Matfys library

Spatial densities of fermionic quantum systems typically exhibit
oscillations
that are connected to shell effects. We present a semiclassical theory [1]
in which these oscillations are described in terms of the closed (but not
periodic) orbits of the corresponding classical system. We also discuss
the
Friedel oscillations near a steep surface and present a case study of the
two-dimensional circular billiard in which all periodic and non-periodic
orbits can be classified through analytic relations [2]. Finally, we
discuss
local virial theorems that can be derived from this semiclassical theory [3].

[1] J. Roccia and M. Brack, Phys. Rev. Lett.**100**, 200408 (2008);

J. Roccia, M. Brack, A. Koch, Phys. Rev. E**81**, 011118 (2010).

[2] M. Brack and J. Roccia, J. Phys. A**42**, 355210 (2009).

[3] M. Brack, A. Koch, M. V. N. Murthy, J. Roccia, J. Phys. A**43**, 255204
(2010).

[1] J. Roccia and M. Brack, Phys. Rev. Lett.

J. Roccia, M. Brack, A. Koch, Phys. Rev. E

[2] M. Brack and J. Roccia, J. Phys. A

[3] M. Brack, A. Koch, M. V. N. Murthy, J. Roccia, J. Phys. A