Inverse Monte Carlo study on effective interaction potential of Ag--Rh alloy from pair correlation functions

This paper presents an inverse Monte Carlo method to reconstruct pair interaction potential from pair correlation function. This approach adopts an iterative algorithm on interaction potential to fit known pair correlation function by compelling deviations of canonical average to meet with Hamiltonian parameters on a basis of statistical mechanism. The effective interaction potential between particles in liquid Ag--Rh alloys has been calculated with the inverse Monte Carlo method. It demonstrates an effective and simple way to obtain the effective potential of complex melt systems.     

Mirror nesting of the Fermi contour and zero line of the superconducting order parameter

The superconducting order parameter that emerges owing to pairing of charge carriers with a large total momentum of the pair during screened Coulomb repulsion in a degenerate quasi-two-dimensional electronic system is determined as a function of the momentum of relative motion of the pair. In view of the kinematic constraint associated with Fermi filling, the ordered state exists in a limited domain of the momentum space, the shape and size of this domain being determined by the total momentum of the pair. The order parameter is not a constant-sign function of the momentum and reverses its sign on a certain line in a kinematically allowed domain. Superconducting instability arises for an arbitrarily small value of the repulsive interaction for certain momenta of the pair, for which the mirror nesting condition is satisfied; this results in the formation of a pair Fermi contour, i.e., the line of coincidence of segments of the Fermi contour with the isoline of the kinetic energy of relative motion of the pair. The temperature dependence of the superconducting order parameter is studied. Owing to the proximity effect in the momentum space, superconducting ordering is extended to the kinematically forbidden domain.     

准一维体系的电子关联的变分计算

对于具有库仑相互作用的准一维电子体系,本文提出了一种新的模型,得到了准一维体系的电子有效库仑势形式。在相关基函数理论框架下,根据电子气的集体振荡行为,给出该体系的多体波函数,并得到不同密度的电子体系的关联函数和关联能,本文得到的关联函数是恒正的,且满足归一化条件。     

Classical Representation of a Quantum System at Equilibrium

A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g., MD, integral equations, DFT) to describe quantum systems. The classical system has an effective temperature, local chemical potential, and pair interaction that are defined by requiring equivalence of the grand potential and its functional derivatives with respect to the external and pair potentials for the classical and quantum systems. Practical inversion of this mapping for the classical properties is effected via the hypernetted chain approximation, leading to representations as functionals of the quantum pair correlation function. As an illustration, the parameters of the classical system are determined approximately such that ideal gas and weak coupling RPA limits are preserved (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Mean Pair Correlation Function of ±J Ising Spin Glasses

We provide a formula and an upper bound for the average over the disorder of the pair correlation function of ±J Ising spin glasses by using the symmetries of the system, We show the decay of the mean spin pair correlation function when the proportion of antiferromagnetic bonds is larger than the critical parameter associated with the pair dissociation phase transition.     

Short distance behaviour of the pair correlation function for classical plasmas

The screening effects on two like charges at short distances in a classical plasma are computed using a cluster expansion for the pair correlation function. We obtain numerically accurate results for the intermediate screening region, Λ 1, where Λ is Coulomb interaction parameter.     

Ultrafast dynamics of strongly coupled plasmas

The ultrafast dynamics of a strongly coupled plasma following an energy landscape shift is studied theoretically and with simulation. To lowest order in time, the inertial dynamics on the new landscape can be characterized by the plasma microfield, which, for the randomly ordered case of an ultracold neutral plasma, is dominated by nearest neighbor interactions. Formation of the pair correlation function arises after ballistic overshoot, which leads to oscillations in the effective temperature. Warm dense matter systems are also considered in this context.     

Population dynamics on random networks: simulations and analytical models

We study the phase diagram of the standard pair approximation equations for two different models in population dynamics, the susceptible-infective-recovered-susceptible model of infection spread and a predator-prey interaction model, on a network of homogeneous degree k. These models have similar phase diagrams and represent two classes of systems for which noisy oscillations, still largely unexplained, are observed in nature. We show that for a certain range of the parameter k both models exhibit an oscillatory phase in a region of parameter space that corresponds to weak driving. This oscillatory phase, however, disappears when k is large. For k = 3, 4, we compare the phase diagram of the standard pair approximation equations of both models with the results of simulations on regular random graphs 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. We discuss this failure of the standard pair approximation model to capture even the qualitative behavior of the simulations on large regular random graphs and the relevance of the oscillatory phase in the pair approximation diagrams to explain the cycling behavior found in real populations.     

Equilibrium theory of molecular fluids: Structure and freezing transitions

In this article we review equilibrium theory of molecular fluids which includes structure and freezing transitions. The application of the theory to evaluate the pair correlation functions using Integral Equation methods and Computer Simulations have been discussed. Freezing of classical complex fluids based on the density functional approach is also discussed and compare a variety of its versions. Transitions discussed are sensitive to the value of direct correlation functions of the effective liquid which is required as an input information in the theory. Accurate evaluation of pair correlation functions is emphasized. Calculation of these correlation functions which pose problems in the case of ordered phases is discussed. The pair correlation functions of the ordered phase, which are supposed to be made up of two contributions, one that preserves the symmetry of the isotropic phase and a second that breaks it, are discussed. A new free-energy functional developed for an inhomogeneous system that contains both symmetry conserved and symmetry broken parts of the direct pair correlation function is discussed. The most useful three dimensional reference interaction site model (3D-RISM) and its extension done recently by many workers is discussed. Application of this theory to a large variety of complex systems in combination with the density functional theory method implemented in the Amsterdam density functional software package is discussed. Coupling of the 3D-RISM salvation theory with molecular dynamics in the Amber molecular dynamics package is also given.     

Spatial nonlocal pair correlations in a repulsive 1D Bose gas

We analytically calculate the spatial nonlocal pair correlation function for an interacting uniform 1D Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms, including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects.     

The two-dimensional coulomb gas in the critical region

We consider the two-dimensional Coulomb gas in the critical region. To avoid the well-known collapse of the system below a certain temperature, the Coulomb interaction is cut inside a core radius. By analysis of the pair correlation function we find that this system exhibits a phase transition with a critical point. Below the critical temperature the ions are unable to shield each other, and they all may be considered as bound in neutral dipolar pairs. The density of dipolar pairs affects the critical temperature. In the critical region we obtain explicit results, and we are able to extract the leading singular behavior of the pair correlation function.     

Yang-Lee zeros for an urn model for the separation of sand

We apply the Yang-Lee theory of phase transitions to an urn model for the separation of sand. The effective partition function of this nonequilibrium system can be expressed as a polynomial of the size-dependent effective fugacity z. Numerical calculations show that in the thermodynamic limit the zeros of the effective partition function are located on the unit circle in the complex z plane. In the complex plane of the actual control parameter, certain roots converge to the transition point of the model. Thus, the Yang-Lee theory can be applied to a wider class of nonequilibrium systems than those considered previously.     

An investigation of the 2D attractive Hubbard model

We present an investigation of the 2D attractive Hubbard model, considered as an effective model relevant to superconductivity in strongly interacting electron systems. We use both hybrid Monte-Carlo simulations and existing hopping parameter expansions to explore the low temperature domain. The increase of the static S-wave pair correlation with decreasing temperature, which depends weakly on the band filling in the explored temperature range, is analyzed in terms of an expected Kosterlitz-Thouless superconducting transition. Using both our data and previously published results, we show that the evidence for this transition is weak: If it exists, its temperature is very low. The number of unpaired electrons remains nearly constant with temperature at fixed attractive potential strength. In contrast, the static magnetic susceptibility decreases fast with temperature, and cannot be related only to pair formation. We introduce a method by which the Padé approximants of the existing series for the susceptibility give sensible results down to rather low temperature region, as shown by comparison with our numerical data. Received: 30 October 1996 / Revised: 23 October 1997 / Accepted: 29 January 1998     

Correlation Functions by Cluster Variation Method for Ising Model with NN, NNN, and Plaquette Interactions

We consider a procedure for calculating the pair correlation function in the context of cluster variation methods (CVM). As specific cases, we study the pair correlation function in the paramagnetic phase of the Ising model with nearest neighbors, next to nearest neighbors, and plaquette interactions in two and three dimensions. In presence of competing interactions, the so-called disorder line separates in the paramagnetic phase a region where the correlation function has the usual exponential behavior from a region where the correlation has an oscillating, exponentially damped behavior. In two dimensions, using the plaquette as the maximal cluster of the CVM approximation, we calculate the phase diagram and the disorder line for a case where a comparison is possible with known results for the eight-vertex model. In three dimensions, in the CVM cube approximation, we calculate the phase diagram and the disorder line in some cases of particular interest. The relevance of our results for experimental systems like mixtures of oil, water, and surfactant is also discussed.     

Pair correlation function in a dense plasma and pycnonuclear reactions in stars

The short-range behavior of the pair correlation function in a dense onecomponent plasma (jellium) is investigated. As an intermediate step, the short-range behavior of the classical pair correlation function is obtained. Actually, although the temperature and the density are assumed to be such that the thermodynamic properties are almost classical, quantum mechanics (tunnel effect) always dominates the pair correlation function at short distances. The quantum pair correlation function is calculated by treating the many-body quantum effects by a perturbation theory, and by using a semiclassical approximation based on path integrals. The results are applied to the computation of the nuclear reaction rate in dense stellar matter (pycnonuclear reactions).Laboratoire associé au Centre National de la Recherche Scientifique.     

一类时变时滞混沌系统的参数辨识方法

时变的未知时滞参数普遍存在于混沌系统中,它使得混沌系统同步控制变得非常困难. 针对时滞混沌系统中参数时变且未知的问题, 提出了一种新颖的辨识方法. 该方法首先将未知时变参数用分段常数函数来近似, 把求解非线性函数的问题转化为参数向量选择问题, 其中分段常数函数的高度向量成为待求解参数向量; 然后推导了目标函数对分段常数高度向量的梯度信息, 结合序列二次规划法求解得最优分段函数; 随着分段数的增加, 最优分段函数将逼近原非线性时变函数. 数值实例结果验证了该方法的有效性.     

On the determination of the particle interaction potential in a dusty plasma from a pair correlation function

The effect of confinement on the pair correlation function of microparticles whose interaction is described by a screened Coulomb potential (Yukawa potential) has been investigated by the molecular dynamics simulations. The data are used to solve the inverse problem of the reconstruction of the particle interaction potential. It has been shown that such a reconstruction is likely impossible for a strongly nonideal system (with the coupling parameter Γ > 1). For systems with Γ ≤ 1, reconstruction is possible if confinement does not lead to the strong inhomogeneity of the system of microparticles.     

Odd-parity triplet pair induced by Hund's rule coupling

We discuss microscopic aspects of the odd-parity triplet pair in orbital degenerate systems. From the concept of off-diagonal long-range order, a pair state is unambiguously defined as the eigenstate with the maximum eigenvalue of a pair correlation function. Performing this scheme by a numerical technique, we clarify that the odd-parity triplet pair occurs as an out-of-phase combination of local triplets induced by Hund's rule coupling for the lattice including two sites in the unit cell.