3 research outputs found
Quantum thermodynamic fluctuations of a chaotic Fermi-gas model
We investigate the thermodynamics of a Fermi gas whose single-particle energy
levels are given by the complex zeros of the Riemann zeta function. This is a
model for a gas, and in particular for an atomic nucleus, with an underlying
fully chaotic classical dynamics. The probability distributions of the quantum
fluctuations of the grand potential and entropy of the gas are computed as a
function of temperature and compared, with good agreement, with general
predictions obtained from random matrix theory and periodic orbit theory (based
on prime numbers). In each case the universal and non--universal regimes are
identified.Comment: 23 pages, 4 figures, 1 tabl
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