15 research outputs found
Level density of a Fermion gas: average growth, fluctuations, universality
It has been shown by H. Bethe more than 70 years ago that the number of
excited states of a Fermi gas grows, at high excitation energies , like the
exponential of the square root of . This result takes into account only the
average density of single particle (SP) levels near the Fermi energy. It
ignores two important effects, namely the discreteness of the SP spectrum, and
its fluctuations. We show that the discreteness of the SP spectrum gives rise
to smooth finite-- corrections. Mathematically, these corrections are
associated to the problem of partitions of an integer. On top of the smooth
growth of the many--body density of states there are, generically,
oscillations. An explicit expression of these oscillations is given. Their
properties strongly depend on the regular or chaotic nature of the SP motion.
In particular, we analyze their typical size, temperature dependence and
probability distribution, with emphasis on their universal aspects.Comment: 8 pages, 4 figures. Lecture delivered at the workshop ``Nuclei and
Mesoscopic Physics'', NSCL MSU, USA, October 23-26, 2004. To be published by
American Institute of Physics, V. Zelevinsky e
Large geometric phases and non-elementary monopoles
Degeneracies in the spectrum of an adiabatically transported quantum system are important to determine the geometrical phase factor, and may be interpreted as magnetic monopoles. We investigate the mechanism by which constraints acting on the system, related to local symmetries, can create arbitrarily large monopole charges. These charges are associated with different geometries of the degeneracy. An explicit method to compute the charge as well as several illustrative examples are given
El lĂmite semiclásico de sistemas clásicamente no integrables
Fil: Leboeuf, Patricio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina
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
Superfluid Motion of Light
Superfluidity, the ability of a fluid to move without dissipation, is one of
the most spectacular manifestations of the quantum nature of matter. We explore
here the possibility of superfluid motion of light. Controlling the speed of a
light packet with respect to a defect, we demonstrate the presence of
superfluidity and, above a critical velocity, its breakdown through the onset
of a dissipative phase. We describe a possible experimental realization based
on the transverse motion through an array of waveguides. These results open new
perspectives in transport optimization.Comment: 4 pages, 3 figure
Level density of a Fermi gas and integer partitions: a Gumbel-like finite-size correction
We investigate the many-body level density of gas of non-interacting
fermions. We determine its behavior as a function of the temperature and the
number of particles. As the temperature increases, and beyond the usual
Sommerfeld expansion that describes the degenerate gas behavior, corrections
due to a finite number of particles lead to Gumbel-like contributions. We
discuss connections with the partition problem in number theory, extreme value
statistics as well as differences with respect to the Bose gas.Comment: 5 pages, 1 figure, one figure added, accepted for publication in
Phys. Rev.
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
Localization by bichromatic potentials versus Anderson localization
The one-dimensional propagation of waves in a bichromatic potential may be
modeled by the Aubry-Andr\'e Hamiltonian. The latter presents a
delocalization-localization transition, which has been observed in recent
experiments using ultracold atoms or light. It is shown here that, in contrast
to Anderson localization, this transition has a classical origin, namely the
localization mechanism is not due to a quantum suppression of a classically
allowed transport process. Explicit comparisons with the Anderson model, as
well as with experiments, are done.Comment: 8 pages, 4 figure
Periodic orbit spectrum in terms of Ruelle--Pollicott resonances
Fully chaotic Hamiltonian systems possess an infinite number of classical solutions which are periodic, e.g. a trajectory ``p'' returns to its initial conditions after some fixed time tau_p. Our aim is to investigate the spectrum tau_1, tau_2, ... of periods of the periodic orbits. An explicit formula for the density rho(tau) = sum_p delta (tau - tau_p) is derived in terms of the eigenvalues of the classical evolution operator. The density is naturally decomposed into a smooth part plus an interferent sum over oscillatory terms. The frequencies of the oscillatory terms are given by the imaginary part of the complex eigenvalues (Ruelle--Pollicott resonances). For large periods, corrections to the well--known exponential growth of the smooth part of the density are obtained. An alternative formula for rho(tau) in terms of the zeros and poles of the Ruelle zeta function is also discussed. The results are illustrated with the geodesic motion in billiards of constant negative curvature. Connections with the statistical properties of the corresponding quantum eigenvalues, random matrix theory and discrete maps are also considered. In particular, a random matrix conjecture is proposed for the eigenvalues of the classical evolution operator of chaotic billiards
Level density of a Fermi gas: average growth and fluctuations
4 pages, 1 figureWe 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