4,063 research outputs found
Regularity and chaos in the nuclear masses
Shell effects in atomic nuclei are a quantum mechanical manifestation of the
single--particle motion of the nucleons. They are directly related to the
structure and fluctuations of the single--particle spectrum. Our understanding
of these fluctuations and of their connections with the regular or chaotic
nature of the nucleonic motion has greatly increased in the last decades. In
the first part of these lectures these advances, based on random matrix
theories and semiclassical methods, are briefly reviewed. Their consequences on
the thermodynamic properties of Fermi gases and, in particular, on the masses
of atomic nuclei are then presented. The structure and importance of shell
effects in the nuclear masses with regular and chaotic nucleonic motion are
analyzed theoretically, and the results are compared to experimental data. We
clearly display experimental evidence of both types of motionComment: 40 pages, 10 figures, Lectures delivered at the VIII Hispalensis
International Summer School, Sevilla, Spain, June 2003 (to appear in Lecture
Notes in Physics, Springer--Verlag, Eds. J. M. Arias and M. Lozano
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
Random matrices, random polynomials and Coulomb systems
It is well known that the joint probability density of the eigenvalues of
Gaussian ensembles of random matrices may be interpreted as a Coulomb gas. We
review these classical results for hermitian and complex random matrices, with
special attention devoted to electrostatic analogies. We also discuss the joint
probability density of the zeros of polynomials whose coefficients are complex
Gaussian variables. This leads to a new two-dimensional solvable gas of
interacting particles, with non-trivial interactions between particles.Comment: 8 pages, to appear in the Proceedings of the International Conference
on Strongly Coupled Coulomb Systems, Saint-Malo, 199
Correlations in Nuclear Masses
It was recently suggested that the error with respect to experimental data in
nuclear mass calculations is due to the presence of chaotic motion. The theory
was tested by analyzing the typical error size. A more sensitive quantity, the
correlations of the mass error between neighboring nuclei, is studied here. The
results provide further support to this physical interpretation.Comment: 4 pages, 2 figure
Normal forms and complex periodic orbits in semiclassical expansions of Hamiltonian systems
Bifurcations of periodic orbits as an external parameter is varied are a
characteristic feature of generic Hamiltonian systems. Meyer's classification
of normal forms provides a powerful tool to understand the structure of phase
space dynamics in their neighborhood. We provide a pedestrian presentation of
this classical theory and extend it by including systematically the periodic
orbits lying in the complex plane on each side of the bifurcation. This allows
for a more coherent and unified treatment of contributions of periodic orbits
in semiclassical expansions. The contribution of complex fixed points is find
to be exponentially small only for a particular type of bifurcation (the
extremal one). In all other cases complex orbits give rise to corrections in
powers of and, unlike the former one, their contribution is hidden in
the ``shadow'' of a real periodic orbit.Comment: better ps figures available at http://www.phys.univ-tours.fr/~mouchet
or on request to [email protected]
Thermodynamics of small Fermi systems: quantum statistical fluctuations
We investigate the probability distribution of the quantum fluctuations of
thermodynamic functions of finite, ballistic, phase-coherent Fermi gases.
Depending on the chaotic or integrable nature of the underlying classical
dynamics, on the thermodynamic function considered, and on temperature, we find
that the probability distributions are dominated either (i) by the local
fluctuations of the single-particle spectrum on the scale of the mean level
spacing, or (ii) by the long-range modulations of that spectrum produced by the
short periodic orbits. In case (i) the probability distributions are computed
using the appropriate local universality class, uncorrelated levels for
integrable systems and random matrix theory for chaotic ones. In case (ii) all
the moments of the distributions can be explicitly computed in terms of
periodic orbit theory, and are system-dependent, non-universal, functions. The
dependence on temperature and number of particles of the fluctuations is
explicitly computed in all cases, and the different relevant energy scales are
displayed.Comment: 24 pages, 7 figures, 5 table
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