Jordan-Wigner Approach to Dynamic Correlations in 2D Spin-1/2 Models

We discuss the dynamic properties of the square-lattice spin-1/2 XY model obtained using the two-dimensional Jordan-Wigner fermionization approach. We argue the relevance of the fermionic picture for interpreting the neutron scattering measurements in the two-dimensional frustrated quantum magnet Cs₂CuCl₄.     

Resonance states in 12C and α-particle condensation

The states with J^π = 0⁺, 2⁺, and 4⁺ of ¹²C with excitation energies less than about 15 MeV are investigated with the alpha condensate wave function with spatial deformation and by using the method of ACCC (analytic continuation in the coupling constant) which is necessary for a proper treatment of resonance states. The calculated energy and width of the recently observed 2₂⁺ state are found to be well reproduced. The obtained 2₂⁺ wave function has a large overlap with a single condensate wave function of 3α gas-like structure. The density distribution is shown to be almost the same as that of the 0₂⁺ state that is regarded as a 3α Bose-condensed state, if the energy of the 2₂⁺ state is scaled down to the same value as the one of the 0₂⁺ state. Furthermore, the kinetic energy, nuclear interaction energy, and Coulomb interaction energy of the calculated 2₂⁺ state are shown to be very similar to those of the 0₂⁺ state. We conclude that the 2₂⁺ state has a structure similar to the 0₂⁺ state of Bose-condensate character with a dilute 3α gas-like structure. In addition, the resonance states, 0₃⁺, 0₄⁺, 4₂⁺, are also discussed.     

Analysis of hydrogen bonds by the IR spectra of thymine and N<Subscript>1</Subscript>,N<Subscript>3</Subscript>-deuterothymine

Calculations of the frequencies and absolute intensities of the IR bands of plane vibrations of thymine and N₁,N₃-deuterothymine in various phase states have been carried out. It has been shown that in the polycrystalline state thymine forms hydrogen bonds C₂=O₈...HN₁ and C₂=O₈...HN₃, and in an aqueous solution the intermolecular interaction is realized by means of the hydrogen bonds O₈...HO and O...HN₁.__________Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 1, pp. 99–105, January–February, 2005.     

The ground state energy of the Edwards-Anderson spin glass model with a parallel tempering Monte Carlo algorithm

We study the efficiency of parallel tempering Monte Carlo technique for calculating true ground states of the Edwards-Anderson spin glass model. Bimodal and Gaussian bond distributions were considered in two- and three-dimensional lattices. By a systematic analysis we find a simple formula to estimate the values of the parameters needed in the algorithm to find the GS with a fixed average probability. We also study the performance of the algorithm for single samples, quantifying the difference between samples where the GS is hard, or easy, to find. The GS energies we obtain are in good agreement with the values found in the literature. Our results show that the performance of the parallel tempering technique is comparable to more powerful heuristics developed to find the ground state of Ising spin glass systems.     

平行双射流场纳米颗粒的形成与凝聚的研究

对平行双射流中H2SO4蒸气扩散进行了大涡模拟,给出了硫酸/水系统成核生成纳米颗粒及颗粒的凝聚过程中颗粒的分布特性,分析了燃料中硫的浓度、环境相对湿度以及射流Reynolds数对于颗粒浓度和粒径分布的影响．结果表明,硫酸/水系统会成核生成大量的纳米颗粒,在双管射流的中间和射流场周围,颗粒具有较高的浓度;颗粒的凝聚过程使颗粒的数量减少、直径变大;随着硫的浓度的增加,流场中的颗粒浓度有明显增加,而成核后形成的颗粒直径减小;环境湿度和Reynolds数的增大,有利于成核过程,因而导致形成更多的颗粒．     

Threshold behaviour of a stochastic SIR model

In this paper, we investigate the threshold behaviour of a susceptible-infected-recovered (SIR) epidemic model with stochastic perturbation. When the noise is small, we show that the threshold determines the extinction and persistence of the epidemic. Compared with the corresponding deterministic system, this value is affected by white noise, which is less than the basic reproduction number of the deterministic system. On the other hand, we obtain that the large noise will also suppress the epidemic to prevail, which never happens in the deterministic system. These results are illustrated by computer simulations.     

Gravitational effects in quantum mechanics

To date, both quantum theory and Einstein’s theory of general relativity have passed every experimental test in their respective regimes. Nevertheless, almost since their inception, there has been debate surrounding whether they should be unified, and by now, there exists strong theoretical arguments pointing to the necessity of quantising the gravitational field. In recent years, a number of experiments have been proposed which, if successful, should give insight into features at the Planck scale. Here, we review some of the motivations, from the perspective of semi-classical arguments, to expect new physical effects at the overlap of quantum theory and general relativity. We conclude with a short introduction to some of the proposals being made to facilitate empirical verification.     

On the Choice of Nugget in Kriging Modeling for Deterministic Computer Experiments

Kriging is commonly used for developing emulators as surrogates for computationally intensive simulations. One difficulty with kriging is the potential numerical instability in the computation of the inverse of the covariance matrix, which can lead to large variability and poor performance of the kriging predictor. First, we study some causes of ill-conditioning in kriging. We then study the use of nugget in kriging to overcome the numerical instability. Some asymptotic results on its interpolation bias and mean squared prediction errors are presented. Finally, we study the choice of the nugget parameter based on some algebraic lower bounds and use of a regularizing trace. A simulation study is performed to show the differences between kriging with and without nugget and to demonstrate the advantages of the former. This article has supplementary materials online.     

American Options in the Heston Model with Stochastic Interest Rate and Its Generalizations

Abstract

We consider the Heston model with the stochastic interest rate of Cox–Ingersoll–Ross (CIR) type and more general models with stochastic volatility and interest rates depending on two CIR-factors; the price, volatility and interest rate may correlate. Time-derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options arising in the time discretization of a Markov-modulated Lévy model. Options in this sequence are solved using an iteration method based on the Wiener–Hopf factorization. Typical shapes of the early exercise boundary are shown, and good agreement of option prices with prices calculated with the Longstaff–Schwartz method and Medvedev–Scaillet asymptotic method is demonstrated.