2,520 research outputs found
Periodic orbit theory including spin degrees of freedom
We summarize recent developments of the semiclassical description of shell
effects in finite fermion systems with explicit inclusion of spin degrees of
freedom, in particluar in the presence of spin-orbit interactions. We present a
new approach that makes use of spin coherent states and a correspondingly
enlarged classical phase space. Taking suitable limits, we can recover some of
the earlier approaches. Applications to some model systems are presented.Comment: LaTeX2e, 10pp, 5 figs; contribution to 10th Nuclear Physics Workshop
"Marie and Pierre Curie", 24 - 28 Sept. 2003, Kazimierz Dolny (Poland
Unitary Fermi Gas in a Harmonic Trap
We present an {\it ab initio} calculation of small numbers of trapped,
strongly interacting fermions using the Green's Function Monte Carlo method
(GFMC). The ground state energy, density profile and pairing gap are calculated
for particle numbers using the parameter-free "unitary"
interaction. Trial wave functions are taken of the form of correlated pairs in
a harmonic oscillator basis. We find that the lowest energies are obtained with
a minimum explicit pair correlation beyond that needed to exploit the
degeneracy of oscillator states. We find that energies can be well fitted by
the expression where is the
Thomas-Fermi energy of a noninteracting gas in the trap and is a
pairing gap. There is no evidence of a shell correction energy in the
systematics, but the density distributions show pronounced shell effects. We
find the value for the pairing gap. This is smaller
than the value found for the uniform gas at a density corresponding to the
central density of the trapped gas.Comment: 2 figures, 2 table
Static Electric Dipole Polarizabilities of Na Clusters
The static electric dipole polarizability of clusters with
even N has been calculated in a collective, axially averaged and a
three-dimensional, finite-field approach for , including the
ionic structure of the clusters. The validity of a collective model for the
static response of small systems is demonstrated. Our density functional
calculations verify the trends and fine structure seen in a recent experiment.
A pseudopotential that reproduces the experimental bulk bond length and atomic
energy levels leads to a substantial increase in the calculated
polarizabilities, in better agreement with experiment. We relate remaining
differences in the magnitude of the theoretical and experimental
polarizabilities to the finite temperature present in the experiments.Comment: 7 pages, 3 figures, accepted for publication in the European Physical
Journal
How harmonic is dipole resonance of metal clusters?
We discuss the degree of anharmonicity of dipole plasmon resonances in metal
clusters. We employ the time-dependent variational principle and show that the
relative shift of the second phonon scales as in energy, being
the number of particles. This scaling property coincides with that for nuclear
giant resonances. Contrary to the previous study based on the boson-expansion
method, the deviation from the harmonic limit is found to be almost negligible
for Na clusters, the result being consistent with the recent experimental
observation.Comment: RevTex, 8 page
On the canonically invariant calculation of Maslov indices
After a short review of various ways to calculate the Maslov index appearing
in semiclassical Gutzwiller type trace formulae, we discuss a
coordinate-independent and canonically invariant formulation recently proposed
by A Sugita (2000, 2001). We give explicit formulae for its ingredients and
test them numerically for periodic orbits in several Hamiltonian systems with
mixed dynamics. We demonstrate how the Maslov indices and their ingredients can
be useful in the classification of periodic orbits in complicated bifurcation
scenarios, for instance in a novel sequence of seven orbits born out of a
tangent bifurcation in the H\'enon-Heiles system.Comment: LaTeX, 13 figures, 3 tables, submitted to J. Phys.
A semiclassical analysis of the Efimov energy spectrum in the unitary limit
We demonstrate that the (s-wave) geometric spectrum of the Efimov energy
levels in the unitary limit is generated by the radial motion of a primitive
periodic orbit (and its harmonics) of the corresponding classical system. The
action of the primitive orbit depends logarithmically on the energy. It is
shown to be consistent with an inverse-squared radial potential with a lower
cut-off radius. The lowest-order WKB quantization, including the Langer
correction, is shown to reproduce the geometric scaling of the energy spectrum.
The (WKB) mean-squared radii of the Efimov states scale geometrically like the
inverse of their energies. The WKB wavefunctions, regularized near the
classical turning point by Langer's generalized connection formula, are
practically indistinguishable from the exact wave functions even for the lowest
() state, apart from a tiny shift of its zeros that remains constant for
large .Comment: LaTeX (revtex 4), 18pp., 4 Figs., already published in Phys. Rev. A
but here a note with a new referece is added on p. 1
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
Periodic-Orbit Bifurcations and Superdeformed Shell Structure
We have derived a semiclassical trace formula for the level density of the
three-dimensional spheroidal cavity. To overcome the divergences occurring at
bifurcations and in the spherical limit, the trace integrals over the
action-angle variables were performed using an improved stationary phase
method. The resulting semiclassical level density oscillations and
shell-correction energies are in good agreement with quantum-mechanical
results. We find that the bifurcations of some dominant short periodic orbits
lead to an enhancement of the shell structure for "superdeformed" shapes
related to those known from atomic nuclei.Comment: 4 pages including 3 figure
Exact results for a charged, harmonically trapped quantum gas at arbitrary temperature and magnetic field strength
An analytical expression for the first-order density matrix of a charged,
two-dimensional, harmonically confined quantum gas, in the presence of a
constant magnetic field is derived. In contrast to previous results available
in the literature, our expressions are exact for any temperature and magnetic
field strength. We also present a novel factorization of the Bloch density
matrix in the form of a simple product with a clean separation of the
zero-field and field-dependent parts. This factorization provides an
alternative way of analytically investigating the effects of the magnetic field
on the system, and also permits the extension of our analysis to other
dimensions, and/or anisotropic confinement.Comment: To appear in Phys. Rev.
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