8,471 research outputs found
Degree growth for tame automorphisms of an affine quadric threefold
In this paper, we consider the degree sequences of the tame automorphisms
preserving an affine quadric threefold. Using some valuatives estimates derived
from the work of Shestakov-Umirbaev and the action of this group on a CAT(0),
Gromov-hyperbolic square complex constructed by Bisi-Furter-Lamy, we prove that
the dynamical degrees of tame elements avoid any value strictly between 1 and
4/3. As an application, these methods allow us to characterize when the growth
exponent of the degree of a random product of finitely many tame automorphisms
is positive.Comment: This paper is part of the author's PhD thesi
Energies of the ground state and first excited state in an exactly solvable pairing model
Several approximations are tested by calculating the ground-state energy and
the energy of the first excited state using an exactly solvable model
with two symmetric levels interacting via a pairing force. They are the BCS
approximation (BCS), Lipkin - Nogami (LN) method, random-phase approximation
(RPA), quasiparticle RPA (QRPA), the renormalized RPA (RRPA), and renormalized
QRPA (RQRPA). It is shown that, in the strong-coupling regime, the QRPA which
neglects the scattering term of the model Hamiltonian offers the best fit to
the exact solutions. A recipe is proposed using the RRPA and RQRPA in
combination with the pairing gap given by the LN method. Applying this recipe,
it is shown that the normal-superfluid phase transition is avoided, and a
reasonably good description for both of the ground-state energy and the energy
of the first excited state is achieved.Comment: 18 pages, 4 figure
Superfluid-normal phase transition in finite systems and its effect on damping of hot giant resonances
Thermal fluctuations of quasiparticle number are included making use of the
secondary Bogolyubov's transformation, which turns quasiparticles operators
into modified-quasiparticle ones. This restores the unitarity relation for the
generalized single-particle density operator, which is violated within the
Hartree-Fock-Bogolyubov (HFB) theory at finite temperature. The resulting
theory is called the modified HFB (MHFB) theory, whose limit of a constant
pairing interaction yields the modified BCS (MBCS) theory. Within the MBCS
theory, the pairing gap never collapses at finite temperature T as it does
within the BCS theory, but decreases monotonously with increasing T. It is
demonstrated that this non-vanishing thermal pairing is the reason why the
width of the giant dipole resonance (GDR) does not increase with T up to T
around 1 MeV. At higher T, when the thermal pairing is small, the GDR width
starts to increase with T. The calculations within the phonon-damping model
yield the results in good agreement with the most recent experimental
systematic for the GDR width as a function of T. A similar effect, which causes
a small GDR width at low T, is also seen after thermal pairing is included in
the thermal fluctuation model.Comment: Invited lecture at the Predeal international summer school in nuclear
physics on ``Collective motion and phase transitions in nuclear systems'', 28
August - 9 September, 2006, Predeal, Romania; 18 pages, 3 figures; to be
published by World Scientific in the proceedings of this schoo
- …