50 research outputs found
Baryon-antibaryon annihilation in the Skyrme model
The dynamics of Skyrmion-anti-Skyrmion annihilations in 3+1 dimensions is examined by the numerical integration of the classical Hamilton equations of motion. The baryon number is found to disappear extremely rapidly, close to the causal limit, while the energy distribution still remains concentrated in the annihilation region. The emission of pion waves emitted by the annihilation process is investigated
Level density of a Fermi gas: average growth and fluctuations
We compute the level density of a two--component Fermi gas as a function of
the number of particles, angular momentum and excitation energy. The result
includes smooth low--energy corrections to the leading Bethe term (connected to
a generalization of the partition problem and Hardy--Ramanujan formula) plus
oscillatory corrections that describe shell effects. When applied to nuclear
level densities, the theory provides a unified formulation valid from
low--lying states up to levels entering the continuum. The comparison with
experimental data from neutron resonances gives excellent results.Comment: 4 pages, 1 figur
Level Density of a Bose Gas and Extreme Value Statistics
We establish a connection between the level density of a gas of
non-interacting bosons and the theory of extreme value statistics. Depending on
the exponent that characterizes the growth of the underlying single-particle
spectrum, we show that at a given excitation energy the limiting distribution
function for the number of excited particles follows the three universal
distribution laws of extreme value statistics, namely Gumbel, Weibull and
Fr\'echet. Implications of this result, as well as general properties of the
level density at different energies, are discussed.Comment: 4 pages, no figure
Symmetry conserving non-perturbative s-wave renormalization of the pion in hot and baryon dense medium
A non-perturbative s-wave renormalization of the pion in a hot and baryon
rich medium is presented. This approach proceeds via a mapping of the canonical
pion into the axial Noether's charge. The mapping was made dynamical in the
Hartree-Fock-Bogoliubov random phase approximation (HFB-RPA). It is shown that
this approach, while order mixing, is still symmetry conserving both in the
baryon free and baryon rich sectors, at zero as well as finite temperature. The
systematic character of this approach is emphasized and it is particularly
argued that it may constitute an interesting alternative for the
non-perturbative assessment of the nuclear matter saturation properties.Comment: Latex, 22 pages, 3 figure
Two Skyrmion Dynamics with Omega Mesons
We present our first results of numerical simulations of two skyrmion
dynamics using an -meson stabilized effective Lagrangian. We consider
skyrmion-skyrmion scattering with a fixed initial velocity of , for
various impact parameters and groomings. The physical picture that emerges is
surprisingly rich, while consistent with previous results and general
conservation laws. We find meson radiation, skyrmion scattering out of the
scattering plane, orbiting and capture to bound states.Comment: 19 pages, 22 figure
Symmetry Decomposition of Potentials with Channels
We discuss the symmetry decomposition of the average density of states for
the two dimensional potential and its three dimensional
generalisation . In both problems, the energetically
accessible phase space is non-compact due to the existence of infinite channels
along the axes. It is known that in two dimensions the phase space volume is
infinite in these channels thus yielding non-standard forms for the average
density of states. Here we show that the channels also result in the symmetry
decomposition having a much stronger effect than in potentials without
channels, leading to terms which are essentially leading order. We verify these
results numerically and also observe a peculiar numerical effect which we
associate with the channels. In three dimensions, the volume of phase space is
finite and the symmetry decomposition follows more closely that for generic
potentials --- however there are still non-generic effects related to some of
the group elements
Collision-Induced Decay of Metastable Baby Skyrmions
Many extensions of the standard model predict heavy metastable particles
which may be modeled as solitons (skyrmions of the Higgs field), relating their
particle number to a winding number. Previous work has shown that the
electroweak interactions admit processes in which these solitons decay,
violating standard model baryon number. We motivate the hypothesis that
baryon-number-violating decay is a generic outcome of collisions between these
heavy particles. We do so by exploring a 2+1 dimensional theory which also
possesses metastable skyrmions. We use relaxation techniques to determine the
size, shape and energy of static solitons in their ground state. These solitons
could decay by quantum mechanical tunneling. Classically, they are metastable:
only a finite excitation energy is required to induce their decay. We attempt
to induce soliton decay in a classical simulation by colliding pairs of
solitons. We analyze the collision of solitons with varying inherent
stabilities and varying incident velocities and orientations. Our results
suggest that winding-number violating decay is a generic outcome of collisions.
All that is required is sufficient (not necessarily very large) incident
velocity; no fine-tuning of initial conditions is required.Comment: 24 pages, 7 figures, latex. Very small changes onl
Hartree Fock Calculations in the Density Matrix Expansion Approach
The density matrix expansion is used to derive a local energy density
functional for finite range interactions with a realistic meson exchange
structure. Exchange contributions are treated in a local momentum
approximation. A generalized Slater approximation is used for the density
matrix where an effective local Fermi momentum is chosen such that the next to
leading order off-diagonal term is canceled. Hartree-Fock equations are derived
incorporating the momentum structure of the underlying finite range
interaction. For applications a density dependent effective interaction is
determined from a G-matrix which is renormalized such that the saturation
properties of symmetric nuclear matter are reproduced. Intending applications
to systems far off stability special attention is paid to the low density
regime and asymmetric nuclear matter. Results are compared to predictions
obtained from Skyrme interactions. The ground state properties of stable nuclei
are well reproduced without further adjustments of parameters. The potential of
the approach is further exemplified in calculations for A=100...140 tin
isotopes. Rather extended neutron skins are found beyond 130Sn corresponding to
solid layers of neutron matter surrounding a core of normal composition.Comment: Revtex, 29 pages including 14 eps figures, using epsfig.st
Semiclassical Trace Formulas for Noninteracting Identical Particles
We extend the Gutzwiller trace formula to systems of noninteracting identical
particles. The standard relation for isolated orbits does not apply since the
energy of each particle is separately conserved causing the periodic orbits to
occur in continuous families. The identical nature of the particles also
introduces discrete permutational symmetries. We exploit the formalism of
Creagh and Littlejohn [Phys. Rev. A 44, 836 (1991)], who have studied
semiclassical dynamics in the presence of continuous symmetries, to derive
many-body trace formulas for the full and symmetry-reduced densities of states.
Numerical studies of the three-particle cardioid billiard are used to
explicitly illustrate and test the results of the theory.Comment: 29 pages, 11 figures, submitted to PR