arXiv subjects
Publications and source records attributed to Aurel Bulgac.
We calculate the oscillation frequencies of trapped Fermi condensate with particular emphasis on the equation of state of the interacting Fermi system. We confirm Stringari's finding that the frequencies are independent of the interaction in the unitary limit, and we extend the theory away from that limit, where the interaction does affect the frequencies of the compressional modes only.
We discuss the transition of fermion systems to a condensate of Bose dimers, when the interaction is varied by use of a Feshbach resonance. We argue that there is an intermediate phase between the superfluid Fermi gas and the Bose condensate of molecules, consisting of extended dimers.
A dilute atomic-molecular fermion in a trap acquires a rather complex layered spatial structure. At very low temperatures, typically at the center of the trap, a superfluid bosonic core is formed out of dimers, weakly bound pairs of fermionic atoms. Surrounding this core is a mantle, formed by a mixture of superfluid bosonic dimers and superfluid fermionic atoms. The outermost layer consists of only fermionic atoms, forming mostly a normal Fermi gas.
We show that a dilute atomic Fermi system at sufficiently low temperatures, can display fermionic superfluidity, even in the case of a repulsive atom-atom interaction, when the scattering length is positive. The attraction leading to the formation of Cooper pairs is provided by the exchange of Bogoliubov phonons if a fraction of the atoms form a BEC of weakly bound molecules.
In the inner crust of a neutron star, due to the high density and pressure, nuclei which are still present, are immersed in a neutron superfluid. One then expects that the dynamical properties of nuclei are significantly affected. In order to estimate the magnitude of the effect associated with the presence of a superfluid medium, we formulate the hydrodynamical approach to the nuclear dynamics in the inner crust of neutron stars. We calculate the renormalized nuclear mass and the strength of the medium-induced interaction between nuclei. We argue that these effects noticeably modify the properties of the Coulomb crystal in the inner crust.
We present a concise account of our development of the first genuine Local Density Approximation (LDA) to the Energy Density Functional (EDF) for fermionic systems with superfluid correlations, with a particular emphasis to nuclear systems.
We show that in a dilute Fermionic superfluid, when the Fermions interact with an infinite scattering length, a vortex state is characterized by a strong density depletion along the vortex core. This feature can make a direct visualization of vortices in Fermionic superfluids possible.
It was recently shown (A. Bulgac. Phys. Rev. Lett. {\bf 89}, 050402 (2002)) that an entirely new class of quantum liquids with widely tunable properties could be manufactured from bosons (boselets), fermions (fermilets) and their mixtures (ferbolets) by controlling their interaction properties by the means of a Feshbach resonance. We extend the previous mean--field analysis of these quantum liquids by computing the lowest order quantum corrections to the ground state energy and the depletion of the Bose--Einstein condensate and by estimating higher order corrections as well. We show that the quantum corrections are relatively small and controlled by the diluteness parameter $\sqrt{n|a|^3} \ll 1$, even though strictly speaking in this case there is no low density expansion.
We show that within the framework of a simple local nuclear energy density functional (EDF), one can describe accurately the one-- and two--nucleon separation energies of semi--magic nuclei. While for the normal part of the EDF we use previously suggested parameterizations, for the superfluid part of the EDF we use the simplest possible local form compatible with known nuclear symmetries.
We study in a fully selfconsistent approach the structure of a vortex in low density superfluid neutron matter. We determine that the matter density profile of a vortex shows a significant depletion in the region of the core, a feature never reported for a vortex state in a Fermi superfluid.
We show that in the limit of large and positive atom--atom scattering length the properties of an atomic--molecular Bose--Einstein Condensate (amBEC) are determined by an universal energy density functional (EDF). We find that the optimal conditions for the formation of a stable amBEC are in the regime where there are no shallow trimers and the atom--dimer scattering length is negative and comparable in magnitude with the atom--atom scattering length. At temperatures lower than $T_c$ the chemical potentials for the atoms and molecules can be specified independently. Besides three--body recombinations processes into dimers of large size, inelastic processes involving the formation of deeply bound small size molecular states are possible. These inelastic processes do not lead to an efficient heating of the amBEC and can be used for its mostly non--destructive monitoring.
This report is not meant to be submitted for publication at the present time and it is simply a supplement to our work nucl-th/0210047. We have collected together all our results for one--nucleon and two--nucleon separation energies for several isotope and isotone chains and compare them to the values extracted from the 1995 Audi and Wapstra table of recommended masses. Where it was possible we have compared our results to the results of Fayans et al. and Goriely et al. We also present results for the charge radii and compare them to experiment and results of Goriely et al.
The bottom part of the neutron star crust is investigated using the Skyrme-Hartree-Fock approach with the Coulomb interaction treated beyond the Wigner-Seitz approximation. A variety of nuclear phases is found to coexist in this region. Their stability and relative energies are governed by the Coulomb, surface and shell energies. We have also found that a substantial contribution is coming from the spin-orbit interaction.
In the limit when the two-body scattering length $a$ is negative and much larger than the effective two-body interaction radius the contribution to the ground state energy due to the three-body correlations is given by the Efimov effect. For particular values of the diluteness parameter $ρ|a|^3$ the three-body contribution can become the dominant term of the energy density functional. Under these conditions both Bose-Einstein and Fermi-Dirac systems could become self-bound and either boson droplets or fermion ``designer nuclei'' of various sizes and densities could be manufactured.
I formulate a local density approximation for fermion systems with pairing correlations based on a rapidly converging renormalization scheme for the pairing gap.
We estimate the quantum corrections to the ground state energy in neutron matter (which could be termed as well either shell correction energy or Casimir energy) at subnuclear densities, where various types of inhomogeneities (bubbles, rods, plates) are energetically favorable. We show that the magnitude of these energy corrections are comparable to the energy differences between various types of inhomogeneous phases. We discuss the dependence of these corrections on a number of physical parameters (density, filling factor, temperature, lattice distortions).
We discuss properties of the Fermi system which contain one or more spherical (or almost spherical) objects. The interplay between various effects, such as shell correction and chaotic behavior is considered. We briefly mention the role of the temperature, pairing, and effects associated with bubble dynamics.
In the present study we investigate the static properties of nuclei in the inner crust of neutron stars. Using the Hartree-Fock method in coordinate space, together with the semiclassical approximation, we examine the patterns of phase transitions.