Semiclassical approaches to mesoscopic systems
M. Brack

Lectures held at the Les Houches Summer School on Atomic Clusters and Nanoparticles, Session LXXIII, July 3 - 28, 2000.
Edited by C. Guet et al. (Springer-Verlag Berlin, 2001), pp. 161 - 219.

We review semiclassical methods of determining both average trends and quantum shell effects in the properties of finite fermion systems.
I. Extended Thomas-Fermi model (ETF): The average, selfconsistent mean field can be determined by density variational calculations using the semiclassical gradient-expanded ETF density functional for the kinetic energy. From this, average ground-state properties such as binding energies, densities, separation energies, etc., can be derived.
II. Periodic orbit theory (POT): Quantum oscillations in a mean-field system can be obtained from the semiclassical trace formula that expresses the quantum-mechanical density of states in terms of the periodic orbits of the corresponding classical system. Only the shortest periodic orbits with highest degeneracy are important for the coarse-grained level density, i.e., for the gross shell effects. Particular uniform approximations are required to treat systems with mixed classical dynamics due to the effects of symmetry breaking and orbit bifurcations.
III. Local-current approximation (LCA): The collective dynamics of the fermions can be described in linear-response theory, approximating the particle-hole excitation operators semiclassically by local current distributions. The method is suitable in combination with both the ETF density variational approach or with the Kohn-Sham density functional approach for the ground state, and allows one to describe optic response properties such as static polarizabilities and plasmon resonances.
Applications of all methods to metal clusters and various mesoscopic nanostructures are given.

Script in pdf-Format (2.9MB)   (version 30.3.2001 with updates and corrections to Refs. [59,65,111])