Dynamics of the entanglement spectrum in spin chains

We study the dynamics of the entanglement spectrum, that is the time evolution of the eigenvalues of the reduced density matrices after a bipartition of a one-dimensional spin chain. Starting from the ground state of an initial Hamiltonian, the state of the system is evolved in time with a new Hamiltonian. We consider both instantaneous and quasi adiabatic quenches of the system Hamiltonian across a quantum phase transition. We analyse the Ising model that can be exactly solved and the XXZ for which we employ the time-dependent density matrix renormalisation group algorithm. Our results show once more a connection between the Schmidt gap, i.e. the difference of the two largest eigenvalues of the reduced density matrix and order parameters, in this case the spontaneous magnetisation.

Energy conserving schemes for the simulation of musical instrument contact dynamics

Collisions are an innate part of the function of many musical instruments. Due to the nonlinear nature of contact forces, special care has to be taken in the construction of numerical schemes for simulation and sound synthesis. Finite difference schemes and other time-stepping algorithms used for musical instrument modelling purposes are normally arrived at by discretising a Newtonian description of the system. However because impact forces are non-analytic functions of the phase space variables, algorithm stability can rarely be established this way. This paper presents a systematic approach to deriving energy conserving schemes for frictionless impact modelling. The proposed numerical formulations follow from discretising Hamilton׳s equations of motion, generally leading to an implicit system of nonlinear equations that can be solved with Newton׳s method. The approach is first outlined for point mass collisions and then extended to distributed settings, such as vibrating strings and beams colliding with rigid obstacles. Stability and other relevant properties of the proposed approach are discussed and further demonstrated with simulation examples. The methodology is exemplified through a case study on tanpura string vibration, with the results confirming the main findings of previous studies on the role of the bridge in sound generation with this type of string instrument.

Later prehistoric vegetation dynamics and Bronze Age agriculture at Hobbister, Orkney, Scotland

The Bronze Age in Britain was a time of major social and cultural changes, reflected in the division of the landscape into field systems and the establishment of new belief systems and ritual practices. Several hypotheses have been advanced to explain these changes, and assessment of many of them is dependent on the availability of detailed palaeoenvironmental data from the sites concerned. This paper explores the development of a later prehistoric landscape in Orkney, where a Bronze Age field system and an apparently ritually-deposited late Bronze Age axe head are located in an area of deep blanket peat from which high-resolution palaeoenvironmental sequences have been recovered. There is no indication that the field system was constructed to facilitate agricultural intensification, and it more likely reflects a cultural response to social fragmentation associated with a more dispersed settlement pattern. There is evidence for wetter conditions during the later Bronze Age, and the apparent votive deposit may reflect the efforts of the local population to maintain community integrity during a time of perceptible environmental change leading to loss of farmland. The study emphasises the advantages of close integration of palaeoenvironmental and archaeological data for interpretation of prehistoric human activity. The palaeoenvironmental data also provide further evidence for the complexity of prehistoric woodland communities in Orkney, hinting at greater diversity than is often assumed. Additionally, differing dates for woodland decline in the two sequences highlight the dangers of over-extrapolation from trends observed in a single pollen profile, even at a very local scale.

Experimental Reconstruction of Work Distribution and Study of Fluctuation Relations in a Closed Quantum System

We report the experimental reconstruction of the nonequilibrium work probability distribution in a closed quantum system, and the study of the corresponding quantum fluctuation relations. The experiment uses a liquid-state nuclear magnetic resonance platform that offers full control on the preparation and dynamics of the system. Our endeavors enable the characterization of the out-of-equilibrium dynamics of a quantum spin from a finite-time thermodynamics viewpoint.

Nonconservative dynamics in long atomic wires

The effect of nonconservative current-induced forces on the ions in a defect-free metallic nanowire is investigated using both steady-state calculations and dynamical simulations. Nonconservative forces were found to have a major influence on the ion dynamics in these systems, but their role in increasing the kinetic energy of the ions decreases with increasing system length. The results illustrate the importance of nonconservative effects in short nanowires and the scaling of these effects with system size. The dependence on bias and ion mass can be understood with the help of a simple pen and paper model. This material highlights the benefit of simple preliminary steady-state calculations in anticipating aspects of brute-force dynamical simulations, and provides rule of thumb criteria for the design of stable quantum wires.

Dynamics of interacting Dicke model in a coupled-cavity array

We consider the dynamics of an array of mutually interacting cavities, each containing an ensemble of N two-level atoms. By exploring the possibilities offered by ensembles of various dimensions and a range of atom-light and photon-hopping values, we investigate the generation of multisite entanglement, as well as the performance of excitation transfer across the array, resulting from the competition between on-site nonlinearities of the matter-light interaction and intersite photon hopping. In particular, for a three-cavity interacting system it is observed that the initial excitation in the first cavity completely transfers to the ensemble in the third cavity through the hopping of photons between the adjacent cavities. Probabilities of the transfer of excitation of the cavity modes and ensembles exhibit characteristics of fast and slow oscillations governed by coupling and hopping parameters, respectively. In the large-hopping case, by seeding an initial excitation in the cavity at the center of the array, a tripartite W state, as well as a bipartite maximally entangled state, is obtained, depending on the interaction time. Population of the ensemble in a cavity has a positive impact on the rate of excitation transfer between the ensembles and their local cavity modes. In particular, for ensembles of five to seven atoms, tripartite W states can be produced even when the hopping rate is comparable to the cavity-atom coupling rate. A similar behavior of the transfer of excitation is observed for a four-coupled-cavity system with two initial excitations.

Non-Markovianity and system-environment correlations in a microscopic collision model

We show that the use of a recently proposed iterative collision model with interenvironment swaps displays a signature of strongly non-Markovian dynamics that is highly dependent on the establishment of system-environment correlations. Two models are investigated: one in which such correlations are canceled iteratively and one in which they are kept all across the dynamics. The degree of non-Markovianity, quantified using a measure based on the trace distance, is found to be much greater for all coupling strengths, when system-environment correlations are maintained.

Dynamical symmetries and crossovers in a three-spin system with collective dissipation

We consider the non-equilibrium dynamics of a simple system consisting of interacting spin-1/2 particles subjected to a collective damping. The model is close to situations that can be engineered in hybrid electro/opto-mechanical settings. Making use of large-deviation theory, we find a Gallavotti-Cohen symmetry in the dynamics of the system as well as evidence for the coexistence of two dynamical phases with different activity levels. We show that additional damping processes smooth out this behavior. Our analytical results are backed up by Monte Carlo simulations that reveal the nature of the trajectories contributing to the different dynamical phases.

Non-Markovian qubit dynamics in a circuit-QED setup

We consider a circuit-QED setup that allows the induction and control of non-Markovian dynamics of a qubit. Non-Markovianity is enforced over the qubit by means of its direct coupling to a bosonic mode which is controllably coupled to another qubit-mode system. We show that this configuration can be achieved in a circuit-QED setup consisting of two initially independent superconducting circuits, each formed by one charge qubit and one transmission-line resonator, which are put in interaction by coupling the resonators to a current-biased Josephson junction. We solve this problem exactly and then proceed with a thorough investigation of the emergent non-Markovianity in the dynamics of the qubits. Our study might serve the context for the first experimental assessment of non-Markovianity in a multielement solid-state device.

Ecological dynamics of extinct species in empty habitat networks. 1. The role of habitat pattern and quantity, stochasticity and dispersal

We examined a remnant host plant (Primula veris L.) habitat network that was last inhabited by the rare butterfly Hamearis lucina L. in north Wales in 1943, to assess the relative contribution of several spatial parameters to its regional extinction. We first examined relationships between P. veris characteristics and H. lucina eggs in surviving H. lucina populations, and used these to predict the suitability and potential carrying capacity of the habitat network in north Wales. This resulted in an estimate of roughly 4500 eggs (ca 227 adults). We developed a discrete space, discrete time metapopulation model to evaluate the relative contribution of dispersal distance, habitat and environmental stochasticity as possible causes of extinction. We simulated the potential persistence of the butterfly in the current network as well as in three artificial (historical and present) habitat networks that differed in the quantity (current and X3) and fragmentation of the habitat (current and aggregated). We identified that reduced habitat quantity and increased isolation would have increased the probability of regional extinction, in conjunction with environmental stochasticity and H. lucina's dispersal distance. This general trend did not change in a qualitative manner when we modified the ability of dispersing females to stay in, and find suitable habitats (by changing the size of the grid cells used in the model). Contrary to most metapopulation model predictions, system persistence declined with increasing migration rate, suggesting that the mortality of migrating individuals in fragmented landscapes may pose significant risks to system-wide persistence. Based on model predictions for the present landscape we argue that a major programme of habitat restoration would be required for a re-established metapopulation to persist for > 100 years.

Ecological dynamics of extinct species in empty habitat networks. 2. The role of host plant dynamics

This paper explores the relative effects of host plant dynamics and butterfly-related parameters on butterfly persistence. It considers an empty habitat network where a rare butterfly (Cupido minimus) became extinct in 1939 in part of its historical range in north Wales, UK. Surviving populations of the butterfly in southern Britain were visited to assess use of its host plant (Anthyllis vulneraria) in order to calibrate habitat suitability and carrying capacity in the empty network in north Wales. These data were used to deduce that only a portion ( similar to 19%) of the host plant network from north Wales was likely to be highly suitable for oviposition. Nonetheless, roughly 65,460 eggs (3273 adult equivalents) could be expected to be laid in north Wales, were the empty network to be populated at the same levels as observed on comparable plants in surviving populations elsewhere. Simulated metapopulations of C. minimus in the empty network revealed that time to extinction and patch occupancy were significantly influenced by carrying capacity, butterfly mean dispersal distance and environmental stochasticity, although for most reasonable parameter values, the model system persisted. Simulation outputs differed greatly when host plant dynamics was incorporated into the modelled butterfly dynamics. Cupido minimus usually went extinct when host plant were at low densities. In these simulations host plant dynamics appeared to be the most important determinant of the butterfly's regional extirpation. Modelling the outcome of a reintroduction programme to C. minimus variation at high quality locations, revealed that 65% of systems survived at least 100 years. Given the current amount of resources of the north Wales landscape, the persistence of C. minimus under a realistic reintroduction programme has a good chance of being successful, if carried out in conjunction with a host plant management programme.

Hierarchical energy management system for multi-source multi-product microgrids

This paper proposes a hierarchical energy management system for multi-source multi-product (MSMP) microgrids. Traditional energy hub based scheduling method is combined with a hierarchical control structure to incorporate transient characteristics of natural gas flow and dynamics of energy converters in microgrids. The hierarchical EMS includes a supervisory control layer, an optimizing control layer, and an execution control layer. In order to efficiently accommodate the systems multi time-scale characteristics, the optimizing control layer is decomposed into three sub-layers: slow, medium and fast. Thermal, gas and electrical management systems are integrated into the slow, medium, and fast control layer, respectively. Compared with wind energy, solar energy is easier to integrate and more suitable for the microgrid environment, therefore, potential impacts of the hierarchical EMS on MSMP microgrids is investigated based on a building energy system integrating photovoltaic and microturbines. Numerical studies indicate that by using a hierarchical EMS, MSMP microgrids can be economically operated. Also, interactions among thermal, gas, and electrical system can be effectively managed.

Identification of Dynamics of Surface Suction Over an Airfoil at Low Reynolds Numbers

This paper deals with identification of dynamics in suction control of airfoils for low Reynolds number regimes (8 x 10^4 - 5 x 10^5). In particular, the dynamics of interest is the map that relates suction pressure and surface pressure. Identification of such dynamics is of use to a variety of active control applications including suction control in small/medium wind turbines which operate in these Reynolds number regimes. Prior research has largely focused on higher Reynolds number regimes, creating a need for such a study. Towards identifying the said dynamic relations, experiments were conducted on NACA0012 airfoil in a wind tunnel. The dynamic relation between suction and surface pressure was identified as an overdamped second order system.

Irish Power System Primary Frequency Response Metrics during Different System Non Synchronous Penetrations.

This paper discusses the use of primary frequency response metrics to assess the dynamics of frequency disturbance data with the presence of high system non synchronous penetration (SNSP) and system inertia variation. The Irish power system has been chosen as a study case as it experiences a significant level of SNSP from wind turbine generation and imported active power from HVDC interconnectors. Several recorded actual frequency disturbances were used in the analysis. These data were measured and collected from the Irish power system from October 2010 to June 2013. The paper has shown the impact of system inertia and SNSP variation on the performance of primary frequency response metrics, namely: nadir frequency, rate of change of frequency, inertial and primary frequency response.