Ladder Model Research Articles

Synthesis, Structure and Properties of a New Strong‐Rung Spin Ladder Compound Cu(2‐Ethylpyrazine)Br2

AbstractWe report the structure and magnetism of a newly synthesized coordination polymer Cu(2‐ethylpyrazine)Br2. Its crystal structure was determined by both single crystal and powder X‐ray diffractions. We find the compound crystallizes in the space group C2 with a ladder structure in which the copper ions are bridged by bromide ions and 2‐ethylpyrazine molecules along the rung and rail direction, respectively. The magnetic susceptibility is consistent with the strong‐rung spin ladder model which yields Jrung/kB=−33.819(1) K, Jrail/kB=−25.206(3) K. The obtained spin gap is Δ=18.01 K. Both magnetic susceptibility and heat capacity measurements show the absence of low range magnetic order down to 2 K, indicating weak inter‐ladder coupling in the compound.

Higher order RG flow on the Wilson line in mathcal{N} = 4 SYM

Extending earlier work, we find the two-loop term in the beta-function for the scalar coupling ζ in a generalized Wilson loop operator of the mathcal{N} = 4 SYM theory, working in the planar weak-coupling expansion. The beta-function for ζ has fixed points at ζ = ±1 and ζ = 0, corresponding respectively to the supersymmetric Wilson-Maldacena loop and to the standard Wilson loop without scalar coupling. As a consequence of our result for the beta-function, we obtain a prediction for the two-loop term in the anomalous dimension of the scalar field inserted on the standard Wilson loop. We also find a subset of higher-loop contributions (with highest powers of ζ at each order in ‘t Hooft coupling λ) coming from the scalar ladder graphs determining the corresponding terms in the five-loop beta-function. We discuss the related structure of the circular Wilson loop expectation value commenting, in particular, on consistency with a 1d defect version of the F-theorem. We also compute (to two loops in the planar ladder model approximation) the two-point correlators of scalars inserted on the Wilson line.

A Job Ladder Model of Firm, Worker, and Earnings Dynamics

A Job Ladder Model of Firm, Worker, and Earnings Dynamics

Diffusion with stochastic resetting of interacting particles emerging from a model of population genetics

In this paper, we put forward a connection between diffusion with resetting and a certain extension of Ohta–Kimura model, inspired on what was carried out in Da Silva and Fragoso (2018 J. Phys. A: Math. Theor. 51 505002). The contribution is twofold: (1) we derive a new extension of Ohta–Kimura model, dubbed here new extended version of Ohta–Kimura ladder model (NOKM) which bears a strong liaison with the so-called jump-type Fleming–Viot process. The novelty here, when we compare with the classical Ohta–Kimura model, is that we now have an operator which allows simultaneous interaction among many individuals. It has to do with a generalized branching mechanism i.e. m individual types extinguish and one individual type splits into m copies. The system of evolution equations arising from NOKM can be seen as a system of n-dimensional Kolmogorov forward equations (or Fokker–Planck equations). The analysis requires an amenable armory of concepts and mathematical technique to analyze some relevant issues such as correlation, indistinguishability of individuals and stationarity; (2) nudged by the ideas brought to bear in Da Silva and Fragoso (2018 J. Phys. A: Math. Theor. 51 505002), we advance in this agenda here by making an initial incursion on the connection between diffusion with resetting and the NOKM. The connection which relies on the similarities between the models allows, in some cases, that relevant results obtained for one model can be translated to the other model framework by taking advantage of the technique used to derive a result in one of the models. Through the development of the population genetic model and its reinterpretation in terms of diffusion with stochastic resetting, we show an invariance property of the correlation between two interacting particles that reset at a time-inhomogeneous resetting rate. Pushing forward the ideas we obtain the stationary state of a new model for an n-particle system under an anisotropic diffusion with resetting. Although the results using this approach are of recent vintage, we believe that this avenue of research seems to be very encouraging.

Quantum phases of interacting bosons on biased two-leg ladders with magnetic flux

The realization and detection of various phase transitions in interacting two-leg bosonic flux ladders are at the frontier of the present theoretical and experimental research in condensed-matter physics. We develop a biased two-leg Bose-Hubbard flux ladder model and first achieve the ground states and phase transition conditions of this system by the mean-field approach and variational analysis. Rich phases are revealed, including two different kinds of plane-wave phase, i.e., plane wave I (characterized with one single energy minimum of the energy band) and plane wave II (characterized with two nondegenerate local energy minima of the energy band), and interestingly the asymmetry vortex phase with the breaking of both ${Z}_{2}$ reflection symmetry and translational symmetry of space, which is characterized by the vortex with imbalanced density distributions on two legs. Moreover, the corresponding quantum phases can also be distinguished by the order parameters and the excitation spectra of the plane-wave phase intuitively. Furthermore, we demonstrate that this biased ladder system also makes it possible to realize a different dynamical asymmetric vortex state, which shows a dynamical supersolidlike property.

Topological properties of non-Hermitian Creutz ladders

We study topological properties of the one-dimensional Creutz ladder model with different non-Hermitian asymmetric hoppings and on-site imaginary potentials, and obtain phase diagrams regarding the presence and absence of an energy gap and in-gap edge modes. The non-Hermitian skin effect (NHSE), which is known to break the bulk–boundary correspondence (BBC), emerges in the system only when the non-Hermiticity induces certain unbalanced non-reciprocity along the ladder. The topological properties of the model are found to be more sophisticated than that of its Hermitian counterpart, whether with or without the NHSE. In one scenario without the NHSE, the topological winding is found to exist in a two-dimensional plane embedded in a four-dimensional space of the complex Hamiltonian vector. The NHSE itself also possesses some unusual behaviors in this system, including a high spectral winding without the presence of long-range hoppings, and a competition between two types of the NHSE, with the same and opposite inverse localization lengths for the two bands, respectively. Furthermore, it is found that the NHSE in this model does not always break the conventional BBC, which is also associated with whether the band gap closes at exceptional points under the periodic boundary condition.

Copula-based Modeling for IBNR Claim Loss Reserving

There are growing concerns for reserves estimation of incurred but not reported (IBNR) claims in actuarialsciences. In this paper, we propose a copula-based dependency model to capture the relationship betweentwo main IBNR reserve variables, i.e., the “time between two successive occurrences” and “delay time”.A maximum likelihood estimation (MLE) method is used to estimate the parameters of the model. Asimulation study is conducted to evaluate the validity of the theoretical results. Moreover, the proposedmethod is applied to predict the number of claims for the next years of a portfolio from a major automobileinsurer and is compared to the classical Chain Ladder model forecasting.

Optimal factor taxation in a scale free model of vertical innovation

AbstractThe objective of the paper is to study how the tax burden arising from an exogenous stream of public expenditures and transfers should be distributed between labor and capital in a scale‐less endogenous growth model, where the engine of growth are successful innovations. Our laboratory is a prototypical quality ladder model with a labor/leisure choice where research and development productivity is decreasing in the size of the economy. Our contribution is to show that even when labor supply has no effects on growth in the long run, it will still be optimal to tax capital for reasonable parametrizations of the model.

A ladder that matters: Conceptual development of a clinical ladder program for nurse practitioners and physician assistants.

Clinical ladders are professional enhancement models that encourage and reward participants for continued professional engagement and leadership development. They have the potential to affect patient care through improved provider retention, advanced and refined clinical skills, and increased engagement. Recent literature has demonstrated development and implementation of clinical ladder models for nurse practitioners (NPs) in the acute care setting. A free standing pediatric academic hospital in Florida identified the need for such a program for nurse practitioners and given its increased utilization of physician assistants, these providers were also targeted for inclusion. This new clinical ladder included development strategies appropriate and attainable for both NP and PA scopes of practice. Consistent with Benner's theory of novice to expert (1982), each advancing rung in the ladder contains more stringent criteria and additional competencies demonstrating increased engagement, learning, and leadership. As this was a development project only, future directions for the new model include implementation and evaluation of various metrics including nurse practitioner and physician assistant retention and satisfaction. This model has laid the foundation for ladder development for additional health care professions within the institution.

Envisioning alternatives in pre-structured urban sustainability transformations: Too late to change the future?

In the governance of urban sustainability transformations, participatory futures practices are increasingly popular. Yet there is a rising awareness that the success or failure of these practices depends on how they are staged and the context in which they are conducted. These contextual factors are often less than ideal, and futures practices take place at the crossroads of many pre-determined agendas and priorities. We distinguish four factors that shape the effects of participatory futures practices: 1) how the institutional landscape constrains or enables a project aimed at urban sustainability transformations; 2) the participatory culture surrounding the project; 3) the project design; and 4) the futures methods applied. We assess these factors in three cities within the European H2020 IRIS Smart Cities project. In each city, project members participated in sessions where they designed citizen engagement using a futures methodology: the novel Scope and Ladder models. Each city reflects a different combination of the four contextual factors. We find that space for exploration and re-imagining can be found and optimized under imperfect conditions. Drawing on the results of the three cases, we conclude with a set of recommendations for the funders, project members and futures organizers of urban sustainability transformation projects.

Calendar Effect and In-Sample Forecasting Applied to Mesothelioma Mortality Data

In this paper, we apply and further illustrate a recently developed extended continuous chain ladder model to forecast mesothelioma deaths. Making such a forecast has always been a challenge for insurance companies as exposure is difficult or impossible to measure, and the latency of the disease usually lasts several decades. While we compare three approaches to this problem, we show that the extended continuous chain ladder model is a promising benchmark candidate for asbestosis mortality forecasting due to its flexible and simple forecasting strategy. Furthermore, we demonstrate how the model can be used to provide an update for the forecast of the number of deaths due to mesothelioma in Great Britain using in recent Health and Safety Executive (HSE) data.

Localization dynamics from static and mobile impurities

We study the superfluid response and localization dynamics from static and mobile impurities. The superfluidity is formed in the rung-Mott phase of a bosonic ladder model producing spin-Meissner currents induced by a $\mathbb{U}(1)$ gauge field or a uniform magnetic field. Impurities are described through two-state systems which act as a two-peak random potential. An impurity sits either at the top or at the bottom of the ladder on each rung equally, producing a telegraph signal. The impurities-matter coupling gives rise to a classical Ising symmetry for static and mobile impurities associated to the inversion symmetry of the two legs of the ladder. From the decoupled rungs limit, we also identify a local $\mathbb{Z}_2$ gauge theory for mobile impurities. The properties of the system are studied from an effective quantum spin model including the possibility of four-body coupling in the limit of a strong interaction between bosons and impurities. Through analytical approaches and numerical exact diagonalization, we study the superfluid currents both in the weakly-coupled and strongly-coupled rungs limits for the bosons. In the weakly-coupled rungs situation, we find a smooth power-law localization whereas the strongly-coupled rungs limit produces a steep localization or insulating phase for various configurations of the two-peak random potential. In the strongly disordered situation, through entanglement and bipartite fluctuation measures, we also identify a many-body localization regime in time after a quench of the system when prepared in a N\' eel state.

One-Year and Ultimate Reserve Risk in Mack Chain Ladder Model

We investigate the relation between one-year reserve risk and ultimate reserve risk in Mack Chain Ladder model in a simulation study. The first goal is to validate the so-called linear emergence pattern formula, which maps the ultimate loss to the one-year loss, in case when we measure the risks with Value-at-Risk. The second goal is to estimate the true emergence pattern of the ultimate loss, i.e., the conditional distribution of the one-year loss given the ultimate loss, from which we can properly derive a risk measure for the one-year horizon from the simulations of ultimate losses. Finally, our third goal is to test if classical actuarial distributions can be used for modelling of the outstanding loss from the ultimate and the one-year perspective. In our simulation study, we investigate several synthetic loss triangles with various duration of the claims development process, volatility, skewness, and distributional assumptions of the individual development factors. We quantify the reserve risks without and with the estimation error of the claims development factors.

Cook stove technology adoption: Evidence from Kenya

Policies aimed at enhancing adoption of energy efficient, less polluting fuels, stoves and cooking practices need to be aligned to the realities of household multiple uses of fuels and stoves. In this paper we assess energy ladder model by using large nationwide survey data of 3665 Kenyan households collected in 2009. We show that the energy ladder is still sufficient to explain multiple fuel use and stove, and that the use of ‘fuel or stove staking’ metaphor was unnecessarily. Instead, we propose a metaphor ‘fuel and stove balancing’ to explain how uptake of single to multiple fuels or stoves happens gradually, through upwards and downwards movement on the ladder. Factors that influence stove balancing go beyond socio-economic and demographic characteristics to include stove type technology, markets, and financial factors. These factors are systematical analyzed using the Unified Theory of Acceptance and Use of Technology (UTAUT-2) framework that is based on seven constructs of technology adoption. They include performance expectancy, effort expectancy, social influence, facilitating conditions, hedonic motivation, price value and habit.

Effective narrow ladder model for two quantum wires on a semiconducting substrate

We present a theoretical study of two spinless fermion wires coupled to a three dimensional semiconducting substrate. We develop a mapping of wires and substrate onto a system of two coupled two-dimensional ladder lattices using a block Lanczos algorithm. We then approximate the resulting system by narrow ladder models, which can be investigated using the density-matrix renormalization group method. In the absence of any direct wire-wire hopping we find that the substrate can mediate an effective wire-wire coupling so that the wires could form an effective two-leg ladder with a Mott charge-density-wave insulating ground state for arbitrarily small nearest-neighbor repulsion. In other cases the wires remain effectively uncoupled even for strong wire-substrate hybridizations leading to the possible stabilization of the Luttinger liquid phase at finite nearest-neighbor repulsion as found previously for single wires on substrates. These investigations show that it may be difficult to determine under which conditions the physics of correlated one-dimensional electrons can be realized in arrays of atomic wires on semiconducting substrates because they seem to depend on the model (and consequently material) particulars.

Situation analysis of energy use and consumption in Cambodia: household access to energy

The aim of this article is to analyse the current situation of access to energy (in relation to SDG 7) and energy usage behaviour in households in two provinces in Cambodia, namely Pursat and Kampong Cham. The analytical framework is based on the energy ladder model and the energy stacking model as a starting point for assessing the current household energy profiles. A quantitative survey carried out in late 2015 in 970 households revealed differences in access to electricity between urban, electrified rural, and non-electrified rural districts. In urban areas, households are using multiple (3–4) energy sources compared to rural areas (2–3). The use of electricity through batteries in the non-electrified rural areas remains notable (43%) despite no access to the national grid. The dependence on traditional biomass, especially firewood, remains high (91% of all respondents) for all the sampled households, especially so in rural non-electrified households. The study confirms that households’ energy mix is composed of various energy sources, even when modern energy sources are available as opposed to complete fuel switch. The results also show that electricity use does not automatically lead to increased household income, but is much more complex process than discussed in existing research. The article further discusses the possible causes behind the phenomenon, proposes recommendations for better-informed energy policy, and provides important insights towards sustainable energy transition in Cambodia in the future.

Nonthermalized dynamics of flat-band many-body localization

We find that a flat-band fermion system with interactions and without disorders exhibits non-thermalized ergodicity-breaking dynamics, an analog of many-body localization (MBL). In the previous works, we observed flat-band many-body localization (FMBL) in the Creutz ladder model. The origin of FMBL is a compact localized state governed by local integrals of motion (LIOMs), which are to be obtained explicitly. In this work, we clarify the dynamical aspects of FMBL. We first study dynamics of two-particles, and find that the states are not substantially modified by weak interactions, but the periodic time evolution of entanglement entropy emerges as a result of a specific mechanism inherent in the system. On the other hand, as the strength of the interactions is increased, the modification of the states takes place with inducing instability of the LIOMs. Furthermore, many-body dynamics of the system at finite fillings is numerically investigated by time-evolving block decimation (TEBD) method. For a suitable choice of the filling, non-thermal and low entangled dynamics appears. This behavior is a typical example of the disorder-free FMBL.

Finite size effects around pseudo-transition in one-dimensional models with nearest neighbor interaction

Recently gigantic peaks in thermodynamic response functions have been observed at finite temperature for one-dimensional models with short-range coupling, closely resembling a second-order phase transition. Thus, we will analyze the finite temperature pseudo-transition property observed in some one-dimensional models and its relationship with finite size effect. In particular, we consider two chain models to study the finite size effects; these are the Ising-Heisenberg tetrahedral chain and an Ising-Heisenberg-type ladder model. Although the anomalous peaks of these one-dimensional models have already been studied in the thermodynamic limit, here we will discuss the finite size effects of the chain and why the peaks do not diverge in the thermodynamic limit. So, we discuss the dependence of the finite size effects, for moderately and sufficiently large systems, in which the specific heat and magnetic susceptibility exhibit peculiar rounded towering peaks for a given temperature. This behavior is quite similar to a continuous phase transition, but there is no singularity. For moderately large systems, the peaks narrow and increase in height as the number of unit cells is increased, and the location of peak shifts slightly. Hence, one can naively induce that the sharp peak should lead to a divergence in the thermodynamic limit. However, for a rather large system, the height of a peak goes asymptotically to a finite value. Our result rigorously confirms the dependence of the peak height with the number of unit cells at the pseudo-critical temperature. We also provide an alternative empirical function that satisfactorily fits specific heat and magnetic susceptibility at pseudo-critical temperature. Certainly, our result is crucial to understand the finite size correction behavior in quantum spin models, which in general are only numerically tractable within the framework of the finite size analysis.

One-year and ultimate reserve risk in Mack Chain Ladder model

We investigate the relation between one-year reserve risk and ultimate reserve risk in Mack Chain Ladder model in a simulation study. The first goal is to validate the so-called linear emergence pattern formula, which maps the ultimate loss to the one-year loss, in case when we measure the risks with Value-at-Risk. The second goal is to estimate the true emergence pattern of the ultimate loss, i.e. the conditional distribution of the one-year loss given the ultimate loss, from which we can properly derive a risk measure for the one-year horizon from the simulations of ultimate losses. Finally, our third goal is to test if classical actuarial distributions can be used for modelling of the outstanding loss from the ultimate and the one-year perspective. In our simulation study we investigate several synthetic loss triangles with various duration of the claims development process, volatility, skewness and distributional assumptions of the individual development factors. We quantify the reserve risks without and with the estimation error of the claims development factors.

Job Displacement and Job Mobility: The Role of Joblessness

Who is harmed by and who benefits from worker reallocation? We investigate the earnings consequences of changing jobs and find a wide dispersion in outcomes. This dispersion is driven not by whether the worker was displaced, but by the duration of joblessness between job spells. Job movers who experience joblessness suffer a persistent reduction in earnings and tend to move to lower-paying firms, suggesting that job ladder models offer a useful lens through which to understand the negative consequences of job separations.