Critical temperature of trapped interacting bosons from large-N based theories

Ultracold atoms provide clues to an important many-body problem regarding the dependence of Bose-Einstein condensation (BEC) transition temperature $T_c$ on interactions. However, cold atoms are trapped in harmonic potentials and theoretical evaluations of the $T_c$ shift of trapped interacting Bose gases are challenging. While previous predictions of the leading-order shift have been confirmed, more recent experiments exhibit higher-order corrections beyond available mean-field theories. By implementing two large-N based theories with the local density approximation (LDA), we extract next-order corrections of the $T_c$ shift. The leading-order large-N theory produces results quantitatively different from the latest experimental data. The leading-order auxiliary field (LOAF) theory containing both normal and anomalous density fields captures the $T_c$ shift accurately in the weak interaction regime. However, the LOAF theory shows incompatible behavior with the LDA and forcing the LDA leads to density discontinuities in the trap profiles. We present a phenomenological model based on the LOAF theory, which repairs the incompatibility and provides a prediction of the $T_c$ shift in stronger interaction regime.Comment: 11 pages, 3 figure

Easing Embedding Learning by Comprehensive Transcription of Heterogeneous Information Networks

Heterogeneous information networks (HINs) are ubiquitous in real-world applications. In the meantime, network embedding has emerged as a convenient tool to mine and learn from networked data. As a result, it is of interest to develop HIN embedding methods. However, the heterogeneity in HINs introduces not only rich information but also potentially incompatible semantics, which poses special challenges to embedding learning in HINs. With the intention to preserve the rich yet potentially incompatible information in HIN embedding, we propose to study the problem of comprehensive transcription of heterogeneous information networks. The comprehensive transcription of HINs also provides an easy-to-use approach to unleash the power of HINs, since it requires no additional supervision, expertise, or feature engineering. To cope with the challenges in the comprehensive transcription of HINs, we propose the HEER algorithm, which embeds HINs via edge representations that are further coupled with properly-learned heterogeneous metrics. To corroborate the efficacy of HEER, we conducted experiments on two large-scale real-words datasets with an edge reconstruction task and multiple case studies. Experiment results demonstrate the effectiveness of the proposed HEER model and the utility of edge representations and heterogeneous metrics. The code and data are available at https://github.com/GentleZhu/HEER.Comment: 10 pages. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, London, United Kingdom, ACM, 201

Wertheim perturbation theory: thermodynamics and structure of patchy colloids

We critically discuss the application of the Wertheim's theory to classes of complex associating fluids that can be today engineered in the laboratory as patchy colloids and to the prediction of their peculiar gas-liquid phase diagrams. Our systematic study, stemming from perturbative version of the theory, allows us to show that, even at the simplest level of approximation for the inter-cluster correlations, the theory is still able to provide a consistent and stable picture of the behavior of interesting models of self-assembling colloidal suspension. We extend the analysis of a few cases of patchy systems recently introduced in the literature. In particular, we discuss for the first time in detail the consistency of the structural description underlying the perturbative approach and we are able to prove a consistency relationship between the valence as obtained from thermodynamics and from the structure for the one-site case. A simple analytical expression for the structure factor is proposed.Comment: 25 pages, 10 figure

Consumer myopia, compatibility and aftermarket monopolization

In this paper, I show that the standard Bertrand competition argument does not apply when firms compete for myopic consumers who optimize period-by-period. I develop the model in the context of aftermarket. With overlapping-generations of consumers, simultaneous product offerings in the primary market and aftermarket establishes a price floor for the primary good. This constraint prevents aftermarket rents from being dissipated by the primary market competition. Duopoly firms earn positive profits despite price competition with undifferentiated products. Nonetheless, government interventions to reinforce aftermarket competition such as a standardization requirement may lead to the partial collapse of the primary market.aftermarket, Bertrand competition, bounded rationality, standardization.

Quantum Gravity: Has Spacetime Quantum Properties?

The incompatibility between GR and QM is generally seen as a sufficient motivation for the development of a theory of Quantum Gravity. If - so a typical argumentation - QM gives a universally valid basis for the description of all natural systems, then the gravitational field should have quantum properties. Together with the arguments against semi-classical theories of gravity, this leads to a strategy which takes a quantization of GR as the natural avenue to Quantum Gravity. And a quantization of the gravitational field would in some sense correspond to a quantization of geometry. Spacetime would have quantum properties. But, this strategy will only be successful, if gravity is a fundamental interaction. - What, if gravity is instead an intrinsically classical phenomenon? Then, if QM is nevertheless fundamentally valid, gravity can not be a fundamental interaction. An intrinsically classical gravity in a quantum world would have to be an emergent, induced or residual, macroscopic effect, caused by other interactions. The gravitational field (as well as spacetime) would not have any quantum properties. A quantization of GR would lead to artifacts without any relation to nature. The serious problems of all approaches to Quantum Gravity that start from a direct quantization of GR or try to capture the quantum properties of gravity in form of a 'graviton' dynamics - together with the, meanwhile, rich spectrum of approaches to an emergent gravity and/or spacetime - make this latter option more and more interesting for the development of a theory of Quantum Gravity. The most advanced emergent gravity (and spacetime) scenarios are of an information-theoretical, quantum-computational type.Comment: 31 page