4 research outputs found
Super-shell structure in harmonically trapped fermionic gases and its semi-classical interpretation
It was recently shown in self-consistent Hartree-Fock calculations that a
harmonically trapped dilute gas of fermionic atoms with a repulsive two-body
interaction exhibits a pronounced {\it super-shell} structure: the shell
fillings due to the spherical harmonic trapping potential are modulated by a
beat mode. This changes the ``magic numbers'' occurring between the beat nodes
by half a period. The length and amplitude of the beating mode depends on the
strength of the interaction. We give a qualitative interpretation of the beat
structure in terms of a semiclassical trace formula that uniformly describes
the symmetry breaking U(3) SO(3) in a 3D harmonic oscillator potential
perturbed by an anharmonic term with arbitrary strength. We show
that at low Fermi energies (or particle numbers), the beating gross-shell
structure of this system is dominated solely by the two-fold degenerate
circular and (diametrically) pendulating orbits.Comment: Final version of procedings for the 'Nilsson conference
Supershell structure in trapped dilute Fermi gases
We show that a dilute harmonically trapped two-component gas of fermionic
atoms with a weak repulsive interaction has a pronounced super-shell structure:
the shell fillings due to the spherical harmonic trapping potential are
modulated by a beat mode. This changes the ``magic numbers'' occurring between
the beat nodes by half a period. The length and amplitude of this beating mode
depend on the strength of the interaction. We give a simple interpretation of
the beat structure in terms of a semiclassical trace formula for the symmetry
breaking U(3) --> SO(3).Comment: 4 pages, 4 figures; In version 2, references added. The semiclassical
explanation of super-shell structure is refined. Version 3, as appeared in
Phys. Rev.
Uniform semiclassical trace formula for U(3) --> SO(3) symmetry breaking
We develop a uniform semiclassical trace formula for the density of states of
a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term
. This term breaks the U(3) symmetry of the HO, resulting in a
spherical system with SO(3) symmetry. We first treat the anharmonic term in
semiclassical perturbation theory by integration of the action of the perturbed
periodic HO orbits over the manifold P which characterizes
their 4-fold degeneracy. Then we obtain an analytical uniform trace formula
which in the limit of strong perturbations (or high energy) asymptotically goes
over into the correct trace formula of the full anharmonic system with SO(3)
symmetry, and in the limit (or energy) restores the HO trace
formula with U(3) symmetry. We demonstrate that the gross-shell structure of
this anharmonically perturbed system is dominated by the two-fold degenerate
diameter and circular orbits, and {\it not} by the orbits with the largest
classical degeneracy, which are the three-fold degenerate tori with rational
ratios of radial and angular frequencies. The same
holds also for the limit of a purely quartic spherical potential .Comment: LaTeX (revtex4), 26pp., 5 figures, 1 table; final version to be
published in J. Phys. A (without appendices C and D
Semiclassical description of shell effects in finite fermion systems
A short survey of the semiclassical periodic orbit theory, initiated by M.
Gutzwiller and generalized by many other authors, is given. Via so-called
semiclassical trace formmulae, gross-shell effects in bound fermion systems can
be interpreted in terms of a few periodic orbits of the corresponding classical
systems. In integrable systems, these are usually the shortest members of the
most degenerate families or orbits, but in some systems also less degenerate
orbits can determine the gross-shell structure. Applications to nuclei, metal
clusters, semiconductor nanostructures, and trapped dilute atom gases are
discussed.Comment: LaTeX (revteX4) 6 pages; invited talk at Int. Conference "Finite
Fermionic Systems: Nilsson Model 50 Years", Lund, Sweden, June 14-18, 200