A universal GRB photon energy-peak luminosity relation

The energetics and emission mechanism of GRBs are not well understood. Here we demonstrate that the instantaneous peak flux or equivalent isotropic peak luminosity, L_iso ergs s^-1, rather than the integrated fluence or equivalent isotropic energy, E_iso ergs, underpins the known high-energy correlations. Using new spectral/temporal parameters calculated for 101 bursts with redshifts from BATSE, BeppoSAX, HETE-II and Swift we describe a parameter space which characterises the apparently diverse properties of the prompt emission. We show that a source frame characteristic-photon-energy/peak luminosity ratio, K_z, can be constructed which is constant within a factor of 2 for all bursts whatever their duration, spectrum, luminosity and the instrumentation used to detect them. The new parameterization embodies the Amati relation but indicates that some correlation between E_peak and E_iso follows as a direct mathematical inference from the Band function and that a simple transformation of E_iso to L_iso yields a universal high energy correlation for GRBs. The existence of K_z indicates that the mechanism responsible for the prompt emission from all GRBs is probably predominantly thermal.Comment: Submitted to Ap

Quantum Phase Transitions of Hard-Core Bosons in Background Potentials

We study the zero temperature phase diagram of hard core bosons in two dimensions subjected to three types of background potentials: staggered, uniform, and random. In all three cases there is a quantum phase transition from a superfluid (at small potential) to a normal phase (at large potential), but with different universality classes. As expected, the staggered case belongs to the XY universality, while the uniform potential induces a mean field transition. The disorder driven transition is clearly different from both; in particular, we find z~1.4, \nu~1, and \beta~0.6.Comment: 4 pages (6 figures); published version-- 2 references added, minor clarification

Time-resolved measurement of Landau--Zener tunneling in different bases

A comprehensive study of the tunneling dynamics of a Bose--Einstein condensate in a tilted periodic potential is presented. We report numerical and experimental results on time-resolved measurements of the Landau--Zener tunneling of ultracold atoms introduced by the tilt, which experimentally is realized by accelerating the lattice. The use of different protocols enables us to access the tunneling probability, numerically as well as experimentally, in two different bases, namely, the adiabatic basis and the diabatic basis. The adiabatic basis corresponds to the eigenstates of the lattice, and the diabatic one to the free-particle momentum eigenstates. Our numerical and experimental results are compared with existing two-state Landau--Zener models

Low temperature electron transfer in strongly condensed phase

Electron transfer coupled to a collective vibronic degree of freedom is studied in strongly condensed phase and at lower temperatures where quantum fluctuations are essential. Based on an exact representation of the reduced density matrix of the electronic+reaction coordinate compound in terms of path integrals, recent findings on the overdamped limit in quantum dissipative systems are employed. This allows to give for the first time a consistent generalization of the well-known Zusman equations to the quantum domain. Detailed conditions for the range of validity are specified. Using the Wigner transform these results are also extended to the quantum dynamics in full phase space. As an important application electronic transfer rates are derived that comprise adiabatic and nonadiabatic processes in the low temperature regime including nuclear tunneling. Accurate agreement with precise quantum Monte Carlo data is observed.Comment: 16 pages, 6 figures, revised version with minor change

Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system

The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching rate. Our results supply the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena.Comment: Title changed, authors added, and some experimental data update

Minimizing Polarization and Disagreement in Social Networks

The rise of social media and online social networks has been a disruptive force in society. Opinions are increasingly shaped by interactions on online social media, and social phenomena including disagreement and polarization are now tightly woven into everyday life. In this work we initiate the study of the following question: given $n$ agents, each with its own initial opinion that reflects its core value on a topic, and an opinion dynamics model, what is the structure of a social network that minimizes {\em polarization} and {\em disagreement} simultaneously? This question is central to recommender systems: should a recommender system prefer a link suggestion between two online users with similar mindsets in order to keep disagreement low, or between two users with different opinions in order to expose each to the other's viewpoint of the world, and decrease overall levels of polarization? Our contributions include a mathematical formalization of this question as an optimization problem and an exact, time-efficient algorithm. We also prove that there always exists a network with $O(n/\epsilon^2)$ edges that is a $(1+\epsilon)$ approximation to the optimum. For a fixed graph, we additionally show how to optimize our objective function over the agents' innate opinions in polynomial time. We perform an empirical study of our proposed methods on synthetic and real-world data that verify their value as mining tools to better understand the trade-off between of disagreement and polarization. We find that there is a lot of space to reduce both polarization and disagreement in real-world networks; for instance, on a Reddit network where users exchange comments on politics, our methods achieve a $\sim 60\,000$-fold reduction in polarization and disagreement.Comment: 19 pages (accepted, WWW 2018