Quantum Monte Carlo and variational approaches to the Holstein model

Based on the canonical Lang-Firsov transformation of the Hamiltonian we develop a very efficient quantum Monte Carlo algorithm for the Holstein model with one electron. Separation of the fermionic degrees of freedom by a reweighting of the probability distribution leads to a dramatic reduction in computational effort. A principal component representation of the phonon degrees of freedom allows to sample completely uncorrelated phonon configurations. The combination of these elements enables us to perform efficient simulations for a wide range of temperature, phonon frequency and electron-phonon coupling on clusters large enough to avoid finite-size effects. The algorithm is tested in one dimension and the data are compared with exact-diagonalization results and with existing work. Moreover, the ideas presented here can also be applied to the many-electron case. In the one-electron case considered here, the physics of the Holstein model can be described by a simple variational approach.Comment: 18 pages, 11 Figures, v2: one typo correcte

On the progenitor of binary neutron star merger GW170817

On 2017 August 17 the merger of two compact objects with masses consistent with two neutron stars was discovered through gravitational-wave (GW170817), gamma-ray (GRB 170817A), and optical (SSS17a/AT 2017gfo) observations. The optical source was associated with the early-type galaxy NGC 4993 at a distance of just ∼40 Mpc, consistent with the gravitational-wave measurement, and the merger was localized to be at a projected distance of ∼2 kpc away from the galaxy's center. We use this minimal set of facts and the mass posteriors of the two neutron stars to derive the first constraints on the progenitor of GW170817 at the time of the second supernova (SN). We generate simulated progenitor populations and follow the three-dimensional kinematic evolution from binary neutron star (BNS) birth to the merger time, accounting for pre-SN galactic motion, for considerably different input distributions of the progenitor mass, pre-SN semimajor axis, and SN-kick velocity. Though not considerably tight, we find these constraints to be comparable to those for Galactic BNS progenitors. The derived constraints are very strongly influenced by the requirement of keeping the binary bound after the second SN and having the merger occur relatively close to the center of the galaxy. These constraints are insensitive to the galaxy's star formation history, provided the stellar populations are older than 1 Gyr

Implementation of market methods of price forming in the field of power industry with the application of the consolidated balance-market model of economic systems

Object. The power industry of Russia is being developing with the use of its natural resources, advanced ideas, implementation of existing opportunities. So, the key task of the energy strategy of Russia till 2035 is the transfer from the commodity-heavy to the resource-innovative development of both the power industry and the economics of the country. All conditions have been created for its solution as of now - the power industry is expected to increase by 20-25% if demand for the hydrocarbon raw materials falls on the immediate horizon. In this juncture such branch as the power industry seems to be a crutial and sophisticated object of the research on the dynamics of economic systems infrastructural transformations. Anyway, its implementation in the field of the power industry involved quasi-market mechanisms of the preservation of existing ones and the building of new non-competitive powers with the use of such mechanisms as "adhesion contract"and "marginal price forming". The work shows the inhibiting impact of these mechanisms on the economic system. The offer for its replacement to increase the pace of the power industry development and of the Russian economics substantiates. The research purpose is to substantiate the application of the consolidated balance-market model of economic systems for the analysis of the dynamics of the development of the technologically heterogenic branch, interacting with the other economic system, provided Leontief correlations. The power industry was selected as the studied one. Peculiarities of the reforming of power price rates, combining both market and regulating (quasi-market) mechanisms, were considered. Methods. The random balance-market model became the methodologic basis for mixed economic systems in the option of the self-consistent field of Leontief matrices. It make it possible to solve practical issues of the development of most important multi-agent branches in its interaction with the other economic system. In the work this model is applied in the quasitensor form for the evaluation of mixed mechanisms of the regulation of price rates in the power industry. Results. It was revealed that the common use of such mechanisms as "marginal price forming"and "adhesion contracts"fully suppresses the economic growth in all branches of economics. In order to find the way out was offered the consolidated random model of mixed economic systems in the quasitensor form. Its application will make it possible to obtain the new distribution of the capital by goods and agents with the better use of its technical advantages with such level of power rates. Conclusions. The possibility of the subtle analysis of the dynamics of the specialization and localization of agents was shown for the following development of distributed centralized energoinformational systems in the Russian Federation. It is expedient to use offered approach and developed algorithms of modeling for the evaluation of the accelerated economic growth of other key branches of the Russian economics. © Published under licence by IOP Publishing Ltd

Combined Digital Economic-Epidemic Model for the Evaluation of Economic Results of Several Scenarios of Quarantine Measures

Purpose: Substantiation of the selection of the potential option of the implementation of quarantine measures and of the obtaining of evaluations of its potential economic consequences for Moscow on the basis of the use of instruments of the combined digital economic-epidemic model, developed by authors. Methods: In order to carry out the research the modified SIR-model was used as the basic epidemic one. As the economic growth model was used the model of probability of mixed economic systems, developed by authors. The consolidation of such models to its lowest terms allowed to form the combined digital economic-epidemic model. As basic ones were considered three potentially possible options for the implementation of quarantine measures. On the basis of the model, developed by authors, were developed feasibility studies for each of three options of quarantine measures. While carrying out calculations as initial terms was adopted the dynamics of the daily accrual of people, infected withCOVID-19 for the week between 01.04 and 08.04.2020. Result: On the basis of the combined digital economic-epidemic model were determined possible economic consequences at the implementation of basic options of quarantine measures, feasibility studies were provided, its scientific analysis has been performed with the substantiation of the development of one of considered options. As most optimal option of the implementation of quarantine measures B option was selected. Conclusion: The offered model and settlements, performed on its basis, can be applied in all regions of Russia in order to select the potential option of the implementation of quarantine measures and of the evaluation of possible economic consequences for each region. This is a universal model. With it can be studied events of all epidemiologic periods and world regions. © 2021, Springer Nature Switzerland AG

Combined Digital Economic-Epidemic Model for the Evaluation of Economic Results of Several Scenarios of Quarantine Measures

Purpose: Substantiation of the selection of the potential option of the implementation of quarantine measures and of the obtaining of evaluations of its potential economic consequences for Moscow on the basis of the use of instruments of the combined digital economic-epidemic model, developed by authors. Methods: In order to carry out the research the modified SIR-model was used as the basic epidemic one. As the economic growth model was used the model of probability of mixed economic systems, developed by authors. The consolidation of such models to its lowest terms allowed to form the combined digital economic-epidemic model. As basic ones were considered three potentially possible options for the implementation of quarantine measures. On the basis of the model, developed by authors, were developed feasibility studies for each of three options of quarantine measures. While carrying out calculations as initial terms was adopted the dynamics of the daily accrual of people, infected withCOVID-19 for the week between 01.04 and 08.04.2020. Result: On the basis of the combined digital economic-epidemic model were determined possible economic consequences at the implementation of basic options of quarantine measures, feasibility studies were provided, its scientific analysis has been performed with the substantiation of the development of one of considered options. As most optimal option of the implementation of quarantine measures B option was selected. Conclusion: The offered model and settlements, performed on its basis, can be applied in all regions of Russia in order to select the potential option of the implementation of quarantine measures and of the evaluation of possible economic consequences for each region. This is a universal model. With it can be studied events of all epidemiologic periods and world regions

Possible Atmospheric Diversity of Low Mass Exoplanets – Some Central Aspects

Exoplanetary science continues to excite and surprise with its rich diversity. We discuss here some key aspects potentially influencing the range of exoplanetary terrestrial-type atmospheres which could exist in nature. We are motivated by newly emerging observations, refined approaches to address data degeneracies, improved theories for key processes affecting atmospheric evolution and a new generation of atmospheric models which couple physical processes from the deep interior through to the exosphere and consider the planetary-star system as a whole. Using the Solar System as our guide we first summarize the main processes which sculpt atmospheric evolution then discuss their potential interactions in the context of exoplanetary environments. We summarize key uncertainties and consider a diverse range of atmospheric compositions discussing their potential occurrence in an exoplanetary context

Estimating the contribution of dynamical ejecta in the kilonova associated with GW170817

The source of the gravitational-wave (GW) signal GW170817, very likely a binary neutron star merger, was also observed electromagnetically, providing the first multi-messenger observations of this type. The two-week-long electromagnetic (EM) counterpart had a signature indicative of an r-process-induced optical transient known as a kilonova. This Letter examines how the mass of the dynamical ejecta can be estimated without a direct electromagnetic observation of the kilonova, using GW measurements and a phenomenological model calibrated to numerical simulations of mergers with dynamical ejecta. Specifically, we apply the model to the binary masses inferred from the GW measurements, and use the resulting mass of the dynamical ejecta to estimate its contribution (without the effects of wind ejecta) to the corresponding kilonova light curves from various models. The distributions of dynamical ejecta mass range between Mej = 10 -³ - 10-² M⊙ for various equations of state, assuming that the neutron stars are rotating slowly. In addition, we use our estimates of the dynamical ejecta mass and the neutron star merger rates inferred from GW170817 to constrain the contribution of events like this to the r-process element abundance in the Galaxy when ejecta mass from post-merger winds is neglected. We find that if 10% of the matter dynamically ejected from binary neutron star (BNS) mergers is converted to r-process elements, GW170817-like BNS mergers could fully account for the amount of r-process material observed in the Milky Way