Convergence of density expansions of correlation functions and the Ornstein-Zernike equation

We prove absolute convergence of the multi-body correlation functions as a power series in the density uniformly in their arguments. This is done by working in the context of the cluster expansion in the canonical ensemble and by expressing the correlation functions as the derivative of the logarithm of an appropriately extended partition function. In the thermodynamic limit, due to combinatorial cancellations, we show that the coeffi- cients of the above series are expressed by sums over some class of two-connected graphs. Furthermore, we prove the convergence of the density expansion of the “direct correlation function” which is based on a completely different approach and it is valid only for some inte- gral norm. Precisely, this integral norm is suitable to derive the Ornstein-Zernike equation. As a further outcome, we obtain a rigorous quantification of the error in the Percus-Yevick approximation

Ultrafast terahertz probes of transient conducting and insulating phases in an electron–hole gas

Many-body systems in nature exhibit complexity and self-organization arising from seemingly simple laws. The long-range Coulomb interaction between electrical charges generates a plethora of bound states in matter, ranging from the hydrogen atom to complex biochemical structures. Semiconductors form an ideal laboratory for studying many-body interactions of quasi-particles among themselves and with lattice vibrations and light. Oppositely charged electron and hole quasi-particles can coexist in an ionized but correlated plasma, or form bound hydrogen-like pairs called excitons which strongly affect physical properties. The pathways between such states however remain elusive in near-visible optical experiments that detect a subset of excitons with vanishing center-of-mass momenta. In contrast, transitions between internal exciton levels which occur in the far-infrared at terahertz (10 s) frequencies are in dependent of this restriction suggesting their use as a novel pro be of pair dynamics. Here, we employ an ultrafast terahertz probe to directly investigate the dynamical interplay of optically-generated excitons and unbound electron-hole pairs in GaAs quantum wells. Our observations witness an unexpected quasi-instantaneous excitonic enhancement, reveal formation of insulating excitons on a hundred picosecond timescale and manifest conditions under which excitonic populations prevail

Extended kinetic theory applied to inclined granular flows: role of boundaries

We compare the predictions of extended kinetic theory (EKT), where the roles of surface friction and correlation in fluctuation velocities are taken into account, with discrete element simulations of steady, fully-developed, inclined flows of identical spheres over bumpy bases, in the presence and absence of flat, frictional sidewalls. We show that the constitutive relation for the pressure of EKT must be modified in the proximity of the boundary, because of the influence of excluded volume and shielding associated with collisions of particles with the boundary itself. We also note that currently available boundary conditions for flows over bumpy planes in kinetic theory underestimate the energy dissipation. These two observations explain the lack of agreement of EKT with the simulations, in terms of the maximum angles of inclination for which steady, fully-developed flows are possible. That is, for some high angles of inclination, EKT does not have solutions, while steady flows are predicted in DEM. However, whenever a solution to the system of differential equations of EKT does exist, the predicted distributions of velocity, solid volume fraction and granular temperature satisfactorily match the numerical measurements. The incompressible, algebraic approximation of EKT, which ignores the conduction of energy in the energy balance, admits solutions for a wider range of angles of inclination, as in the simulations, but fails to reproduce the quantitative and qualitative behaviour of solid volume fraction and granular temperature in the two conductive layers at the top and bottom of the flow. When frictional sidewalls are added to the domain, we show that the spanwise ratio of shear stress to pressure is linearly distributed in the dense core region of the flow, confirming that the sidewalls exert, on average, a Coulomb-like resistance to the flow with an effective friction coefficient which is less than half the actual particle-wall friction