VISTAS Interdisciplinary Colloquium on Emerging Research on Education, Economy and Community

Abstracts of presentations given at the VISTAS Interdisciplinary Colloquium on Emerging Research on Education, Economy and Communit

An information and field theoretic approach to the grand canonical ensemble

We present a novel derivation of the constraints required to obtain the underlying principles of statistical mechanics using a maximum entropy framework. We derive the mean value constraints by use of the central limit theorem and the scaling properties of Lagrange multipliers. We then arrive at the same result using a quantum free field theory and the Ward identities. The work provides a principled footing for maximum entropy methods in statistical physics, adding the body of work aligned to Jaynes's vision of statistical mechanics as a form of inference rather than a physical theory dependent on ergodicity, metric transitivity and equal a priori probabilities. We show that statistical independence, in the macroscopic limit, is the unifying concept that leads to all these derivations.Comment: 7 pages, 3 pages of Appendi

Symmetry-protected self-correcting quantum memories

A self-correcting quantum memory can store and protect quantum information for a time that increases without bound with the system size and without the need for active error correction. We demonstrate that symmetry can lead to self-correction in 3D spin-lattice models. In particular, we investigate codes given by 2D symmetry-enriched topological (SET) phases that appear naturally on the boundary of 3D symmetry-protected topological (SPT) phases. We find that while conventional on-site symmetries are not sufficient to allow for self-correction in commuting Hamiltonian models of this form, a generalized type of symmetry known as a 1-form symmetry is enough to guarantee self-correction. We illustrate this fact with the 3D "cluster-state" model from the theory of quantum computing. This model is a self-correcting memory, where information is encoded in a 2D SET-ordered phase on the boundary that is protected by the thermally stable SPT ordering of the bulk. We also investigate the gauge color code in this context. Finally, noting that a 1-form symmetry is a very strong constraint, we argue that topologically ordered systems can possess emergent 1-form symmetries, i.e., models where the symmetry appears naturally, without needing to be enforced externally.Comment: 39 pages, 16 figures, comments welcome; v2 includes much more explicit detail on the main example model, including boundary conditions and implementations of logical operators through local moves; v3 published versio

Statistics of Stellar Variability from Kepler - I: Revisiting Quarter 1 with an Astrophysically Robust Systematics Correction

We investigate the variability properties of main sequence stars in the first month of Kepler data, using a new astrophysically robust systematics correction, and find that 60% of stars are more variable then the active Sun. We define low and high variability samples, with a cut corresponding to twice the variability level of the active Sun, and compare the properties of the stars belonging to each sample. We show tentative evidence that the more active stars have lower proper motions and may be located closer to the galactic plane. We also investigate the frequency content of the variability, finding clear evidence for periodic or quasi-periodic behaviour in 16% of stars, and showing that there exist significant differences in the nature of variability between spectral types. Of the periodic objects, most A and F stars have short periods (< 2 days) and highly sinusoidal variability, suggestive of pulsations, whilst G, K and M stars tend to have longer periods (> 5 days, with a trend towards longer periods at later spectral types) and show a mixture of periodic and stochastic variability, indicative of activity. Finally, we use auto-regressive models to characterise the stochastic component of the variability, and show that its typical amplitude and time-scale both increase towards later spectral types, which we interpret as a corresponding increase in the characteristic size and life-time of active regions.Comment: Accepted A&A, 13 pages, 13 figures, 4 table