Equilibrium time correlation functions in the low-density limit

We consider a system of hard spheres in thermal equilibrium. Using Lanford's result about the convergence of the solutions of the BBGKY hierarchy to the solutions of the Boltzmann hierarchy, we show that in the low-density limit (Boltzmann-Grad limit): (i) the total time correlation function is governed by the linearized Boltzmann equation (proved to be valid for short times), (ii) the self time correlation function, equivalently the distribution of a tagged particle in an equilibrium fluid, is governed by the Rayleigh-Boltzmann equation (proved to be valid for all times). In the latter case the fluid (not including the tagged particle) is to zeroth order in thermal equilibrium and to first order its distribution is governed by a combination of the Rayleigh-Boltzmann equation and the linearized Boltzmann equation (proved to be valid for short times).Supported in part by NSF Grant PHY 78-22302.     

A complementary thermodynamic limit for classical Coulomb matter

The canonical equilibrium measure of classical two-component Coulomb matter with regularized interactions is analyzed in a finite volume. It is shown that, in the mean-field regime, the one-particle density is inhomogeneous on a new characteristic length scale _inh. For a system ofN positive andN negative particles, _inh and the characteristic length scale of correlations _corr (=Debye screening length) are related via _inh=(2N)^1/2 _corr. The major conceptual conclusion that is drawn from this is that one needs two nontrivial complementary thermodynamic limits to define the equilibrium thermodynamics of two-component Coulomb systems. One of them is the standard thermodynamic limit (infinite volume), where one takesN, _corr fixed. Its complementary limit is characterized byN, _inh fixed, and is a finite-volume inhomogeneous mean-field limit. The most prominent new feature in the mean-field thermodynamic limit, which is absent in the standard thermodynamic limit, is an anomalous first-order phase transition where the Coulomb system explodes or implodes, respectively. The phase transition is connected with the existence of a metastable plasma phase far below the ionization temperature.     

Correlation inequalities and the thermodynamic limit for classical and quantum continuous systems II. Bose-Einstein and Fermi-Dirac statistics

We study quantum mechanical systems of particles with Bose or Fermi statistics interacting via two-body potentials of positive type in thermal equilibrium. We rewrite partition functions, reduced density matrices (RDMs), and correlation functions in terms of Wiener and Gaussian functional integrals (sine-Gordon transformation). This permits us, e.g., to apply correlation inequalities. Our main results include an analysis of stability versus instability in the grand canonical ensemble and, for charge-conjugation-invariant systems, upper and lower bounds on RDMs, the existence of the thermodynamic limit of pressure, RDMs and correlation functions, an inequality comparing correlations with Fermi statistics to ones with Bose statistics, and inequalities which are important in the study of Bose-Einstein condensation and of superconductivity.This research was done in part during the author's stay at the Department of Physics of Princeton University and was partially supported by the NSF under grant NSF PHY 76-80958.     

Spectral densities of response functions for the O(3) symmetric Anderson and two channel Kondo models

The O(3) symmetric Anderson model is an example of a system which has a stable low energy marginal Fermi liquid fixed point for a certain choice of parameters. It is also exactly equivalent, in the large U limit, to a localized model which describes the spin degrees of freedom of the linear dispersion two channel Kondo model. We first use an argument based on conformal field theory to establish this precise equivalence with the two channel model. We then use the numerical renormalization group (NRG) approach to calculate both one-electron and two-electron response functions for a range of values of the interaction strength U. We compare the behaviours about the marginal Fermi liquid and Fermi liquid fixed points and interpret the results in terms of a renormalized Majorana fermion picture of the elementary excitations. In the marginal Fermi liquid case the spectral densities of all the Majorana fermion modes display a dependence on the lowest energy scale, and in addition the zero Majorana mode has a delta function contribution. The weight of this delta function is studied as a function of the interaction U and is found to decrease exponentially with U for large U. Using the equivalence with the two channel Kondo model in the large U limit, we deduce the dynamical spin susceptibility of the two channel Kondo model over the full frequency range. We use renormalized perturbation theory to interpret the results and to calculate the coefficient of the ln divergence found in the low frequency behaviour of the T=0 dynamic susceptibility. Received 29 January 1999     

Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems

We develop a level set method for the computation of multi-valued physical observables (density, velocity, energy, etc.) for the high frequency limit of symmetric hyperbolic systems in any number of space dimensions. We take two approaches to derive the method.The first one starts with a weakly coupled system of an eikonal equation for phase S and a transport equation for density ρ:

The main idea is to evolve the density near the n-dimensional bi-characteristic manifold of the eikonal (Hamiltonian–Jacobi) equation, which is identified as the common zeros of n level set functions in phase space . These level set functions are generated from solving the Liouville equation with initial data chosen to embed the phase gradient. Simultaneously, we track a new quantity f = ρ(t,x,k)|det(_k)| by solving again the Liouville equation near the obtained zero level set = 0 but with initial density as initial data. The multi-valued density and higher moments are thus resolved by integrating f along the bi-characteristic manifold in the phase directions.The second one uses the high frequency limit of symmetric hyperbolic systems derived by the Wigner transform. This gives rise to Liouville equations in the phase space with measure-valued solution in its initial data. Due to the linearity of the Liouville equation we can decompose the density distribution into products of function, each of which solves the Liouville equation with L^∞ initial data on any bounded domain. It yields higher order moments such as energy and energy flux.The main advantages of these new approaches, in contrast to the standard kinetic equation approach using the Liouville equation with a Dirac measure initial data, include: (1) the Liouville equations are solved with L^∞ initial data, and a singular integral involving the Dirac-δ function is evaluated only in the post-processing step, thus avoiding oscillations and excessive numerical smearing; (2) a local level set method can be utilized to significantly reduce the computation in the phase space. These methods can be used to compute all physical observables for multi-dimensional problems.Our method applies to the wave fields corresponding to simple eigenvalues of the dispersion matrix. One such example is the wave equation, which will be studied numerically in this paper.     

A variational derivation of the velocity distribution functions for nonequilibrium,multispecies, weakly interacting,spherically symmetric many-body systems

The most probable velocity distribution function of each component,f _a , of a nonequilibrium multispecies spherically symmetric system of particles (stellar plasma atmospheres and winds, stellar systems, pellet-fusion systems) is analytically derived forthe case in which each component is described by the first six moments of f _a . This is achieved by the aid of a variational approach based on the requirement that the BoltzmannH function for the system be a minimum, subject to the constraints provided by the sets of six macroscopic parameters describing the nonequilibrium state. The use of the so-obtained velocity distribution functions for the closure of the moment equations as well as for the calculation of their collisional terms (via the Fokker-Planck equation) is discussed. The limitations on the maximum deviations from the equilibrium state which are consistent with the assumptions used are also indicated.     

A renormalization group analysis of correlation functions for the dipole gas

We develop a renormalization group method for analyzing the generating functional for charge correlations of a dilute classical dipole gas. It is based on and extends the renormalization group analysis introduced by Brydges and Yau for the dipole gas partition function. Our method leads to systematic formulas for the large-distance behavior of correlation functions of all orders. We prove that in any dimensiond2, at any value>0 of the inverse temperature, and at sufficiently small activityz, the correlation functions exhibit at large distances the same behavior as for a vacuum (z=0), but with a new dielectric constant 1+ over which we have good control. The results proved here extend existing results on the two-point correlations to all higher correlations, and constitute a general confirmation of the fact that dipoles do not screen.     

The cluster expansion for classical and quantum lattice systems

We develop a high-temperature expansion for general lattice systems which can be applied to classical as well as quantum systems. Applying the expansion we prove analyticity of correlation functions, uniqueness of equilibrium states, and cluster properties for classical and quantum lattice systems in the high-temperature region.     

The excitation energies and term energies of the excited states 1s2ns (n=3,4,5) and 1s2nf (n=4,5) of lithium-like systems of Z=11－20

In this paper, the full-core plus correlation (FCPC) and the Ritz method is extended to calculate the non-relativistic energies of 1s^2ns (n=3,4,5) and 1s^2nf (n=4,5) states and the wavefunctions of the lithium-like systems from Z=11－20. The mass-polarization and the relativistic correction including the kinetic-energy correction, the Darwin term, the electron－electron contact term, and the orbit－orbit interaction are evaluated perturbatively as the first-order correction. The contribution from quantum electrodynamic is also included by using the effective nuclear charge formula. The excited energies, the term-energy and fine structure, are given and compared with the other theoretical calculation and experimental results. It is shown that the correlative wave in the FCPC method embodies well the strong correlation between the 1s^2 core and the valence electron.     

类锂体系激发态1s2 nd(n=3,4,5)精细结构和项能的理论计算

使用全实加关联(fullcorepluscorrelation缩写为FCPC)和里兹(Ritz)变分方法计算了类锂体系(Z=11—20)激发态1s2nd(n=3,4,5)的非相对论能量和波函数;包括动能修正、电子电子接触项、轨道轨道相互作用项以及Darwin项的相对论修正和质量极化项由全实加关联波函数的一阶微扰给出,量子电动力学(quantumelectronicdynamics缩写为QED)修正由有效核电荷方法和类氢公式计算;给出了高电离类锂体系激发态的激发能、精细结构和项能(termenergy),并 关键词： 类锂体系 全实加关联 精细结构 激发能     

The thermodynamic functions and the regions of (P,T)-states of dense carbon and boron nitride modifications

Abstract

For the first time the thermodynamic functions for boron nitride and carbon were defined in the temperature range 300 to 4000K by a computational procedure which was impossible in the previous empirical approach. This involved the application of the theoretical functions from Refs. 1, 2, and 3. There the temperature dependence of the heat capacity is characterized by a sum of two Debye functions that reflect the contribution of vibration modes of different characteristic temperature to the heat capacity. The above-mentioned theoretical functions make it possible to calculate the thermodynamic function without allowing for the anharmonic effect in the temperature range rather wider th-an the one wherein the initial experiments were conducted. It is sufficient for their computation to define Debye characteristic temperatures. One of the procedures of their calculation using experimental enthalpy data is described in Ref. 4. Besides, this work contains the majority of known experimental and theoretical data which enable various methods of the thermodynamic function characterizations for carbon and boron nitride to be compared.     

Multiscale representation of generating and correlation functions for some models of statistical mechanics and quantum field theory

We consider models of statistical mechanics and quantum field theory (in the Euclidean formulation) which are treated using renormalization group methods and where the action is a small perturbation of a quadratic action. We obtain multiscale formulas for the generating and correlation functions aftern renormalization group transformations which bring out the relation with thenth effective action. We derive and compare the formulas for different RGs. The formulas for correlation functions involve (1) two propagators which are determined by a sequence of approximate wave function renormalization constants and renormalization group operators associated with the decomposition into scales of the quadratic form and (2) field derivatives of the nth effective action. For the case of the block field -function RG the formulas are especially simple and for asymptotic free theories only the derivatives at zero field are needed; the formulas have been previously used directly to obtain bounds on correlation functions using information obtained from the analysis of effective actions. The simplicity can be traced to an orthogonality-of-scales property which follows from an implicit wavelet structure. Other commonly used RGs do not have the orthogonality of scales property.     

First-principles calculation of structural stability,lattice dynamic and thermodynamic properties of BeX (X = S,Se and Te) compounds under high pressure

The phase transitions, lattice dynamical and thermodynamic properties of BeS, BsSe and BeTe at high pressure have been investigated with the density functional theory. The calculated equilibrium structural parameters agree well with the available experimental and theoretical values. The phase transition pressures from the zinc-blende (ZB) to the nickel arsenide (NiAs) phase of these compounds are determined. The calculated phonon dispersion curves of these compounds in ZB phase at zero pressure do not show any anomaly or instability. Dynamically, the ZB phase of BeS, BeSe and BeTe is found to be stable near transition pressures P_T. Within the quasiharmonic approximation, the thermodynamic properties including the thermal expansion coefficient, heat capacity at constant volume, heat capacity at constant pressure and entropy are predicted.     

Low-temperature heat capacities and thermodynamic properties of n-undecylammonium bromide monohydrate C11H28BrNO(s)

Crystal structure of n-undecylammonium bromide monohydrate was determined by X-ray crystallography. Low-temperature heat capacities of the compound were measured by a precision automated adiabatic calorimeter over the temperature range from 78 to 390?K. Two solid–solid phase transitions were observed for the title compound. The temperatures, molar enthalpies, and entropies of the phase transitions were derived based on the analysis of heat–capacity curve. Two polynomial equations of heat capacities as a function of temperature were fitted by least-squares method. Based on the two polynomial equations, smoothed heat capacities and thermodynamic functions of the compound relative to the standard reference temperature 298.15?K were calculated and tabulated at 5 K intervals.     

Derivation and classical limit of the mean-field equation for a quantum Coulomb system: Maxwell-Boltzmann statistics

The mean-field density matrix of a changed plasma of quantum particles with Maxwell-Boltzmann statistics in a confining external potential is obtained as a limit of theN-body canonical states for suitably scaled charges. Also, it is shown that the density profile of the quantum mean-field theory converges to the solution of the classical mean-field equation when the Planck's constant tends to zero.     

5-(2-芳氧甲基苯并咪唑-1-亚甲基)-1,3,4噁二唑-2-硫酮的结构,光谱与热力学性质的理论研究

采用密度泛函理论B3LYP方法对标题化合物分子进行几何构型优化和频率计算,得到红外光谱和拉曼光谱及不同温度下的热力学性质.计算模拟分子在气相和不同溶剂下的电子吸收光谱.结果显示,分子内氢键的形成有利于分子稳定,并与实验晶体结构一致.气相中最大吸收峰出现在236nm处,属于近紫外区,溶剂作用使其蓝移(减小)20nm左右,且与溶剂极性无关.     

Probability distributions for the overlaps and self-correlations of the pure states of ann-vector model

The probability distributions for the overlaps between and the self-correlations of the pure states of the Stanleyn-vector model with infinite-range interactions are derived. These probability distributions represent two new order parameters for the model and are intimately related to the parameters which arise naturally within the replica formalism for the treatment of the corresponding quenched random-bond model. In contrast to then = 1 Ising case, the probability distributions are nontrivial whenn > 1 and an additional parameter for self-correlation has to be introduced.     

2-（甲苯-4-磺酰胺基）-苯甲酸的结构、光谱与热力学性质的理论研究

在B3LYP/6-31++G^**水平对2-（甲苯-4-磺酰胺基）-苯甲酸分子进行几何构型优化和频率的计算,得到红外光谱,拉曼光谱和不同温度下的热力学性质.结果显示,该分子羧基的碳氧原子、磺酰胺基的氮原子与苯环形成不同的离域大π键,空间位阻效应和共轭效应使两个苯环不在同一平面,二面角为63.2°.使用含时密度泛函理论方法计算第一激发态的电子垂直跃迁能,得到最大吸收波长为312.7?nm,属于近紫外区,这与该分子在二氯甲烷溶剂中的实验测得值307?nm一致. 关键词： 2-（甲苯-4-磺酰胺基）-苯甲酸 光谱 热力学性质 密度泛函理论     

Pb-Sn合金及Pb的热力学性质的第一性原理计算

本文基于第一性原理的密度泛函理论(DFT)和密度泛函微扰理论(DFPT)方法,利用虚晶近似的计算方法研究了Pb-Sn合金的晶格结构、电子能带、声子能带及热力学性质,并用晶格能量差可与达到熔化温度时的振动能量相当的固-液相变机理研究了熔化温度,同时与所计算Pb的所有结果进行了对比.     

Phonon frequency shift and effect of correlation on the electron-phonon interaction in heavy fermion systems

The electron-phonon interaction in the periodic Anderson model (PAM) is considered. The PAM incorporates the effect of onsite Coulomb interaction (U) between f-electrons. The influence of Coulomb correlation U on the phonon response of the system is studied by evaluating the phonon spectral function for various parameters of the model. The numerical evaluation of the spectral function is carried out in the long wavelength limit at finite temperatures keeping only linear terms in U. The observed behaviour is found to agree well with the general features obtained experimentally for some heavy fermion (HF) systems.