Work and entropy production in generalised Gibbs ensembles

Recent years have seen an enormously revived interest in the study of thermodynamic notions in the quantum regime. This applies both to the study of notions of work extraction in thermal machines in the quantum regime, as well as to questions of equilibration and thermalisation of interacting quantum many-body systems as such. In this work we bring together these two lines of research by studying work extraction in a closed system that undergoes a sequence of quenches and equilibration steps concomitant with free evolutions. In this way, we incorporate an important insight from the study of the dynamics of quantum many body systems: the evolution of closed systems is expected to be well described, for relevant observables and most times, by a suitable equilibrium state. We will consider three kinds of equilibration, namely to (i) the time averaged state, (ii) the Gibbs ensemble and (iii) the generalised Gibbs ensemble (GGE), reflecting further constants of motion in integrable models. For each effective description, we investigate notions of entropy production, the validity of the minimal work principle and properties of optimal work extraction protocols. While we keep the discussion general, much room is dedicated to the discussion of paradigmatic non-interacting fermionic quantum many-body systems, for which we identify significant differences with respect to the role of the minimal work principle. Our work not only has implications for experiments with cold atoms, but also can be viewed as suggesting a mindset for quantum thermodynamics where the role of the external heat baths is instead played by the system itself, with its internal degrees of freedom bringing coarse-grained observables to equilibrium.Comment: 22 pages, 4 figures, improvements in presentatio

Strong coupling corrections in quantum thermodynamics

Quantum systems strongly coupled to many-body systems equilibrate to the reduced state of a global thermal state, deviating from the local thermal state of the system as it occurs in the weak-coupling limit. Taking this insight as a starting point, we study the thermodynamics of systems strongly coupled to thermal baths. First, we provide strong-coupling corrections to the second law applicable to general systems in three of its different readings: As a statement of maximal extractable work, on heat dissipation, and bound to the Carnot efficiency. These corrections become relevant for small quantum systems and always vanish in first order in the interaction strength. We then move to the question of power of heat engines, obtaining a bound on the power enhancement due to strong coupling. Our results are exemplified on the paradigmatic situation of non-Markovian quantum Brownian motion.Comment: 20 pages, 3 figures, version two is substantially revised and contains new result

The distribution of stars around the Milky Way's central black hole II: Diffuse light from sub-giants and dwarfs

This is the second of three papers that search for the predicted stellar cusp around the Milky Way's central black hole, Sagittarius A*, with new data and methods. We aim to infer the distribution of the faintest stellar population currently accessible through observations around Sagittarius A*. We use adaptive optics assisted high angular resolution images obtained with the NACO instrument at the ESO VLT. Through optimised PSF fitting we remove the light from all detected stars above a given magnitude limit. Subsequently we analyse the remaining, diffuse light density. The analysed diffuse light arises from sub-giant and main-sequence stars with KS ~ 19 - 20 with masses of 1 - 2 Msol . These stars can be old enough to be dynamically relaxed. The observed power-law profile and its slope are consistent with the existence of a relaxed stellar cusp around the Milky Way's central black hole. We find that a Nuker law provides an adequate description of the nuclear cluster's intrinsic shape (assuming spherical symmetry). The 3D power-law slope near Sgr A* is \gamma = 1.23 +- 0.05. At a distance of 0.01 pc from the black hole, we estimate a stellar mass density of 2.3 +- 0.3 x 10^7 Msol pc^-3 and a total enclosed stellar mass of 180 +- 20 Msol. These estimates assume a constant mass-to-light ratio and do not take stellar remnants into account. The fact that no cusp is observed for bright (Ks 16) giant stars at projected distances of roughly 0.1-0.3 pc implies that some mechanism has altered their appearance or distribution.Comment: Accepted for publication A&

The distribution of old stars around the Milky Way's central black hole I: Star counts

(abridged) In this paper we revisit the problem of inferring the innermost structure of the Milky Way's nuclear star cluster via star counts, to clarify whether it displays a core or a cusp around the central black hole. Through image stacking and improved PSF fitting we push the completeness limit about one magnitude deeper than in previous, comparable work. Contrary to previous work, we analyse the stellar density in well-defined magnitude ranges in order to be able to constrain stellar masses and ages. The RC and brighter giant stars display a core-like surface density profile within a projected radius R<0.3 pc of the central black hole, in agreement with previous studies, but show a cusp-like surface density distribution at larger R. The surface density of the fainter stars can be described well by a single power-law at R<2 pc. The cusp-like profile of the faint stars persists even if we take into account the possible contamination of stars in this brightness range by young pre-main sequence stars. The data are inconsistent with a core-profile for the faint stars.Finally, we show that a 3D Nuker law provides a very good description of the cluster structure. We conclude that the observed stellar density at the Galactic Centre, as it can be inferred with current instruments, is consistent with the existence of a stellar cusp around the Milky Way's central black hole, Sgr A*. This cusp is well developed inside the influence radius of about 3 pc of Sgr A* and can be described by a single three-dimensional power-law with an exponent gamma=1.23+-0.05. The apparent lack of RC stars and brighter giants at projected distances of R < 0.3 pc (R<8") of the massive black hole may indicate that some mechanism has altered their distribution or intrinsic luminosity.Comment: Accepted for publication A&

Should I stay or should I go? Exploring the job preferences of allied health professionals working with people with disability in rural Australia

Introduction: The uneven distribution of allied health professionals (AHPs) in rural and remote Australia and other countries is well documented. In Australia, like elsewhere, service delivery to rural and remote communities is complicated because relatively small numbers of clients are dispersed over large geographic areas. This uneven distribution of AHPs impacts significantly on the provision of services particularly in areas of special need such as mental health, aged care and disability services. Objective: This study aimed to determine the relative importance that AHPs (physiotherapists, occupational therapists, speech pathologists and psychologists – “therapists”) living in a rural area of Australia and working with people with disability, place on different job characteristics and how these may affect their retention. Methods: A cross-sectional survey was conducted using an online questionnaire distributed to AHPs working with people with disability in a rural area of Australia over a 3-month period. Information was sought about various aspects of the AHPs’ current job, and their workforce preferences were explored using a best–worst scaling discrete choice experiment (BWSDCE). Conditional logistic and latent class regression models were used to determine AHPs’ relative preferences for six different job attributes. Results: One hundred ninety-nine AHPs completed the survey; response rate was 51 %. Of those, 165 completed the BWSDCE task. For this group of AHPs, “high autonomy of practice” is the most valued attribute level, followed by “travel BWSDCE arrangements: one or less nights away per month”, “travel arrangements: two or three nights away per month” and “adequate access to professional development”. On the other hand, the least valued attribute levels were “travel arrangements: four or more nights per month”, “limited autonomy of practice” and “minimal access to professional development”. Except for “some job flexibility”, all other attributes had a statistical influence on AHPs’ job preference. Preferences differed according to age, marital status and having dependent children. Conclusions: This study allowed the identification of factors that contribute to AHPs’ employment decisions about staying and working in a rural area. This information can improve job designs in rural areas to increase retention

Thermal machines beyond the weak coupling regime

How much work can be extracted from a heat bath using a thermal machine? The study of this question has a very long history in statistical physics in the weak-coupling limit, when applied to macroscopic systems. However, the assumption that thermal heat baths remain uncorrelated with associated physical systems is less reasonable on the nano-scale and in the quantum setting. In this work, we establish a framework of work extraction in the presence of quantum correlations. We show in a mathematically rigorous and quantitative fashion that quantum correlations and entanglement emerge as limitations to work extraction compared to what would be allowed by the second law of thermodynamics. At the heart of the approach are operations that capture the naturally non-equilibrium dynamics encountered when putting physical systems into contact with each other. We discuss various limits that relate to known results and put our work into the context of approaches to finite-time quantum thermodynamics

Renormalization Group and Grand Unification with 331 Models

By making a renormalization group analysis we explore the possibility of having a 331 model as the only intermediate gauge group between the standard model and the scale of unification of the three coupling constants. We shall assume that there is no necessarily a group of grand unification at the scale of convergence of the couplings. With this scenario, different 331 models and their corresponding supersymmetric versions are considered, and we find the versions that allow the symmetry breaking described above. Besides, the allowed interval for the 331 symmetry breaking scale, and the behavior of the running coupling constants are obtained. It worths saying that some of the supersymmetric scenarios could be natural frameworks for split supersymmetry. Finally, we look for possible 331 models with a simple group at the grand unification scale, that could fit the symmetry breaking scheme described above.Comment: 18 pages. 3 figures. Some results reinterpreted, a new section and references added. Version to appear in International Journal of Modern Physics