  A proto-neutron star (PNS) is the first phase of life of a neutron star, and
is likely to origin from a core-collapse supernova. After about 200 ms from
core-collapse, the PNS evolution may be modeled as a sequence of
quasi-stationary configurations. These configurations depend on the PNS
thermodynamic profiles, whose evolution largely depends upon the neutrino
diffusion. We developed a new PNS evolutionary code that solves by iteration
the neutrino number and energy transport equations together with the
relativistic stellar structure equations assuming spherical symmetry. The
neutrino cross sections are determined consistently with the underlying
equation of state (EoS). To include the EoSs in the evolution, we devised and
tested a new fitting formula for the interacting part of the baryon
free-energy, valid at finite temperature and arbitrary degeneracy. Using our
code, we provide estimates for the neutrino signal in the Super-Kamiokande III
detector and the frequencies of the gravitational waves due to stellar
oscillations, for three stellar masses and three nucleonic EoSs. For the first
time we evolve a PNS with a nuclear many-body theory EoS in a consistent way,
that is, we take into account realistic nuclear interactions in the computation
of the neutrino cross sections. By including rotation in an effective way, we
have also determined the time variation of the rotation frequency due to PNS
contraction and neutrino angular momentum loss, and the gravitational wave
signal due to rotation. We find that the mass shedding limit restricts the
initial angular momentum. Consequently, the final rotation frequency has to be
smaller than about 300 Hz for a PNS of about 1.6 solar masses whose EoS is
described by the GM3 mean-field model.
