Some results in the theory of interacting electron systems

The expressions for the longitudinal dielectric function, spin and orbital susceptibilities in the static, long wavelength limit are evaluated by solving the corresponding linearized vertex functions exactly in this limit. The plasma dispersion relation to leading order in the long wave limit is similarly obtained. These are compared with the corresponding results obtained previoulsy by us by a variational solution to the same vertex equations. It is established that the variational method gives the exact results in the static, zero wave vector limit, involving the proper renormalizations. The plasma dispersion relation is found to be the same as in the exact calculation whereas the coefficient of q² in the static density correlation function has an important additional contribution to the variational result. Applications of these results are briefly discussed.     

Probability distribution of the ratio of consecutive level spacings in interacting particle systems

We study the probability distribution of the ratio of consecutive level spacings for embedded one- plus two-body random matrix ensembles with and without spin degree of freedom and for both fermion and boson systems. The agreement between the numerical results and the recently derived analytic form for the distribution and other related quantities is found to be close. This establishes that the statistics of quotients of successive spacings, which do not depend on unfolding, is useful tool in the analysis of local level fluctuations in many-particle systems.     

Uniform upper bounds (and thermodynamic limit) for the correlation functions of symmetric coulomb-type systems

Uniform upper bounds are proven for the correlation functions in the strictly charge-neutral canonical and grand canonical ensembles for charge-symmetric two-component systems. For the grand canonical ensemble the increase of the correlation functions along the thermodynamic-limit sequence is shown as well, implying the existence of the states. The particles have bounded pair interactions of positive type. Both classical and quantum systems with Boltzmann statistics are considered. Coulomb systems with regularized interactions are included as a special case.     

Local methods for constructing stationary distribution functions of systems of stochastic differential Langevin-type equations: Noise influence on simple bifurcation

The influence is considered of two additive correlated noise effects on a two-dimensional quadratic-nonlinear system describing the behavior of two hydrodynamic modes. Using the method of Gaussian approximation, local characteristics of the distribution function are calculated, which are used to construct the global distribution function with the aid of the method of fraction-rational approximations. It is shown that for a system at whose bifurcation point the asymptotic stability is lost, in an expanded space of parameters (bifurcation parameter in the absence of noise plus noise parameters) there appears an instability zone within which the stationary distribution function does not exist. The effect of noise correlation on the stationary characteristics of the system is studied.     

Universal cubic equation of state and contact values of the radial distribution functions for multi-component additive hard-sphere mixtures

A universal cubic equation of state (UC EOS) is proposed based on a modification of the virial Percus-Yevick (PY) integral equation EOS for hard-sphere fluid. The UC EOS is extended to multi-component hard-sphere mixtures based on a modification of Lebowitz solution of PY equation for hard-sphere mixtures. And expressions of the radial distribution functions at contact (RDFC) are improved with the form as simple as the original one. The numerical results for the compressibility factor and RDFC are in good agreement with the simulation results. The average errors of the compressibility factor relative to MC data are 3.40%, 1.84% and 0.92% for CP3P, BMCSL equations and UC EOS, respectively. The UC EOS is a unique cubic one with satisfactory precision among many EOSs in the literature both for pure and mixture fluids of hard spheres.