The theoretical foundations of the phenomenon known as superradiance still continue to attract considerable attention. Despite many valiant attempts at pedagogically clear presentations, the effect nevertheless still continues to generate some significant confusion. Part of the confusion arises from the fact that superradiance in a quantum field theory context is not the same as superradiance (superfluorescence) in some condensed matter contexts; part of the confusion arises from traditional but sometimes awkward normalization conventions, and part is due to sometimes unnecessary confusion between fluxes and probabilities. We shall argue that the key point underlying the effect is flux conservation (and, in the presence of dissipation, a controlled amount of flux nonconservation), and that attempting to phrase things in terms of reflection and transmission probabilities only works in the absence of superradiance. To help clarify the situation we present a simple exactly solvable toy model exhibiting both superradiance and damping.
The theoretical foundations of the phenomenon known as superradiance still continue to attract considerable attention. Despite many valiant attempts at pedagogically clear presentations, the effect nevertheless still continues to generate some significant confusion. Part of the confusion arises from the fact that superradiance in a quantum field theory context is not the same as superradiance (superfluorescence) in some condensed matter contexts; part of the confusion arises from traditional but sometimes awkward normalization conventions, and part is due to sometimes unnecessary confusion between fluxes and probabilities. We shall argue that the key point underlying the effect is flux conservation (and, in the presence of dissipation, a controlled amount of flux nonconservation), and that attempting to phrase things in terms of reflection and transmission probabilities only works in the absence of superradiance. To help clarify the situation we present a simple exactly solvable toy model exhibiting both superradiance and damping.
Abstract This tutorial is the continuation of the previous tutorial part, published in (2013 Laser Phys . 23 062001 ), where the basic mathematical techniques required for an accurate description of cold atoms for both types of quantum statistics are expounded. In the present part, the specifics of the correct theoretical description of atoms obeying Bose–Einstein statistics are explained, including trapped Bose atoms. In the theory of systems exhibiting the phenomenon of Bose–Einstein condensation, there exists a number of delicate mathematical points, whose misunderstanding often results in principally wrong conclusions. This is why the consideration in the present tutorial is sufficiently detailed in order that the reader could clearly understand the underlying mathematics and would avoid confusions.
Despite our familiarity with and fondness of humor, until relatively recently very little was known about the underlying psychology of this complex and nuanced phenomenon. Recently, however, cognitive psychologists have begun investigating how people understand humor and why we find certain things funny. This chapter introduces a new cognitive approach to modeling humor that we refer to as the 'quantum approach', which will be explained here in intuitive, non-mathematical terms later (a formal treatment can be found in Gabora & Kitto, 2017). What makes the quantum approach a promising candidate for a theory of humor is that it can be useful for representing states of ambiguity, and it defines states and variables with reference to a context. Contextuality and ambiguity both play a key role in humor, which often hangs on an ambiguous word, phrase, or situation that might not make sense, or even be socially acceptable outside the specific context of the joke. The quantum approach does not attempt to explain all aspects of humor, such as the contagious quality of laughter, or why children tease each other, or why people might find it funny when someone is hit in the face with a pie (and laugh even if they know it will happen in advance); what it aims to do is to mathematically represent the underlying cognitive process of "getting" a joke. After briefly overviewing the relevant historical antecedents of the quantum approach and other related approaches in cognitive psychology, we present the theoretical basis of our approach, and outline a recent study that provides empirical support for it.
Quantum field theory (QFT) is a rich and robust part of mathematical and theoretical physics, with a wide range of applications in statistical physics, condensed matter physics, particle physics and string theory. Many (if not most) of the applications in four space-time dimensions require some sort of systematic approximations. In contrast, quantum field theories in lower dimensions often display special properties which open the door, at least in principle, to their exact solution. In many cases, the methods used to obtain exact solutions are peculiar to low-dimensional space-times, but the exact solutions thus obtained can teach us a great deal about more realistic QFTs in higher dimensions. Thus, lower-dimensional QFTs provide excellent models for exploring deep theoretical and computational issues, in addition to their direct applications to physical processes in reduced dimensions, which include polymers, boundary fluctuations, spin chains, and quantum Hall systems. Such models are also vital testing grounds for fundamental theoretical ideas such as integrability, phase transitions, collective and non-perturbative quantum behaviour, and non-equilibrium statistical mechanics. We should also mention the effective dimensional reduction which occurs in the high temperature limit, or is induced by disorder. Low-dimensional quantum field theory thus sits at a unique intersection point of contemporary mathematics and physics, allowing many of these issues to be addressed rigorously and analytically. Surprising inter-relations continue to arise, from the ubiquitous nature of the Bethe ansatz and Calogero models, to the link between integrable spin chains and the anomalous dimensions of operators in gauge theories. Aspects of the latter connection have been known at least since the 1990s; they have recently received tremendous attention in connection with N =4 supersymmetric Yang--Mills theory (in four space-time dimensions) and the AdS/CFT correspondence. One unifying idea is the Bethe ansatz, whose 75th anniversary we celebrate this year, and whose wide-ranging impact in diverse branches of modern mathematical physics is made abundantly clear in this special issue. In addition, new ideas and techniques of significance to both mathematics and physics have emerged: the recent and spectacular progress on geometrical aspects of phase transitions made possible through the ideas of stochastic (Schramm) Loewner evolution, or SLE, is a particularly noteworthy example. All papers in this special issue are invited, refereed contributions from leading experts. Many are pedagogical reviews, capturing the current state of knowledge in a particular subject, putting the subject in context and outlining open challenges. Others are research papers, reflecting the rapid flux of new ideas and results in this rich and exciting field. Together, they represent a broad sample of the entire field. We would like to take this opportunity to thank all of the authors for their efforts in making this special issue possible, and Kazuhiro Hikami for his help in the early stages of this project. We hope it inspires many new developments!
Recently Szangolies has argued (in the setting of extended Wigner's-friend scenarios) that quantum theory permits ``Rashomon'' situations: multiple internally coherent accounts of events that cannot be combined into a single, consistent global narrative. This note explains why the Rashomon phenomenon can be understood as a \emph{failure of gluing}: local descriptions over different contexts exist, but they do not admit a single global ``all-perspectives-at-once'' description. This is the same mathematical obstruction that underlies modern sheaf-theoretic treatments of contextuality. I then indicate why the same perspective is useful in parts of the social sciences (quantum-like modelling of cognition, judgment, and decision-making), where ``context effects'' can likewise be interpreted as the absence of a single joint probability space.