction between chiral molecules. Chiral molecules lack any center of inversion nor plane of symmetry. Hence they exist as two distinct enantiomers, left-handed and righthanded, which are related to space inversion. The van der Waals interaction contains discriminatory terms depending on the chiral polarizabilities of the molecular species. We show that the presence of chiral surfaces can enhance these contributions making it possible to measure the chiral contributions to the van der Waals force with current technology. The van der Waals interaction is discriminatory with respect to enantiomers of different handedness and could be used to separate enantiomers.
The discrimination of chiral species could be also achieved in the Casimir–Polder interaction between a chiral molecule and a surface. Switching on the interaction between the molecule and the field at a particular time, we study the resulting temporal evolution of the Casimir–Polder interaction. For short times the evolution of the energy is dominated by oscillations in time with a frequency related to the molecular transition frequency. The dynamical force is particularly strong around the back-reaction time, which is the time needed for the molecule to emit and reabsorb a photon reflected by the surface. Hence the discriminatory dynamical interaction could be used to separate enatiomers, in close analogy with the van der Waals interaction.
Table of contents
List of figures v
List of tables vii
List of abbreviations ix
1 Introduction 1
1.1 Preliminary considerations on what is a quotation? 4
1.1.1 The ordinary concept of quotation in the OED 4
1.1.2 A data-based broad concept of quotation 7
1.2 Methodological considerations 8
1.2.1 The nature of the data and the impact of the quoted text on its quotations 8
1.2.2 The sources of the data and their method of retrieval 10
1.3 Structure of the thesis 16
2 The source of this our study – Shakespeare's times, his art and the question of
2.1 Words, words, words – Shakespeare's vocabulary 21
2.2 Phrases, phrases, phrases – Shakespearean passages and idiomatic
2.3 Shakespeare's fame 25
2.4 Sweet smoke of rhetoric – Shakespeare's rhetoric 26
2.5 Suit the word to the action – The pragmatics of Shakespeare's language 29
2.6 Shakespeare's rhetoric and quotability 31
2.6.1 Positive text-inherent factors for quotability 31
2.6.2 O, this is counter – Inhibiting text-inherent factors for quotability 34
2.6.3 To be, or not to be – An empirical test 36
2.7 Concluding remarks 38
3 Scholarly concepts of quotation 41
3.1 Quotations in the philosophy of language 41
3.1.1 "A certain anomalous feature" – Quine's Proper Name Theory 41
3.1.2 Quotation's journey from scientific to ordinary language –
Davidson's Demonstrative Theory 43
3.1.3 Quotation's journey from semantics to pragmatics –
Saka's Disambiguated Ostention Theory 44
3.1.4 Summarising remarks 46
3.2 Quotations in literary studies 47
3.2.1 The realm of intertextuality studies 48
3.2.2 Definitions of quotation and allusion in intertextuality studies 51
3.2.3 Summarising remarks 55
3.3 Quotations in linguistics 58
3.3.1 Quotations as reported speech 58
3.3.2 Quotations in the language of newspapers – Functional studies 59
3.3.3 Quotations in phraseology 61
3.4 Concluding remarks 65
4 Marking and the role of linguistic knowledge for the identification
of quotations 67
4.1 Global and local marking in fiction 68
4.1.1 Helbig's global account of marking 69
4.1.2 The clue-based approach to marking in HyperHamlet 72
4.2 Local marking in fiction and non-fiction 74
4.2.1 Typographical marking – The quintessential function of quotation marks 75
4.2.2 Other typographical markers 78
4.2.3 Metalinguistic markers 79
4.2.4 Name markers 85
4.2.5 Stylistic markers 91
4.3 Frequencies of markers for quotation as recorded in HyperHamlet 95
4.3.1 Typographical, metalinguistic and stylistic markers in detail 97
4.3.2 Marking for author and work in detail 98
4.4 Summary 101
5 Archaisms in practice – Empirical observations 104
5.1 The use of archaisms in The lady protests too much, methinks 105
5.2 The French word order of to the manner born and its function in discourse 115
5.3 The role of thy in Frailty, thy name is woman 119
5.4 Concluding remarks 124
6 Similarity relations and the role of textual knowledge for the
identification of quotations 126
6.1 Textual knowledge as the main basis for identifying, evaluating,
describing and classifying quotations 127
6.1.1 Thematic quotations 129
6.1.2 Onomastic quotations 134
6.1.3 Verbal quotations 137
6.2 Additional supportive knowledge for the evaluation of quotations 151
6.3 Concluding remarks 154
7 Verbal quotations and phraseology 158
7.1 Issues in phraseology 161
7.2 Definitions of phrasemes 162
7.3 Similarities and differences between quotations and phrasemes 164
7.3.1 Form – Polylexicality and fixedness 166
7.3.2 Meaning – Idiomaticity 173
7.3.3 Grammatical status – Familiarity and conventionalisation 177
7.4 Concluding remarks 184
8 Quotations from Hamlet in the English phrasicon I:
General data on hoist petards, methodical madnesses,
kind cruelties and honourable breaches 187
8.1 General comments on the analysed quotations 188
8.1.1 Comments on
For 'tis sport to have the engineer / Hoist with his own petard (III, iv) 188
8.1.2 Comments on Though this be madness, yet there is method in't (II, ii) 189
8.1.3 Comments on I must be cruel, only to be kind (III, iv) 190
8.1.4 Comments on It is a custom, more honour'd in the breach than
the observance (I, iv) 192
8.2 Finding the data – Search procedures and the range of variability 193
8.2.1 Searching for hoist/petard 194
8.2.2 Searching for method/madness 196
8.2.3 Searching for cruel/kind 198
8.2.4 Searching for honoured/breach 199
8.3 Quantitative overview 200
9 Quotations from Hamlet in the English phrasicon II:
Pattern formation and discourse distribution 204
9.1 Formal patterns 204
9.1.1 Formal patterns of quoting: hoist/petard 205
9.1.2 Formal patterns of quoting: method/madness 211
9.1.3 Formal patterns of quoting: cruel/kind 216
9.1.4 Formal patterns of quoting: honoured/breach 219
9.2 Semantic patterns 224
9.2.1 Semantic patterns of hoist/petard 224
9.2.2 Semantic patterns of honoured/breach 226
9.2.3 Semantic aspects of method/madness and cruel/kind 229
9.3 Discursive distribution 230
9.3.1 Discursive distribution of hoist/petard 231
9.3.2 Discursive distribution of method/madness 234
9.3.3 Discursive distribution of cruel/kind 236
9.3.4 Discursive distribution of honoured/breach 238
9.4 Summary 241
10 Conclusions and outlook 244
Appendix: The 50 most frequently quoted lines from Hamlet in HYHA 253
References and resources 254
Text collections, databases and further resources 266
Index of authors 268
Index of subjects 271,Quotations "oscillate between the occasional and the conventional" as Burger/Buhofer/Sialm (1982) once succinctly formulated. Developed from a PhD thesis, this book explores precisely this "oscillating" character of quotations: It discusses the nature of quotations and the relationship between common quotations and phraseology from a theoretical and an empirical perspective. Shakespeare's Hamlet was chosen as a canonical text whose frequently quoted traces can be followed across centuries.
Scholarly work from various disciplines leads to an understanding of quotations as moving in a space created by the two dimensions of reference and repetition: Quotations are definable by a horizontal communicative axis (reference) and a vertical, intertextual axis of manifest lineages of use (repetition). Empirically, the data led to a categorisation of quotations as verbal, thematic and onomastic, based on the question "what has been repeated: words, themes or names?" Case studies further corroborate the proposition that verbal quotations may become (almost) ordinary multi-word units if the following conditions are met: a) they lose their referential dimension, b) they develop formal and/or semantic usage patterns and/or c) they are no longer limited to their original, literary discourse.,