284 research outputs found
Closed-orbit theory for spatial density oscillations
We briefly review a recently developed semiclassical theory for quantum
oscillations in the spatial (particle and kinetic energy) densities of finite
fermion systems and present some examples of its results. We then discuss the
inclusion of correlations (finite temperatures, pairing correlations) in the
semiclassical theory.Comment: LaTeX, 10pp., 2 figure
On the ground--state energy of finite Fermi systems
We study the ground--state shell correction energy of a fermionic gas in a
mean--field approximation.
Considering the particular case of 3D harmonic trapping potentials, we show
the rich variety of different behaviors (erratic, regular, supershells) that
appear when the number--theoretic properties of the frequency ratios are
varied. For self--bound systems, where the shape of the trapping potential is
determined by energy minimization, we obtain accurate analytic formulas for the
deformation and the shell correction energy as a function of the particle
number . Special attention is devoted to the average of the shell correction
energy. We explain why in self--bound systems it is a decreasing (and negative)
function of .Comment: 10 pages, 5 figures, 2 table
Average ground-state energy of finite Fermi systems
Semiclassical theories like the Thomas-Fermi and Wigner-Kirkwood methods give
a good description of the smooth average part of the total energy of a Fermi
gas in some external potential when the chemical potential is varied. However,
in systems with a fixed number of particles N, these methods overbind the
actual average of the quantum energy as N is varied. We describe a theory that
accounts for this effect. Numerical illustrations are discussed for fermions
trapped in a harmonic oscillator potential and in a hard wall cavity, and for
self-consistent calculations of atomic nuclei. In the latter case, the
influence of deformations on the average behavior of the energy is also
considered.Comment: 10 pages, 8 figure
Experimental study of 199Hg spin anti-relaxation coatings
We report on a comparison of spin relaxation rates in a Hg
magnetometer using different wall coatings. A compact mercury magnetometer was
built for this purpose. Glass cells coated with fluorinated materials show
longer spin coherence times than if coated with their hydrogenated homologues.
The longest spin relaxation time of the mercury vapor was measured with a
fluorinated paraffin wall coating.Comment: 9 pages, 6 figures, submitted to JINS
Level density of a Fermi gas: average growth and fluctuations
We compute the level density of a two--component Fermi gas as a function of
the number of particles, angular momentum and excitation energy. The result
includes smooth low--energy corrections to the leading Bethe term (connected to
a generalization of the partition problem and Hardy--Ramanujan formula) plus
oscillatory corrections that describe shell effects. When applied to nuclear
level densities, the theory provides a unified formulation valid from
low--lying states up to levels entering the continuum. The comparison with
experimental data from neutron resonances gives excellent results.Comment: 4 pages, 1 figur
Closed orbits and spatial density oscillations in the circular billiard
We present a case study for the semiclassical calculation of the oscillations
in the particle and kinetic-energy densities for the two-dimensional circular
billiard. For this system, we can give a complete classification of all closed
periodic and non-periodic orbits. We discuss their bifurcations under variation
of the starting point r and derive analytical expressions for their properties
such as actions, stability determinants, momentum mismatches and Morse indices.
We present semiclassical calculations of the spatial density oscillations using
a recently developed closed-orbit theory [Roccia J and Brack M 2008 Phys. Rev.
Lett. 100 200408], employing standard uniform approximations from perturbation
and bifurcation theory, and test the convergence of the closed-orbit sum.Comment: LaTeX, 42 pp., 17 figures (24 *.eps files, 1 *.tex file); final
version (v3) to be published in J. Phys.
The entropic cost of quantum generalized measurements
Landauer’s principle introduces a symmetry between computational and physical processes: erasure of information, a logically irreversible operation, must be underlain by an irreversible transformation dissipating energy. Monitoring micro- and nano-systems needs to enter into the energetic balance of their control; hence, finding the ultimate limits is instrumental to the development of future thermal machines operating at the quantum level. We report on the experimental investigation of a lower bound to the irreversible entropy associated to generalized quantum measurements on a quantum bit. We adopted a quantum photonics gate to implement a device interpolating from the weakly disturbing to the fully invasive and maximally informative regime. Our experiment prompted us to introduce a bound taking into account both the classical result of the measurement and the outcoming quantum state; unlike previous investigation, our entropic bound is based uniquely on measurable quantities. Our results highlight what insights the information-theoretic approach provides on building blocks of quantum information processors
Semiclassical theory for spatial density oscillations in fermionic systems
We investigate the particle and kinetic-energy densities for a system of
fermions bound in a local (mean-field) potential V(\bfr). We generalize a
recently developed semiclassical theory [J. Roccia and M. Brack, Phys. Rev.\
Lett. {\bf 100}, 200408 (2008)], in which the densities are calculated in terms
of the closed orbits of the corresponding classical system, to
dimensions. We regularize the semiclassical results for the U(1) symmetry
breaking occurring for spherical systems at and near the classical
turning points where the Friedel oscillations are predominant and well
reproduced by the shortest orbit going from to the closest turning point
and back. For systems with spherical symmetry, we show that there exist two
types of oscillations which can be attributed to radial and non-radial orbits,
respectively. The semiclassical theory is tested against exact
quantum-mechanical calculations for a variety of model potentials. We find a
very good overall numerical agreement between semiclassical and exact numerical
densities even for moderate particle numbers . Using a "local virial
theorem", shown to be valid (except for a small region around the classical
turning points) for arbitrary local potentials, we can prove that the
Thomas-Fermi functional reproduces the oscillations in
the quantum-mechanical densities to first order in the oscillating parts.Comment: LaTeX, 22pp, 15 figs, 1 table, to be published in Phys. Rev.
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