Correlation operators in many-particle physics

Correlation functions and thermodynamic Green's functions are expressed as matrix elements of corresponding superoperators. A connection between the super-operator formalism, which has been used extensively in relaxation problems and in magnetism in recent years, and the method of thermodynamic Green's functions is thus established. The introduction of correlation (super-) operators describing dynamical as well as statistical aspects of a physical system allows for an abstract formulation of the theory independent of any special representation which results in considerable formal simplifications. The investigation of the Laplace-transformed correlation operator leads to Dyson's equation with the self-energy explicitly expressed as a superoperator matrix element.     

Dielectric and transport properties of a supercooled symmetrical molten salt

The liquid-glass transition of the restricted primitive model for a symmetrical molten salt is studied using mode-coupling theory. The transition at high densities is predicted to obey the Lindemann criterion for melting, and the charge-density peak found in neutron-scattering experiments on ionic glass formers is qualitatively reproduced. Frequency-dependent dielectric functions, shear viscosities, and dynamical conductivities of the supercooled liquid are presented. Comparing the latter to the diffusion constant, we find that mode-coupling theory reproduces the Nernst-Einstein relation. The Stokes-Einstein radius is found to be approximately equal to the particle radius only near the high-density glass transition.     

Dynamics of uniform quantum gases, I: Density and current correlations

A unified approach valid for any wavenumber q, frequency ω, and temperature T is presented for uniform ideal quantum gases allowing for a comprehensive study of number density and particle-current density response functions. Exact analytical expressions are obtained for spectral functions in terms of polylogarithms. Also, particle-number and particle-current static susceptibilities are presented which, for fugacity less than unity, additionally involve Kummer functions. The q- and T-dependent transverse-current static susceptibility is used to show explicitly that current correlations are of long range in a Bose-condensed uniform ideal gas but for bosons at T>T_c and for Fermi and Boltzmann gases at all temperatures these correlations are of short range. Contact repulsive interactions for systems of neutral quantum particles are considered within the random phase approximation. The expressions for particle-number and transverse-current susceptibilities are utilized to discuss the existence or nonexistence of superfluidity in the systems under consideration.