Alexei Filinov

Progress in Nonequilibrium Green's Functions III

This is the third volume (the first two volumes are Progress in Nonequilibrium Greens Functions, M. Bonitz (ed.) and Progress in Nonequilibrium Greens Functions II, M. Bonitz and D. Semkat (eds.), which were published by World Scientific (Singapore), in 2000 and 2003, respectively, (ISBN 981-02-4218-2 and ISBN 981-238-271-2).) of articles on the theory of Nonequilibrium Greens functions (NGF) and their modern applications in various fields. The refereed papers in this volume are based on talks and posters presented at the interdisciplinary conference Progress in Nonequilibrium Greens Functions III which was held in August 2005 at Kiel University, Germany. The conference was attended by about 70 scientists working in a variety of fields of theoretical physics, including plasma physics, solid state theory, semiconductor optics and transport, nanostructures, nuclear matter and high energy physics. Compared to the previous conferences, new topics were covered, such as transport theory for molecular systems, combinations of NGF with (time-dependent) density functional theory or dynamical mean field theory. This reflects modern developments in many-body theory. As with the two previous volumes, this one, hopefully, will be a valuable and stimulating reference for students and researchers from various fields. In contrast to the previous volumes, this one appears as a volume of Journal of Physics: Conference Series. This option was chosen as Journal of Physics: Conference Series offers free access to the online version which also contains color figures. This, hopefully, will increase the distribution of the articles to the scientific community. This conference would not have been possible without the generous financial support from the Deutsche Forschungsgemeinschaft (DFG) and without help from many people. We are particularly grateful to Andrea Fromm, Fanny Geisler and Doris Schulz from the local organizating committee in Kiel and Wolf Dietrich Kraeft (Rostock) for assistence in the final editing of the papers.

Introduction to Quantum Plasmas

Plasmas are generally associated with a hot gas of charged particles which behave classically. However, when the temperature is lowered and/or the density is increased sufficiently, the plasma particles (most importantly, electrons) become quantum degenerate, that is, the extension of their wave functions becomes comparable to the distance between neighboring particles. This is the case in many astrophysical plasmas, such as those occurring in the interior of giant planets or dwarf and neutron stars, but also in various modern laboratory setups where charged particles are compressed by very intense ion or laser beams to multi-megabar pressures. Furthermore, quantum plasmas exist in solids – examples are the electron gas in metals and the electron–hole plasma in semiconductors. Finally, the exotic state of the Universe immediately after the Big Bang is believed to have been a quantum plasma consisting of electrons, quarks, photons, and gluons. In all these situations, a description in terms of classical mechanics, thermodynamics, or classical kinetic theory fails. In this chapter, an overview of quantum plasma features and their occurrence is given. The conditions for the relevance of quantum effects are formulated and discussed. The key concepts for a theoretical description of quantum plasmas are developed and illustrated by simple examples.

Tuning correlations in multi-component plasmas

Spontaneous, correlation-driven structure formation is one of the most fundamental collective processes in nature. In particular, particle ensembles in externally controlled confinement geometries allow for a systematic investigation of strong correlation and quantum effects over broad ranges of the relevant trap and plasma parameters. An exceptional feature inherent to finite systems is the governing role of symmetry and surface effects leading to similar collective behaviour in physical systems on vastly different length and energy scales. Considering (i) confined complex (dusty) plasmas and (ii) charge asymmetric bilayers, the effective range of the pair interaction emerges as a key quantity taking effect on the self-organized structure formation. Additional interest arises from the possible mass asymmetry of the plasma constituents in bilayers. Translating the results from (unconfined) 3D plasmas to bilayer systems, it is shown that the critical mass ratio required for crystallization of the heavy plasma component can be drastically reduced such that this effect becomes experimentally accessible.

Strongly correlated indirect excitons in quantum wells in high electric fields

We study the Stark effect on excitonic complexes confined in a GaAs-based single quantum well. We approach this problem using Path Integral Monte Carlo methods to compute the many-body density matrix. The developed method is applied for investigation of the electric field-dependence of energies, particle distribution and effective exciton dipole moment. Using these results as an input we apply thermodynamical Monte Carlo methods to investigate systems of several tens to thousands indirect excitons in a 2D quantum well with a lateral confinement arising from the quantum confined Stark effect. Depending on the field strength, exciton density and temperature different phases (gas, liquid and solid) of indirect excitons are predicted.

Wigner Function Quantum Molecular Dynamics

Classical molecular dynamics (MD) is a well established and powerful tool in various fields of science, e.g. chemistry, plasma physics, cluster physics and condensed matter physics. Objects of investigation are few-body systems and many-body systems as well. The broadness and level of sophistication of this technique is documented in many monographs and reviews, see for example \cite{Allan,Frenkel,mdhere}. Here we discuss the extension of MD to quantum systems (QMD). There have been many attempts in this direction which differ from one another, depending on the type of system under consideration. One direction of QMD has been developed for condensed matter systems and will not discussed here, e.g. \cite{fermid}. In this chapter we are dealing with unbound electrons as they occur in gases, fluids or plasmas. Here, one strategy is to replace classical point particles by wave packets, e.g. \cite{fermid,KTR94,zwicknagel06} which is quite successful. At the same time, this method struggles with problems related to the dispersion of such a packet and difficulties to properly describe strong electron-ion interaction and bound state formation. We, therefore, avoid such restrictions and consider a completely general alternative approach. We start discussion of quantum dynamics from a general consideration of quantum distribution functions.

Quantum potential for diffraction and exchange effects

Semiclassical methods of statistical mechanics can incorporate essential quantum effects by using effective quantum potentials. An ideal Fermi gas interacting with an impurity is represented by a classical fluid with effective electron–electron and electron-impurity quantum potentials. The electron-impurity quantum potential is evaluated at weak coupling, leading to a generalization of the Kelbg potential to include both diffraction and degeneracy effects. The electron–electron quantum potential for exchange effects only is the same as that discussed earlier by others.

Path Integral Monte Carlo Simulation of Charged Particles in Traps

This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as a small perturbation. For weakly coupled systems many efficient theoretical and computational techniques do exist. However, for strongly interacting systems such as nonideal gases or plasmas, strongly correlated electrons and so on, perturbation methods fail and alternative approaches are needed. Among them, an extremely successful one is the Monte Carlo (MC) method which we are going to consider in this chapter.