Universality in modelling non-equilibrium pattern formation in polariton condensates

The key to understanding the universal behaviour of systems driven away from equilibrium lies in the common description obtained when particular microscopic models are reduced to order parameter equations. Universal order parameter equations written for complex matter fields are widely used to describe systems as different as Bose-Einstein condensates of ultra cold atomic gases, thermal convection, nematic liquid crystals, lasers and other nonlinear systems. Exciton-polariton condensates recently realised in semiconductor microcavities are pattern forming systems that lie somewhere between equilibrium Bose-Einstein condensates and lasers. Because of the imperfect confinement of the photon component, exciton-polaritons have a finite lifetime, and have to be continuously re-populated. As photon confinement improves, the system more closely approximates an equilibrium system. In this chapter we review a number of universal equations which describe various regimes of the dynamics of exciton-polariton condensates: the Gross-Pitaevskii equation, which models weakly interacting equilibrium condensates, the complex Ginsburg-Landau equation---the universal equation that describes the behaviour of systems in the vicinity of a symmetry--breaking instability, and the complex Swift-Hohenberg equation that in comparison with the complex Ginsburg-Landau equation contains additional nonlocal terms responsible for spacial mode selection. All these equations can be derived asymptotically from a generic laser model given by Maxwell-Bloch equations. Such an universal framework allows the unified treatment of various systems and continuously cross from one system to another. We discuss the relevance of these equations, and their consequences for pattern formation.Comment: 19 pages; Chapter to appear in Springer&Verlag book on "Quantum Fluids: hot-topics and new trends" eds. A. Bramati and M. Modugn

Spontaneous rotating vortex lattices in a pumped decaying condensate

Injection and decay of particles in an inhomogeneous quantum condensate can significantly change its behaviour. We model trapped, pumped, decaying condensates by a complex Gross-Pitaevskii equation and analyse the density and currents in the steady state. With homogeneous pumping, rotationally symmetric solutions are unstable. Stability may be restored by a finite pumping spot. However if the pumping spot is larger than the Thomas-Fermi cloud radius, then rotationally symmetric solutions are replaced by solutions with spontaneous arrays of vortices. These vortex arrays arise without any rotation of the trap, spontaneously breaking rotational symmetry.Comment: Updated title and introduction. 4 pages, 3 figure

SIRS dynamics on random networks: simulations and analytical models

The standard pair approximation equations (PA) for the Susceptible-Infective-Recovered-Susceptible (SIRS) model of infection spread on a network of homogeneous degree $k$ predict a thin phase of sustained oscillations for parameter values that correspond to diseases that confer long lasting immunity. Here we present a study of the dependence of this oscillatory phase on the parameter $k$ and of its relevance to understand the behaviour of simulations on networks. For $k=4$, we compare the phase diagram of the PA model with the results of simulations on regular random graphs (RRG) of the same degree. We show that for parameter values in the oscillatory phase, and even for large system sizes, the simulations either die out or exhibit damped oscillations, depending on the initial conditions. This failure of the standard PA model to capture the qualitative behaviour of the simulations on large RRGs is currently being investigated.Comment: 6 pages, 3 figures, WIPP to be published in Conference proceedings Complex'2009 February 23-25, Shanghai, Chin

Public Security & Digital Forensics in the United States: The Continued Need for Expanded Digital Systems for Security

Digital Forensics is one of the latest challenges for the use of forensics in the investigative process in the United States. Some of the challenges are created by conditions and circumstances present for law enforcement around the world. However, many are unique to the United States and created by the standards of evidence within our courts, nature of our law enforcement organizations, and structure of our judicial and prosecutorial systems. It is essential for the preservation of public security and individual safety that competent systems of digital forensics are developed for law enforcement at all levels. The failure to do so will let the guilty avoid responsibility for their criminal actions while possibly subjecting the innocent to unprecedented government intrusion into their private lives

Stochastic oscillations in models of epidemics on a network of cities

We carry out an analytic investigation of stochastic oscillations in a susceptible-infected-recovered model of disease spread on a network of $n$ cities. In the model a fraction $f_{jk}$ of individuals from city $k$ commute to city $j$, where they may infect, or be infected by, others. Starting from a continuous time Markov description of the model the deterministic equations, which are valid in the limit when the population of each city is infinite, are recovered. The stochastic fluctuations about the fixed point of these equations are derived by use of the van Kampen system-size expansion. The fixed point structure of the deterministic equations is remarkably simple: a unique non-trivial fixed point always exists and has the feature that the fraction of susceptible, infected and recovered individuals is the same for each city irrespective of its size. We find that the stochastic fluctuations have an analogously simple dynamics: all oscillations have a single frequency, equal to that found in the one city case. We interpret this phenomenon in terms of the properties of the spectrum of the matrix of the linear approximation of the deterministic equations at the fixed point.Comment: 13 pages, 7 figure

Analysis of the mean annual cycle of the dissolved oxygen anomaly in the World Ocean

A global climatology of the dissolved oxygen anomaly (the excess over saturation) is created with monthly resolution in the upper 500 m of the ocean. The climatology is based on dissolved oxygen, temperature and salinity data archived at the National Oceanographic Data Center. Examination of this climatology reveals statistically significant annual cycles throughout the upper 500 m of the World Ocean, though seasonal variations are most coherent in the North Atlantic, where data density is greatest. Vertical trends in the phase and amplitude of the annual cycle are noted. The cycle in surface waters is characterized by a summer maximum and a winter minimum, consistent with warming and high rates of photosynthesis during the summer, and cooling and entrainment of oxygen-depleted water during the winter. In low and middle latitudes, the amplitude increases with depth and the maximum occurs later in the year, a trend consistent with the seasonal accumulation of oxygen associated with the shallow oxygen maximum. At a depth that varies between about 30 and 130 m, the phase of the annual cycle undergoes an abrupt shift. We call this depth the oxygen nodal depth. Below the nodal depth, the annual cycle is characterized by an early-spring maximum and a late-fall minimum, consistent with a cycle dominated by respiration during the spring and summer and replenishment of oxygen from the atmosphere by ventilation during the fall and winter. Below the nodal depth, the amplitude of the annual cycle generally decreases with depth, indicative of decreasing respiration and ventilation rates, or less seasonality in both processes. We postulate that the nodal depth in middle and high latitudes corresponds closely to the summertime compensation depth, where photosynthesis and net community respiration are equal. With this interpretation of the nodal depth and a simple model of the penetration of light in the water column, a compensation light intensity of 1 W m−2 (4μE m−2 s−1) is deduced, at the low end of independent estimates. Horizontal trends in the phase and amplitude of the annual cycle are also noted. We find that the nodal depth decreases toward the poles in both hemispheres and is generally greater in the Southern Hemisphere, patterns found to be consistent with light-based estimates of the compensation depth. The amplitude of the annual cycle in the oxygen anomaly increases monotonically with latitude, and higher latitudes lag lower latitudes. In the North Atlantic and North Pacific, the amplitude of the annual cycle tends to increase from east to west at all depths and latitudes, as expected considering that physical forcing has greater seasonal variability in the west. The tropics and the North Indian Ocean have features that distinguish them from other regions. Below about 75 m, these waters have pronounced annual cycles of the oxygen anomaly that are shown to be caused mainly by wind-driven adiabatic displacements of the thermocline. A semiannual cycle of the oxygen anomaly is found in the surface waters of the North Indian Ocean, consistent with the known semiannual cycle of surface heat flux in this region

Preprint arXiv: 2201.05529 Submitted on 14 Jan 2022

We study the thermalization of individual spins of a short XYZ Heisenberg chain with strongly coupled thermal leads by checking the consistency of two-time correlations with the fluctuation-dissipation theorem. To compute these correlations we develop and apply a general numerical method for chains of quantum systems, where each system may couple strongly to a structured environment. The method combines the process tensor formalism for general (possibly non-Markovian) open quantum systems with time evolving block decimation for 1D chains. It systematically reduces the numerical complexity originating from system-environment correlations before integrating them into the full many-body problem, making a wide range of applications numerically feasible. Our results show the complete thermalization of the chain when coupled to a single bath, and reveal distinct effective temperatures in low, mid, and high frequency regimes when placed between a hot and a cold bath

Phase lag in epidemics on a network of cities

We study the synchronisation and phase-lag of fluctuations in the number of infected individuals in a network of cities between which individuals commute. The frequency and amplitude of these oscillations is known to be very well captured by the van Kampen system-size expansion, and we use this approximation to compute the complex coherence function that describes their correlation. We find that, if the infection rate differs from city to city and the coupling between them is not too strong, these oscillations are synchronised with a well defined phase lag between cities. The analytic description of the effect is shown to be in good agreement with the results of stochastic simulations for realistic population sizes.Comment: 10 pages, 6 figure