Volume fraction variations and dilation in colloids and granulars

Discusses the importance of spatial and temporal variations in particle volume fraction to understanding the force response of concentrated colloidal suspensions and granular materials

CECIL G. SHEPS and EUGENE E. TAYLOR. Needed Research in Health and Medical Care: A Bio-Social Approach. Pp. ix, 216. Chapel Hill: The University of North Carolina Press, 1954. $5.00

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68178/2/10.1177_000271625529900153.pd

Correlated hopping of electrons: Effect on the Brinkman-Rice transition and the stability of metallic ferromagnetism

We study the Hubbard model with bond-charge interaction (`correlated hopping') in terms of the Gutzwiller wave function. We show how to express the Gutzwiller expectation value of the bond-charge interaction in terms of the correlated momentum-space occupation. This relation is valid in all spatial dimensions. We find that in infinite dimensions, where the Gutzwiller approximation becomes exact, the bond-charge interaction lowers the critical Hubbard interaction for the Brinkman-Rice metal-insulator transition. The bond-charge interaction also favors ferromagnetic transitions, especially if the density of states is not symmetric and has a large spectral weight below the Fermi energy.Comment: 5 pages, 3 figures; minor changes, published versio

From infinite to two dimensions through the functional renormalization group

We present a novel scheme for an unbiased and non-perturbative treatment of strongly correlated fermions. The proposed approach combines two of the most successful many-body methods, i.e., the dynamical mean field theory (DMFT) and the functional renormalization group (fRG). Physically, this allows for a systematic inclusion of non-local correlations via the flow equations of the fRG, after the local correlations are taken into account non-perturbatively by the DMFT. To demonstrate the feasibility of the approach, we present numerical results for the two-dimensional Hubbard model at half-filling.Comment: 5 pages, 4 figure

Fermion loops, loop cancellation and density correlations in two dimensional Fermi systems

We derive explicit results for fermion loops with an arbitrary number of density vertices in two dimensions at zero temperature. The 3-loop is an elementary function of the three external momenta and frequencies, and the N-loop can be expressed as a linear combination of 3-loops with coefficients that are rational functions of momenta and frequencies. We show that the divergencies of single loops for low energy and small momenta cancel each other when loops with permuted external variables are summed. The symmetrized N-loop, i.e. the connected N-point density correlation function of the Fermi gas, does not diverge for low energies and small momenta. In the dynamical limit, where momenta scale to zero at fixed finite energy variables, the symmetrized N-loop vanishes as the (2N-2)-th power of the scale parameter.Comment: 24 pages (including 3 EPS figures), LaTeX2e; submitted to Phys. Rev.

Hole dynamics in generalized spin backgrounds in infinite dimensions

We calculate the dynamical behaviour of a hole in various spin backgrounds in infinite dimensions, where it can be determined exactly. We consider hypercubic lattices with two different types of spin backgrounds. On one hand we study an ensemble of spin configurations with an arbitrary spin probability on each sublattice. This model corresponds to a thermal average over all spin configurations in the presence of staggered or uniform magnetic fields. On the other hand we consider a definite spin state characterized by the angle between the spins on different sublattices, i.e a classical spin system in an external magnetic field. When spin fluctuations are considered, this model describes the physics of unpaired particles in strong coupling superconductors.Comment: Accepted in Phys. Rev. B. 18 pages of text (1 fig. included) in Latex + 2 figures in uuencoded form containing the 2 postscripts (mailed separately

Numerical renormalization group study of the symmetric Anderson-Holstein model: phonon and electron spectral functions

We study the symmetric Anderson-Holstein (AH) model at zero temperature with Wilson's numerical renormalization group (NRG) technique to study the interplay between the electron-electron and electron-phonon interactions. An improved method for calculating the phonon propagator using the NRG technique is presented, which turns out to be more accurate and reliable than the previous works in that it calculates the phonon renormalization explicitly and satisfies the boson sum rule better. The method is applied to calculate the renormalized phonon propagators along with the electron propagators as the onsite Coulomb repulsion $U$ and electron-phonon coupling constant $g$ are varied. As $g$ is increased, the phonon mode is successively renormalized, and for $g \gtrsim g_{co}$ crosses over to the regime where the mode splits into two components, one of which approaches back to the bare frequency and the other develops into a soft mode. The initial renormalization of the phonon mode, as $g$ is increased from 0, depends on $U$ and the hybridization $\Delta$; it gets softened (hardened) for $U \gtrsim (\lesssim) U_s (\Delta)$. Correlated with the emergence of the soft mode is the central peak of the electron spectral function severely suppressed. These NRG calculations will be compared with the standard Green's function results for the weak coupling regime to understand the phonon renormalization and soft mode.Comment: 18 pages, 4 figures. Submitted to Phys. Rev.