93 research outputs found
Ordered bicontinuous double-diamond morphology in subsaturation nuclear matter
We propose to identify the new "intermediate" morphology in subsaturation
nuclear matter observed in a recent quantum molecular dynamics simulation with
the ordered bicontinuous double-diamond structure known in block copolymers. We
estimate its energy density by incorporating the normalized area-volume
relation given in a literature into the nuclear liquid drop model. The
resulting energy density is higher than the other five known morphologies.Comment: 4 pages, 4 figures, published in Phys. Rev.
Solvable few-body quantum problems
This work is devoted to the study of some exactly solvable quantum problems
of four, five and six bodies moving on the line. We solve completely the
corresponding stationary Schr\"odinger equation for these systems confined in
an harmonic trap, and interacting pairwise, in clusters of two and three
particles, by two-body inverse square Calogero potential. Both translationaly
and non-translationaly invariant multi-body potentials are added. In each case,
the full solutions are provided, namely the normalized regular eigensolutions
and the eigenenergies spectrum. The irregular solutions are also studied. We
discuss the domains of coupling constants for which these irregular solutions
are square integrable. The case of a "Coulomb-type" confinement is investigated
only for the bound states of the four-body systems.Comment: 23 page
Cluster Expansion of Cold Alpha Matter Energy
In the cluster expansion framework of Bose liquids we calculate analytical
expressions of the two-body, three-body and four-body diagrams contributing to
the g.s. energy of an infinite system of neutral alpha-particles at
zero-temperature, interacting via the strong nuclear forces exclusively. This
is analytically tractable by assuming a density dependent two-body correlation
function of Gaussian type. For the alpha-alpha potential we adopt the
phenomenological Ali-Bodmer interaction and semi-microscopic potentials
obtained from the Gogny force parametrizations. We show that under such
assumptions we achieve a rapid convergence in the cluster expansion, the
four-body contributions to the energy being smaller than the two-body and
three-body contributions by at least an order of magnitude.Comment: 22 pages, 13 figure
Piecewise constant potentials and discrete ambiguities
This work is devoted to the study of discrete ambiguities. For parametrized
potentials, they arise when the parameters are fitted to a finite number of
phase-shifts. It generates phase equivalent potentials. Such equivalence was
suggested to be due to the modulo uncertainty inherent to phase
determinations. We show that a different class of phase-equivalent potentials
exists. To this aim, use is made of piecewise constant potentials, the
intervals of which are defined by the zeros of their regular solutions of the
Schr\"odinger equation. We give a classification of the ambiguities in terms of
indices which include the difference between exact phase modulo and the
numbering of the wave function zeros.Comment: 26 pages Subject: Mathematical Physics math-p
Ising analogue to compact-star matter
By constructing an Ising analogue of compact-star matter at sub-saturation
density we explored the effect of Coulomb frustration on the nuclear liquid-gas
phase transition. Our conclusions is twofold. First, the range of temperatures
where inhomogeneous phases form expands with increasing Coulomb-field strength.
Second, within the approximation of uniform electron distribution, the limiting
point upon which the phase-coexistence region ends does not exhibit any
critical behaviour. Possible astrophysics consequences and thermodynamical
connections are discussed.Comment: 4 pages, 3 figure
Simulation of Transitions between "Pasta" Phases in Dense Matter
Calculations of equilibrium properties of dense matter predict that at
subnuclear densities nuclei can be rodlike or slablike. To investigate whether
transitions between phases with non-spherical nuclei can occur during the
collapse of a star, we perform quantum molecular dynamic simulations of the
compression of dense matter. We have succeeded in simulating the transitions
between rodlike and slablike nuclei and between slablike nuclei and cylindrical
bubbles. Our results strongly suggest that non-spherical nuclei can be formed
in the inner cores of collapsing stars.Comment: 4 pages, 4 figures, final version published in Phys. Rev. Lett.,
high-res figures can be seen at http://www.nordita.dk/~gentaro/research/fig
Anyonic Excitations in Fast Rotating Bose Gases Revisited
The role of anyonic excitations in fast rotating harmonically trapped Bose
gases in a fractional Quantum Hall state is examined. Standard Chern-Simons
anyons as well as "non standard" anyons obtained from a statistical interaction
having Maxwell-Chern-Simons dynamics and suitable non minimal coupling to
matter are considered. Their respective ability to stabilize attractive Bose
gases under fast rotation in the thermodynamical limit is studied. Stability
can be obtained for standard anyons while for non standard anyons, stability
requires that the range of the corresponding statistical interaction does not
exceed the typical wavelenght of the atoms.Comment: 5 pages. Improved version to be published in Phys. Rev. A, including
a physical discussion on relevant interactions and scattering regime together
with implication on the nature of statistical interactio
The size of two-body weakly bound objects : short versus long range potentials
The variation of the size of two-body objects is investigated, as the
separation energy approaches zero, with both long range potentials and short
range potentials having a repulsive core. It is shown that long range
potentials can also give rise to very extended systems. The asymptotic laws
derived for states with angular momentum l=1,2 differ from the ones obtained
with short range potentials. The sensitivity of the asymptotic laws on the
shape and length of short range potentials defined by two and three parameters
is studied. These ideas as well as the transition from the short to the long
range regime for the l=0 case are illustrated using the Kratzer potential.Comment: 5 pages, 3 figures, submitted to Physical Review Letter
Using mixed data in the inverse scattering problem
Consider the fixed- inverse scattering problem. We show that the zeros
of the regular solution of the Schr\"odinger equation, , which are
monotonic functions of the energy, determine a unique potential when the domain
of the energy is such that the range from zero to infinity. This
suggests that the use of the mixed data of phase-shifts
, for which the zeros of the regular solution are monotonic in both domains,
and range from zero to infinity, offers the possibility of determining the
potential in a unique way.Comment: 9 pages, 2 figures. Talk given at the Conference of Inverse Quantum
Scattering Theory, Hungary, August 200
S-matrix poles and the second virial coefficient
For cutoff potentials, a condition which is not a limitation for the
calculation of physical systems, the S-matrix is meromorphic. We can express it
in terms of its poles, and then calculate the quantum mechanical second virial
coefficient of a neutral gas.
Here, we take another look at this approach, and discuss the feasibility,
attraction and problems of the method. Among concerns are the rate of
convergence of the 'pole' expansion and the physical significance of the
'higher' poles.Comment: 20 pages, 8 tables, submitted to J. Mol. Phy
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