Some aspects of the dynamics of many-body systems

In this thesis multiple aspects of several many-body systems are studied using different techniques. Most of the chapters are self-contained and I will now briefly summarize their content. Chapter 1 is introductory and gives a brief overview of the topics. In chapter 2, after solving the Schrodinger equation for a time dependent two-electron system, we calculate the enact exchange-correlation potential vxc, that, in the mainframe of Time Dependent Density Functional Theory, enters the "Kohn-Sham" equations. This enact result will be compared with various approximate forms for vxc 1. In chapter 3 we study the collective dynamics of electrons at the edge of a system. Using the continuum elasticity theory, we analyze the modes that propagate along the edge of a two-dimensional electron system (liquid or crystal) in a magnetic field. We find that, if the wave vector q is sufficiently small, the system presents a universal dispersion curve and we provide analytical formulas for the dispersion and damping of the modes in various physical regimes2. In chapter 4 we develop the theory of the spin Coulomb drag: in spin polarized transport there is an intrinsic source of friction for spin currents due to the fact that, because of Coulomb interactions, the up and down components of the momentum are not separately conserved. We calculate the "spin trans-resistivity" and suggest an experiment to measure it3. Chapter 5 is dedicated to further study spin transport. We examine the mobility and diffusion constants of a spin packet in semiconductors doped with (i) non-magnetic and (ii) magnetic impurities. In the paramagnetic phase we find that the diffusion constant Ds is always reduced by interactions. On the other hand our formulas show that Ds is a critical quantity---i.e. vanishes at the onset of the ferromagnetic transition. For temperatures lower than the critical temperature, the diffusion constant can be greatly increased by the enhancement of the carrier spin stiffness due to polarization4. In the last chapter I sketch part of my work on charged colloidal system. I will focus on the possibility of effective attraction between like-charged macroions, i.e. what happens when the Coulomb coupling between macroions and counterions becomes very strong. I will introduce and point out the importance of the "depletion force", that, in the regime we studied, is responsible for attraction5.; 1I. D'Amico and G. Vignale, Phys. Rev. B 59, 7876 (1999). 2I. D'Amico and G. Vignale, Phys. Rev. B 60, 2084 (1999). 3I. D'Amico and G. Vignale, in print, Phys. Rev. B (2000). 4I. D'Amico and G. Vignale, submitted to Phys. Rev. Lett. (2000); I. D'Amico and G. Vignale, in progress (2000). 5E. Allahyarov, I. D'Amico and H. Loewen, Phys. Rev. Lett . 81, 1334 (1998)...