Spin-orbit coupling in nuclei and realistic nucleon-nucleon potentials

We analyze the spin-orbit coupling term in the nuclear energy density functional in terms of a zero-range NN-contact interaction and finite-range contributions from two-pion exchange. We show that the strength of the spin-orbit contact interaction as extracted from high-precision nucleon-nucleon potentials is in perfect agreement with that of phenomenological Skyrme forces employed in non-relativistic nuclear structure calculations. Additional long-range contributions from chiral two-pion exchange turn out to be relatively small. These explicitly density-dependent contributions reduce the ratio of the isovector to the isoscalar spin-orbit strength significantly below the Skyrme value 1/3. We perform a similar analysis for the strength function of the $(\vec \nabla \rho)^2$-term and find values not far from those of phenomenological Skyrme parameterizations.Comment: 10 pages, 3 figures, accepted for publication in Physical Review C70 (2004

Levy flights and Levy -Schroedinger semigroups

We analyze two different confining mechanisms for L\'{e}vy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Levy-Schroedinger semigroups which induce so-called topological Levy processes (Levy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological L\'{e}vy process with the very same invariant pdf and in the reverse.Comment: To appear in Cent. Eur. J. Phys. (2010

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e., by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic N\'eel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.Comment: 23 pages, 8 figure

Particle Dispersion on Rapidly Folding Random Hetero-Polymers

We investigate the dynamics of a particle moving randomly along a disordered hetero-polymer subjected to rapid conformational changes which induce superdiffusive motion in chemical coordinates. We study the antagonistic interplay between the enhanced diffusion and the quenched disorder. The dispersion speed exhibits universal behavior independent of the folding statistics. On the other hand it is strongly affected by the structure of the disordered potential. The results may serve as a reference point for a number of translocation phenomena observed in biological cells, such as protein dynamics on DNA strands.Comment: 4 pages, 4 figure

Effective DBHF Method for Asymmetric Nuclear Matter and Finite Nuclei

A new decomposition of the Dirac structure of nucleon self-energies in the Dirac Brueckner-Hartree-Fock (DBHF) approach is adopted to investigate the equation of state for asymmetric nuclear matter. The effective coupling constants of $\sigma$, $\omega$, $\delta$ and $\rho$ mesons with a density dependence in the relativistic mean field approach are deduced by reproducing the nucleon self-energy resulting from the DBHF at each density for symmetric and asymmetric nuclear matter. With these couplings the properties of finite nuclei are investigated. The agreement of charge radii and binding energies of finite nuclei with the experimental data are improved simultaneously in comparison with the projection method. It seems that the properties of finite nuclei are sensitive to the scheme used for the DBHF self-energy extraction. We may conclude that the properties of the asymmetric nuclear matter and finite nuclei could be well described by the new decomposition approach of the G matrix.Comment: 16 pages, 5 figure

In-medium chiral SU(3) dynamics and hypernuclear structure

A previously introduced relativistic energy density functional, successfully applied to ordinary nuclei, is extended to hypernuclei. The density-dependent mean field and the spin-orbit potential are consistently calculated for a $\Lambda$ hyperon in the nucleus using the SU(3) extension of in-medium chiral perturbation theory. The leading long range $\Lambda N$ interaction arises from kaon-exchange and $2\pi$-exchange with $\Sigma$ hyperon in the intermediate state. Scalar and vector mean fields reflecting in-medium changes of the quark condensates are constrained by QCD sum rules. The model, applied to oxygen as a test case, describes spectroscopic data in good agreement with experiment. In particular, the smallness of the $\Lambda$ spin-orbit interaction finds a natural explanation in terms of an almost complete cancellation between scalar-vector background contributions and long-range terms generated by two-pion exchange.Comment: 10 pages, 2 figures, elsart class. Minor revision

Quark mean field model with density dependent couplings for finite nuclei

The quark mean field model, which describes the nucleon using the constituent quark model, is applied to investigate the properties of finite nuclei. The couplings of the scalar and vector mesons with quarks are made density dependent through direct coupling to the scalar field so as to reproduce the relativistic Brueckner-Hartree-Fock results of nuclear matter. The present model provides satisfactory results on the properties of spherical nuclei, and predicts an increasing size of the nucleon as well as a reduction of the nucleon mass in the nuclear environmentComment: 8 pages, REVTeX, 8 ps figures, accepted for publication in Phys. Rev.

Neutron star properties and the equation of state of neutron-rich matter

We calculate total masses and radii of neutron stars (NS) for pure neutron matter and nuclear matter in beta-equilibrium. We apply a relativistic nuclear matter equation of state (EOS) derived from Dirac-Brueckner-Hartree-Fock (DBHF) calculations. We use realistic nucleon-nucleon (NN) interactions defined in the framework of the meson exchange potential models. Our results are compared with other theoretical predictions and recent observational data. Suggestions for further study are discussed.Comment: 13 pages, 9 figures, 1 table; Revised version, accepted for publication in Physical Review