Gauge fixing and equivariant cohomology

The supersymmetric model developed by Witten to study the equivariant cohomology of a manifold with an isometric circle action is derived from the BRST quantization of a simple classical model. The gauge-fixing process is carefully analysed, and demonstrates that different choices of gauge-fixing fermion can lead to different quantum theories.Comment: 18 pages LaTe

On the completeness of quantum computation models

The notion of computability is stable (i.e. independent of the choice of an indexing) over infinite-dimensional vector spaces provided they have a finite "tensorial dimension". Such vector spaces with a finite tensorial dimension permit to define an absolute notion of completeness for quantum computation models and give a precise meaning to the Church-Turing thesis in the framework of quantum theory. (Extra keywords: quantum programming languages, denotational semantics, universality.)Comment: 15 pages, LaTe

In-situ velocity imaging of ultracold atoms using slow--light

The optical response of a moving medium suitably driven into a slow-light propagation regime strongly depends on its velocity. This effect can be used to devise a novel scheme for imaging ultraslow velocity fields. The scheme turns out to be particularly amenable to study in-situ the dynamics of collective and topological excitations of a trapped Bose-Einstein condensate. We illustrate the advantages of using slow-light imaging specifically for sloshing oscillations and bent vortices in a stirred condensate

Scaled penalization of Brownian motion with drift and the Brownian ascent

We study a scaled version of a two-parameter Brownian penalization model introduced by Roynette-Vallois-Yor in arXiv:math/0511102. The original model penalizes Brownian motion with drift $h\in\mathbb{R}$ by the weight process ${\big(\exp(\nu S_t):t\geq 0\big)}$ where $\nu\in\mathbb{R}$ and $\big(S_t:t\geq 0\big)$ is the running maximum of the Brownian motion. It was shown there that the resulting penalized process exhibits three distinct phases corresponding to different regions of the $(\nu,h)$-plane. In this paper, we investigate the effect of penalizing the Brownian motion concurrently with scaling and identify the limit process. This extends a result of Roynette-Yor for the ${\nu<0,~h=0}$ case to the whole parameter plane and reveals two additional "critical" phases occurring at the boundaries between the parameter regions. One of these novel phases is Brownian motion conditioned to end at its maximum, a process we call the Brownian ascent. We then relate the Brownian ascent to some well-known Brownian path fragments and to a random scaling transformation of Brownian motion recently studied by Rosenbaum-Yor.Comment: 32 pages; made additions to Section

Spectral Theory of Sparse Non-Hermitian Random Matrices

Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these matrices provide crucial information on system stability and susceptibility, however, their study is greatly complicated by the twin challenges of a lack of symmetry and a sparse interaction structure. In this review we provide a concise and systematic introduction to the main tools and results in this field. We show how the spectra of sparse non-Hermitian matrices can be computed via an analogy with infinite dimensional operators obeying certain recursion relations. With reference to three illustrative examples --- adjacency matrices of regular oriented graphs, adjacency matrices of oriented Erd\H{o}s-R\'{e}nyi graphs, and adjacency matrices of weighted oriented Erd\H{o}s-R\'{e}nyi graphs --- we demonstrate the use of these methods to obtain both analytic and numerical results for the spectrum, the spectral distribution, the location of outlier eigenvalues, and the statistical properties of eigenvectors.Comment: 60 pages, 10 figure

2d Gauge Theories and Generalized Geometry

We show that in the context of two-dimensional sigma models minimal coupling of an ordinary rigid symmetry Lie algebra $\mathfrak{g}$ leads naturally to the appearance of the "generalized tangent bundle" $\mathbb{T}M \equiv TM \oplus T^*M$ by means of composite fields. Gauge transformations of the composite fields follow the Courant bracket, closing upon the choice of a Dirac structure $D \subset \mathbb{T}M$ (or, more generally, the choide of a "small Dirac-Rinehart sheaf" $\cal{D}$), in which the fields as well as the symmetry parameters are to take values. In these new variables, the gauge theory takes the form of a (non-topological) Dirac sigma model, which is applicable in a more general context and proves to be universal in two space-time dimensions: A gauging of $\mathfrak{g}$ of a standard sigma model with Wess-Zumino term exists, \emph{iff} there is a prolongation of the rigid symmetry to a Lie algebroid morphism from the action Lie algebroid $M \times \mathfrak{g}\to M$ into $D\to M$ (or the algebraic analogue of the morphism in the case of $\cal{D}$). The gauged sigma model results from a pullback by this morphism from the Dirac sigma model, which proves to be universal in two-spacetime dimensions in this sense.Comment: 22 pages, 2 figures; To appear in Journal of High Energy Physic

Random Sequential Addition of Hard Spheres in High Euclidean Dimensions

Employing numerical and theoretical methods, we investigate the structural characteristics of random sequential addition (RSA) of congruent spheres in $d$-dimensional Euclidean space $\mathbb{R}^d$ in the infinite-time or saturation limit for the first six space dimensions ($1 \le d \le 6$). Specifically, we determine the saturation density, pair correlation function, cumulative coordination number and the structure factor in each =of these dimensions. We find that for $2 \le d \le 6$, the saturation density $\phi_s$ scales with dimension as $\phi_s= c_1/2^d+c_2 d/2^d$, where $c_1=0.202048$ and $c_2=0.973872$. We also show analytically that the same density scaling persists in the high-dimensional limit, albeit with different coefficients. A byproduct of this high-dimensional analysis is a relatively sharp lower bound on the saturation density for any $d$ given by $\phi_s \ge (d+2)(1-S_0)/2^{d+1}$, where $S_0\in [0,1]$ is the structure factor at $k=0$ (i.e., infinite-wavelength number variance) in the high-dimensional limit. Consistent with the recent "decorrelation principle," we find that pair correlations markedly diminish as the space dimension increases up to six. Our work has implications for the possible existence of disordered classical ground states for some continuous potentials in sufficiently high dimensions.Comment: 38 pages, 9 figures, 4 table

Why, what, and how? case study on law, risk, and decision making as necessary themes in built environment teaching

The paper considers (and defends) the necessity of including legal studies as a core part of built environment undergraduate and postgraduate curricula. The writer reflects upon his own experience as a lawyer working alongside and advising built environment professionals in complex land remediation and site safety management situations in the United Kingdom and explains how themes of liability, risk, and decision making can be integrated into a practical simulation in order to underpin more traditional lecture-based law teaching. Through reflection upon the writer's experiments with simulation-based teaching, the paper suggests some innovations that may better orientate law teaching to engage these themes and, thereby, enhance the relevance of law studies to the future needs of built environment professionals in practice.</p

Designing Chatbots for Crises: A Case Study Contrasting Potential and Reality

Chatbots are becoming ubiquitous technologies, and their popularity and adoption are rapidly spreading. The potential of chatbots in engaging people with digital services is fully recognised. However, the reputation of this technology with regards to usefulness and real impact remains rather questionable. Studies that evaluate how people perceive and utilise chatbots are generally lacking. During the last Kenyan elections, we deployed a chatbot on Facebook Messenger to help people submit reports of violence and misconduct experienced in the polling stations. Even though the chatbot was visited by more than 3,000 times, there was a clear mismatch between the users’ perception of the technology and its design. In this paper, we analyse the user interactions and content generated through this application and discuss the challenges and directions for designing more effective chatbots

A Modeling Study on the Sensitivities of Atmospheric Charge Separation According to the Relative Diffusional Growth Rate Theory to Nonspherical Hydrometeors and Cloud Microphysics

Collisional charge transfer between graupel and ice crystals in the presence of cloud droplets is considered the dominant mechanism for charge separation in thunderclouds. According to the relative diffusional growth rate (RDGR) theory, the hydrometeor with the faster diffusional radius growth is charged positively in such collisions. We explore sensitivities of the RDGR theory to nonspherical hydrometeors and six parameters (pressure, temperature, liquid water content, sizes of ice crystals, graupel, and cloud droplets). Idealized simulations of a thundercloud with two‐moment cloud microphysics provide a realistic sampling of the parameter space. Nonsphericity and anisotropic diffusional growth strongly control the extent of positive graupel charging. We suggest a tuning parameter to account for anisotropic effects not represented in bulk microphysics schemes. In a susceptibility analysis that uses automated differentiation, we identify ice crystal size as most important RDGR parameter, followed by graupel size. Simulated average ice crystal size varies with temperature due to ice multiplication and heterogeneous freezing of droplets. Cloud microphysics and ice crystal size thus indirectly determine the structure of charge reversal lines in the traditional temperature‐water‐content representation. Accounting for the variability of ice crystal size and potentially habit with temperature may help to explain laboratory results and seems crucial for RDGR parameterizations in numerical models. We find that the contribution of local water vapor from evaporating rime droplets to diffusional graupel growth is only important for high effective water content. In this regime, droplet size and pressure are the dominant RDGR parameters. Otherwise, the effect of local graupel growth is masked by small ice crystal sizes that result from ice multiplication