This chapter explores to what extent the closed-contour Schwinger–Keldysh approach and the Lindblad Master equation can be connected with each other. Here, the connection with the Schwinger–Keldysh closed-contour approach does not involve the full machinery of the Green’s functions method, but rather refers directly to the time evolution of the many-body density matrix, which contains a forward evolution operator from the reference time t₀ to the measuring time t and a backward evolution operator from t back to t₀. The key approximations to derive the Lindblad Master equation are specified in detail. As an example, a two-level system coupled to a phonon bath is explicitly considered.

In the present chapter, the authors offer a social exchange theory analysis of processes within intraracial versus interracial relationships. After commenting upon “the rise in intermarriage” (particularly within the United States during the past 50 years), the authors draw upon Levinger’s (1980) Acquaintance-Buildup-Continuation-Deterioration-Ending (ABCDE) model regarding stages of relationship development, highlighting several quantitative studies that examine social exchange processes at each transition or turning point between stages of intraracial and (especially) interracial relationships. Furthermore, the authors address implications of certain interdependence processes for the stability of intraracial and interracial relationships, as well as gaps in the evidence that is available concerning turning points within both types of relationships. Subsequently, the authors identify particular studies that serve as points of departure for suggestions about methodological changes and theoretical additions in future research on intraracial and interracial relationships. Finally, the authors provide examples of still-unanswered questions within the literature on interracial relationships in particular.

Chapter 6 tests and illustrates the argument that protest broker availability helps to shape where protests occur by affecting the ability of elites to mobilize collective action. Drawing on a unique combination of original protest data from South Africa, over two years of fieldwork, and a new survey with local elites, the chapter demonstrates that both elites and citizens recognize the pivotal role of protest brokers in enabling protest. The evidence shows that broker presence is a critical factor in explaining geographic variation in protest activity. Through three detailed case studies, the chapter further unpacks the mechanisms behind this relationship. First, it examines repeated failures to mobilize protest in a broker-absent community. Second, it shows how the loss of a broker reduces protest activity in a previously mobilized area. And finally, it analyzes regional protest efforts, revealing that communities with brokers are more likely to participate. These findings confirm that broker availability not only affects local mobilization capacity but also helps to explain larger patterns of protest distribution. The chapter underscores the broader importance of brokerage in collective action, particularly under conditions of elite-led mobilization.

In the decades of Romanticism a new view on culture emerged: one in which culture was nationally specific (each nation having its own characteristic cultural traditions) and should be seen as process of historical development (rather than the condition of being civilized and refined). In the emergence of this new, historicist and nationally specific idea of culture, an initial impetus was provided by the ‘discovery’ in the 1760s of the epic poems of the ancient Scottish bard Ossian. The figure of Ossian amplified the aesthetics of the ‘sublime’ and a view of the poet as a prophetic, even mantic figure, drawing on a transcendent-spiritual intuition and hence being able to speak with an inspired wisdom that went beyond mere rational cognition. This became enshrined in the poetics of the nascent Romantic movement and fed into the Hegelian notion of poet–prophets as world-historical figures articulating the consciousness of their national communities.

The general expressions for the number density and current are first considered under the action of an external time-dependent perturbing potential of arbitrary strength and cast in terms of the single-particle lesser Green’s function. The expansion of the number density up to linear order in the perturbing potential is then considered, yielding the density–density correlation function of linear-response theory. A connection is also considered with the temperature correlation function of the Matsubara formalism via an analytic continuation in frequency space.

This chapter explores the role of linguistics in language teacher preparation. Against a profound demographic shift currently underway in the US, it provides a rationale for preparing ESL and bilingual teachers who are well-equipped to work with diverse students in K-12 contexts. Crucially, the chapter explores two key points: the value of linguistic analysis and an equity-based approach to language teaching. Linguistic analysis allows teachers to recognize patterns in the language of their students; in doing so, teachers can isolate recurring errors, recognize where their students are in the learning process, and better target their teaching to address the errors and move students forward. The chapter also shows how linguistics training helps teachers understand language variation, dialects, and the role of society, especially for languages with less social power and prestige. It argues that teachers’ awareness of harmful language ideologies helps combat societal inequities that use language as a proxy for discrimination and subjugation. The chapter ends with suggestions for further reading and discussion questions for teachers and teacher educators.

Chapter 9 covers the remaining aspects of the visual atmospherics – colours and signage. Colours are often said to comprise three dimensions: hue, brightness contrast, and saturation. The dimension that has been studied the most is hue. Hue is often described as on a scale from warm colours (red) to cool colours (blue). Research has shown that warmer colours tend to take over the visual scene and force their way into the s consciousness of shoppers. A red colour therefore makes shoppers more aroused or even confused and may interfere with the shoppers' ability to notice other stimuli. A store with too many red objects would overload the senses of the shoppers, and therefore it makes sense to instead work with brightness contrast. The eye's ability to detect brightness contrast primarily resides in the rods in the retina, while the cones primarily are responsible for colour vision. Research has shown that independent of hue, a contrast in the brightness level can create an even stronger visual pop-out effect. Regarding signage, it is found that a sign’s primary task is to attract attention. The attention-grabbing aspect is often more important than the communication. The optimal way to write prices is covered in Chapter 13.

This chapter reconsiders the original derivation of the Kadanoff and Baym equations, which relies on a procedure of analytic continuation from imaginary to real time in terms of an “extended” Matsubara approach. The procedure of analytic continuation proves useful for formal developments, like those to be considered in Chapters 28 and 29. The case when the system Hamiltonian does not depend on time is first treated, and the procedure is then extended under appropriate assumptions to the case when the Hamiltonian depends on time.

This chapter will provide a forensic analysis of the threshold of NIAC and is divided into five sections. The first section briefly explores the distinction and relationship between the material elements of NIAC and the threshold of NIAC. In particular, it identifies the overarching theme of NIACs threshold and proposes a three-step analytical process for determining its existence in practice. The second section explores the first step in identifying the existence of a NIAC, referred to here as the qualification of armed violence, which involves identifying the material elements of NIAC within a situation of armed violence. The third section examines how armed violence is evaluated when determining the threshold of NIAC, and in particular, how the expression ‘protracted armed violence’ has been and should be interpreted. The fourth section explores the organizational requirement of NIACs threshold, including the rationale for this requirement, the degree of organization necessary to qualify as a Party to a NIAC, and what organisation looks like in practice. The fifth section provides a typology of armed group organisation, which is examined through the lens of the ability to engage in NIAC. The sixth section concludes by examining the very fulcrum of conflict identification: the question of who or what decides when a situation of armed violence amounts to a NIAC.