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])