338 research outputs found
Sample-size dependence of the ground-state energy in a one-dimensional localization problem
We study the sample-size dependence of the ground-state energy in a
one-dimensional localization problem, based on a supersymmetric quantum
mechanical Hamiltonian with random Gaussian potential. We determine, in the
form of bounds, the precise form of this dependence and show that the
disorder-average ground-state energy decreases with an increase of the size
of the sample as a stretched-exponential function, , where the
characteristic exponent depends merely on the nature of correlations in the
random potential. In the particular case where the potential is distributed as
a Gaussian white noise we prove that . We also predict the value of
in the general case of Gaussian random potentials with correlations.Comment: 30 pages and 4 figures (not included). The figures are available upon
reques
Stellar evolution and modelling stars
In this chapter I give an overall description of the structure and evolution
of stars of different masses, and review the main ingredients included in
state-of-the-art calculations aiming at reproducing observational features. I
give particular emphasis to processes where large uncertainties still exist as
they have strong impact on stellar properties derived from large compilations
of tracks and isochrones, and are therefore of fundamental importance in many
fields of astrophysics.Comment: Lecture presented at the IVth Azores International Advanced School in
Space Sciences on "Asteroseismology and Exoplanets: Listening to the Stars
and Searching for New Worlds" (arXiv:1709.00645), which took place in Horta,
Azores Islands, Portugal in July 201
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