Systematics of properties of the electron gas in deep-etched quantum wires

An efficient method is developed for an iterative solution of the Poisson and Schro¿dinger equations, which allows systematic studies of the properties of the electron gas in linear deep-etched quantum wires. A much simpler two-dimensional (2D) approximation is developed that accurately reproduces the results of the 3D calculations. A 2D Thomas-Fermi approximation is then derived, and shown to give a good account of average properties. Further, we prove that an analytic form due to Shikin et al. is a good approximation to the electron density given by the self-consistent methods.

Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.