The Coulomb gap and low energy statistics for Coulomb glasses
We study the statistics of local energy minima in the configuration space of two-dimensional lattice Coulomb glasses with site disorder and the behavior of the Coulomb gap depending on the strength of random site energies. At intermediate disorder, i.e., when the typical strength of the disorder is of the same order as the nearest-neighbor Coulomb energy, the high energy tail of the distribution of the local minima is exponential. We furthermore analyze the structure of the local minima and show that most sites of the system have the same occupation numbers in all of these states. The density of states (DOS) shows a transition from the crystalline state at zero disorder (with a hard gap) to an intermediate, probably glassy state with a Coulomb gap. We analyze this Coulomb gap in some detail and show that the DOS deviates slightly from the traditional linear behavior in 2D. For finite systems these intermediate Coulomb gap states disappear for large disorder strengths and only a random localized state in which all electrons are in the minima of the random potential exists. Dedication: This paper is dedicated to Thomas Nattermann, our dearest friend, brilliant colleague, and outstanding teacher.
Coulomb gap in disordered systems: Computer simulation
Abstract The density of states (DS) of a disordered system with localized electronic states is studied with the Monte Carlo computer simulation for the two- and three-dimensional simple models. The electron - electron interaction drastically changes the DS in the vicinity of the Fermi level. The DS is shown to have a “soft” gap, and the self-consistent equation fits well the result of simulation.
Heat Recovery Systems
Geothermal energy is recovered from an underground zone of relatively hot strata via a borehole into which is inserted a heat pipe system containing a working fluid, the heat pipe system comprising an assembly of two tubes in concentric relation, the inner tube being constituted by a relatively small diameter capillary for the return of working fluid to the vicinity of the zone of the relatively hot strata. The working fluid is preferably assisted in its return under gravity by means of a pump. The system includes heat exchange means operable to recover thermal energy from the working fluid. A third and outermost tube may be used to reduce heat losses, this third tube enclosing the two tubes over all but that part of their length which is in the zone of relatively hot strata.