54,232 research outputs found
On the distribution of the total energy of a system on non-interacting fermions: random matrix and semiclassical estimates
We consider a single particle spectrum as given by the eigenvalues of the
Wigner-Dyson ensembles of random matrices, and fill consecutive single particle
levels with n fermions. Assuming that the fermions are non-interacting, we show
that the distribution of the total energy is Gaussian and its variance grows as
n^2 log n in the large-n limit. Next to leading order corrections are computed.
Some related quantities are discussed, in particular the nearest neighbor
spacing autocorrelation function. Canonical and gran canonical approaches are
considered and compared in detail. A semiclassical formula describing, as a
function of n, a non-universal behavior of the variance of the total energy
starting at a critical number of particles is also obtained. It is illustrated
with the particular case of single particle energies given by the imaginary
part of the zeros of the Riemann zeta function on the critical line.Comment: 28 pages in Latex format, 5 figures, submitted for publication to
Physica
Scaling forces to asteroid surfaces: The role of cohesion
The scaling of physical forces to the extremely low ambient gravitational
acceleration regimes found on the surfaces of small asteroids is performed.
Resulting from this, it is found that van der Waals cohesive forces between
regolith grains on asteroid surfaces should be a dominant force and compete
with particle weights and be greater, in general, than electrostatic and solar
radiation pressure forces. Based on this scaling, we interpret previous
experiments performed on cohesive powders in the terrestrial environment as
being relevant for the understanding of processes on asteroid surfaces. The
implications of these terrestrial experiments for interpreting observations of
asteroid surfaces and macro-porosity are considered, and yield interpretations
that differ from previously assumed processes for these environments. Based on
this understanding, we propose a new model for the end state of small, rapidly
rotating asteroids which allows them to be comprised of relatively fine
regolith grains held together by van der Waals cohesive forces.Comment: 54 pages, 7 figure
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