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Chapter 8 is devoted to the study of the dynamics of quantum systems, based on the formalism presented in Chapter 7 and previous chapters. The operator notation and its matrix representation are used without distinction, moving freely from one to the other as convenient. This allows us to study the evolution of the system from different perspectives, depending on the description adopted. The chapter includes a discussion of the statistical information contained in the quantum formalism, a formal derivation of the Heisenberg inequalities and a clarification of their physical meaning. A section is dedicated to quantum canonical and related transformations. More advanced topics, which provide a valuable complement, include Noether’s theorem on the relationship between the symmetry properties and the conserved dynamical variables of the system.
Christopher Arthur’s 2022 book The Spectre of Capital presents a systematic-dialectical exposition of the capitalist economy, focussing on the forms of capital. The book is a specific synthesis of much of Arthur’s earlier writings (the relevant works are listed in Arthur 2022: 441–42). Inherently the book goes beyond those earlier writings, because ‘synthesis’ and the associated interconnectedness of ‘moments’ is the true art of the book.
A thin, evaporating sessile droplet with a pinned contact line containing inert particles is considered. In the limit in which the liquid flow decouples from the particle transport, we discuss the interplay between particle advection, diffusion and adsorption onto the solid substrate on which the droplet sits. We perform an asymptotic analysis in the physically relevant regime in which the Péclet number is large, i.e. ${\textit{Pe}}\gg 1$, so that advection dominates diffusion in the droplet except in a boundary layer near the contact line, and in which the ratio of the particle velocities due to substrate adsorption and diffusion is at most of order unity as ${\textit{Pe}}\rightarrow \infty$. We use the asymptotic model alongside numerical simulations to demonstrate that substrate adsorption leads to a different leading-order distribution of particle mass compared with cases with negligible substrate adsorption, with a significant reduction of the mass in the suspension – the nascent coffee ring reported in Moore et al. (J. Fluid Mech., vol. 920, 2021, A54). The redistribution leads to an extension of the validity of the dilute suspension assumption, albeit at the cost of breakdown due to the growth of the deposited layer, which are important considerations for future models that seek to accurately model the porous deposit regions.
In this paper, we study the cohomology of the unitary unramified PEL Rapoport-Zink space of signature $(1,n-1)$ at hyperspecial level. Our method revolves around the spectral sequence associated to the open cover by the analytical tubes of the closed Bruhat-Tits strata in the special fiber, which were constructed by Vollaard and Wedhorn. The cohomology of these strata, which are isomorphic to generalized Deligne-Lusztig varieties, has been computed in an earlier work. This spectral sequence allows us to prove the semisimplicity of the Frobenius action and the non-admissibility of the cohomology in general. Via p-adic uniformization, we relate the cohomology of the Rapoport-Zink space to the cohomology of the supersingular locus of a Shimura variety with no level at p. In the case $n=3$ or $4$, we give a complete description of the cohomology of the supersingular locus in terms of automorphic representations.
Chapter 11 is devoted to the quantum theory of angular momentum. As in classical mechanics, working with angular momentum requires leaving the one-dimensional space, with all the complications that this entails. The importance of angular momentum resides in at least three facts: i) central problems are of particular interest; (ii) many particles have an intrinsic angular momentum (the spin); and iii) the physics of angular momentum involves features such as the so-called space quantization. The first part of the chapter deals with the orbital angular momentum and its eigenfunctions, the spherical harmonics. Its algebraic properties, embodied in the matrix representation, allow for an extension of the theory to half-integer angular momentum in terms of Pauli matrices, as well as the addition of angular momenta.
Artificial intelligence is reshaping the contemporary world. Trickling deeper into archaeology and history, these technological changes will influence how the past is written about and visualized. Through the evaluation of text and images generated using AI, this article considers the systemic biases present in reconstructed archaeological scenes. We draw on advances in computer science, running large-scale, computational analyses to evaluate patterns in content. We present a case study examining Neanderthal behavior, juxtaposing published archaeological knowledge with images and text made using AI. Our study reveals a low correspondence between scientific literature and artificially intelligent material, which reflects dated knowledge and cultural anachronisms. Used to identify patterns in (mis)representations of the past, the methodology can be applied to understand the distance between scholarly knowledge and any domain of content generated using AI, across any archaeological time depth and beyond the discipline.
The Arctic is one of the fastest-warming places on Earth. The High Arctic Archipelago of Svalbard contains over 1500 glaciers that have, overall, experienced widespread thinning and recession since the Little Ice Age (LIA; ∼1900 CE), and this recession has accelerated since 1990. Here, we showcase the terminal decline since the end of the LIA of Elsabreen and Ferdinandbreen, two small land-terminating glaciers in Petuniabukta, Dickson Land. We map glacier areal extents using previously published data, aerial photographs and satellite imagery (LIA to 2024) and derive ice volume changes by differencing digital elevation models (1938 to 2023). Both glaciers have lost over 93% of their glacier area since the LIA and over 96% of their ice volume since 1938. By 2024, Elsabreen had reduced to a small glacier remnant with little evidence of ice flow, and Ferdinandbreen had fragmented into several separate ice units and completely detached from its original accumulation areas. Both of these vanishing glaciers merit inclusion on the Global Glacier Casualty List.
The questions of accountability, legality, and legitimacy in regard to economic sanctions are remarkably convoluted. While they are distinct concepts, in the context of economic sanctions they are closely intertwined. Accountability can be found in many forms, including judicial venues, institutional oversight, political mechanisms, and public protest. In the case of the UNSC sanctions on Iraq in the 1990s, it might be said that the main forms of accountability that came into play were public pressure, as well as political pressure within the UN and outside of it. In the case of “targeted” sanctions, the perception that these measures are genuinely limited in their effects has obscured the fact that they are often indiscriminate and disproportionate, raising questions of legitimacy and legality, while undermining efforts at accountability. With regard to unilateral sanctions imposed by states, there are often significant issues of legality, where these measures do not properly constitute either retorsions or countermeasures. While asset freezes and similar blacklists of individuals (SDNs) appear to address the legal and ethical objections to comprehensive sanctions, there are issues related to the lack of due process, with implications for both the legality and legitimacy of these measures.
Consultation-liaison psychiatry (CLP) refers to the subspecialty of psychiatry and the specialist clinical services that deliver care at the intersection of mental and physical healthcare. CLP services provide specialist medical and multidisciplinary expertise for managing conditions in these areas of mental and physical healthcare overlap, and comorbidity. The Model of Care for CLP was identified as a key priority in Sharing the Vision, the 2020 national mental health policy in Ireland. Following four years of work by a writing group initiated by the Faculty of Liaison Psychiatry at the College of Psychiatrists of Ireland, the Model of Care for CLP in Ireland was launched in May 2025 (Cpsychi H (2025). Consultation-Liaison Psychiatry: A Model of Care for Ireland. Dublin: HSE.).). Consultation-Liaison Psychiatry: A Model of Care for Ireland. Dublin: HSE.). This reflects the collaborative efforts between the Liaison Faculty and the Irish Health Service Executive (HSE). This Model of Care, developed in collaboration with clinicians and patients, the College of Psychiatrists of Ireland, and the HSE, provides a potential template for future collaborations in the development and implementation of National Mental Health policy.
Chapter 3 introduces the student to the matrix formulation of quantum mechanics, pioneered by Heisenberg in collaboration with Born and Jordan. It provides the basic formal elements of the Heisenberg description in terms of operators and their matrix representation, derives the Heisenberg inequality, and applies the formalism to the harmonic oscillator as a central and particularly simple quantum problem. It introduces the state vectors and their Hilbert space, and concludes with a brief discussion hinting at the physical significance of the replacement of classical continuous dynamical variables with operators as a manifestation of the coupling of the particle to the radiation field.
Sanctions regimes can and have had both direct and indirect negative impacts on humanitarian action. These include restrictions on goods necessary for a humanitarian response, and de-risking by private sector actors, which restricts or prevents humanitarian organizations from accessing the services these actors provide, such as banking or transport. These challenges have been documented in humanitarian crises across the world, from Syria to Somalia, Afghanistan, and Sudan, hindering the ability of those in need to access and receive assistance and protection. There are several ways in which we can ensure sanctions regimes do not hinder aid. Chief among them is the inclusion in sanctions regimes of humanitarian exemptions, which explicitly exclude humanitarian action from their scope of application. Although progress on that front in recent years has helped, challenges remain. This chapter highlights the need for continued efforts to ensure that humanitarian action is safeguarded. These include the development of guidance on the scope of sanctions and on humanitarian exemptions, continued awareness-raising of the issue, stronger dialogue and engagement between governments, the private sector, and humanitarian organizations, and better risk sharing. Overall, there is a need to continue to put the focus on the dramatic needs of millions of people who depend on humanitarian organizations being able to do their work without hindrance and in accordance with international humanitarian law (IHL).
As a step towards realising a skin-friction drag reduction technique that scales favourably with Reynolds number, the impact of a synthetic jet on a turbulent boundary layer was explored through a study combining wind-tunnel measurements and large eddy simulations. The jet was ejected in the wall-normal direction through a rectangular slot whose spanwise dimension matched that of dominant large-scale structures in the logarithmic region to target structures of that size and smaller simultaneously. Local skin-friction reduction was observed at both $x/\delta =2$ and $x/\delta =5$ downstream of the orifice centreline, where $\delta$ is the boundary-layer thickness. At $x/\delta =2$, the skin-friction reduction was observed to be due to the synthetic-jet velocity deficit intersecting the wall. At $x/\delta =5$, evidence from the simulations and wind-tunnel measurements suggests that a weakening of wall-coherent velocity scales is primarily responsible for the skin-friction reduction. Local skin-friction reduction which scales favourably with Reynolds number may be achievable with the synthetic jet employed in this study. However, there are many technical hurdles to overcome to achieve net skin-friction drag reduction over the entire region of influence. For instance, regions of skin-friction increase were observed close to the orifice ($x/\delta \lt 2$) and downstream of the orifice edge due to the induced motion of synthetic-jet vortical structures. Additionally, a recirculation region was seen to form during expulsion, which has implications for pressure drag on non-planar surfaces.
Northern Calabria forms part of the Calabrian Arc, a geologically complex region in southern Italy shaped by the convergence between the Eurasian and African plates. This convergence drove the closure of the Tethys Ocean and produced the subsequent phases of collisional and extensional tectonics. Thrusting during the Alpine orogeny produced extensive nappe stacking, followed by structural reorganization and exhumation during the Oligocene-Miocene. Tectonostratigraphically, the Apennine carbonate platform forms the lowest structural unit, overlain successively by the Liguride Oceanic Complex and the Calabride Complex, which includes the Sila nappe stack. Along Calabria’s eastern Ionian margin, forearc basins developed in response to the retreating subduction zone. To better constrain sediment routing pathways and regional uplift in northern Calabria from early to late Miocene, a multi-proxy provenance study was applied to four forearc basins: Rossano, Cirò, Crotone and Catanzaro. Quantitative heavy-mineral analysis, single-grain garnet and apatite chemistry, and apatite U–Pb chronology reveal spatial and temporal variations in sediment sources. Siliciclastic samples, spanning Aquitanian to Messinian in age, record changing contributions from a combination of low- to high-grade metamorphic and plutonic sources, including mafic Liguride units. Up-section shifts in sediment sourcing patterns indicate that Calabrian Arc exhumation and uplift, characterized by a rapid increase in the middle Miocene followed by a slow reduction in relief, played a pivotal role in controlling the timing and direction of sediment transport. This study demonstrates the benefits of multi-method provenance approaches to achieve valuable insights into relief build-up and demise, associated divide migration and sedimentary responses within a young and complex, zircon-poor orogenic arc system.
Building on Oliver’s (2020) concept of governmentality-effected neglect and applying an ethical lens, this paper examines how ideas and discourse shape migration and social policy during crises, particularly the role of state assumptions in fostering ethical contradictions in policy. We analyse secondary material and original qualitative data from semi-structured interviews with macro-level policymakers, meso-level civil societal actors and individuals at the micro-level directly affected by policy decisions. We argue that the pandemic led to a crisis-induced bricolage of policy, reflecting an ethical void. This approach, rooted in long-standing ideas about the value and role of temporary migrants in Australia, continues to influence policymaking, perpetuating systemic exclusions and reinforcing ethical challenges.