Local-density-functional theory for superfluid fermionic systems: The unitary gas

Bulgac, Aurel

doi:10.1103/physreva.76.040502

Cited by 139 publications

(259 citation statements)

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“…Third, small atomic gases can be viewed as a bridge between two-body and many-body systems (see, e.g., Refs. [21][22][23][24]). In most cases, the two-body system is well characterized, making a bottom-up approach attractive.…”

Section: Introductionmentioning

confidence: 99%

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Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction

Blume¹,

Daily²

2011

Comptes Rendus. Physique

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We investigate small equal-mass two-component Fermi gases under external spherically symmetric confinement in which atoms with opposite spins interact through a short-range two-body model potential. We employ a non-perturbative microscopic framework, the stochastic variational approach, and determine the system properties as functions of the interspecies s-wave scattering length as, the orbital angular momentum L of the system, and the numbers N1 and N2 of spin-up and spin-down atoms (with N1 − N2 = 0 or 1 and N ≤ 6, where N = N1 + N2). At unitarity, we determine the energies of the five-and six-particle systems for various ranges r0 of the underlying two-body model potential and extrapolate to the zero-range limit. These energies serve as benchmark results that can be used to validate and assess other numerical approaches. We also present structural properties such as the pair distribution function and the radial density. Furthermore, we analyze the one-body and two-body density matrices. A measure for the molecular condensate fraction is proposed and applied. Our calculations show explicitly that the natural orbitals and the momentum distributions of atomic Fermi gases approach those characteristic for a molecular Bose gas if the s-wave scattering length as, as > 0, is sufficiently small.

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Section: Introductionmentioning

confidence: 99%

“…[21][22][23][24][31][32][33][34][35][36][37][38][39][40][41][42]). The ground state of trapped equalmass two-component Fermi gases, e.g., has been investigated numerically by the fixed-node diffusion Monte Carlo approach [21][22][23]39] and the stochastic variational approach [21,22,36,40,42].…”

Section: Introductionmentioning

confidence: 99%

Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction

Blume¹,

Daily²

2011

Comptes Rendus. Physique

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“…In the TDDFT extension of the approach, which has been studied for normal systems for quite some time [6,7], one needs to extend the form the energy density functional in order to allow for currents, which are typically absent in the ground states. In many cases requiring that the energy density functional to satisfy Galilean invariance allows to extend the DFT approach to a rather large class of phenomena [31,32]. As in the case of the stationary form of DFT, within TDDFT one can in principle evaluate exactly the one-body observables, when the many-body system under consideration is subject to an arbitrary one-body external potential [6,7].…”

Section: B Time-dependent Density Functional Theory Approach Its Limmentioning

confidence: 99%

“…The second approach is the Density Functional Theory (DFT) [4], extended to describe superfluid systems [31]. In the TDDFT extension of the approach, which has been studied for normal systems for quite some time [6,7], one needs to extend the form the energy density functional in order to allow for currents, which are typically absent in the ground states.…”

Section: B Time-dependent Density Functional Theory Approach Its Limmentioning

confidence: 99%

The long journey fromab initiocalculations to density functional theory for nuclear large amplitude collective motion

Bulgac

2010

J. Phys. G: Nucl. Part. Phys.

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At present there are two vastly different ab initio approaches to the description of the the manybody dynamics: the Density Functional Theory (DFT) and the functional integral (path integral) approaches. On one hand, if implemented exactly, the DFT approach can allow in principle the exact evaluation of arbitrary one-body observable. However, when applied to Large Amplitude Collective Motion (LACM) this approach needs to be extended in order to accommodate the phenomenon of surface-hoping, when adiabaticity is strongly violated and the description of a system using a single (generalized) Slater determinant is not valid anymore. The functional integral approach on the other hand does not appear to have such restrictions, but its implementation does not appear to be straightforward endeavor. However, within a functional integral approach one seems to be able to evaluate in principle any kind of observables, such as the fragment mass and energy distributions in nuclear fission. These two radically approaches can likely be brought brought together by formulating a stochastic time-dependent DFT approach to many-body dynamics. We know a great deal by now about interactions between nucleons, although one might rightly argue that the link to quarks and gluons through the more fundamental theory Quantum Chromodynamics has not yet been fully established. It will still be a long time until this goal will be reached with the needed degree of accuracy and sophistication. In this respect the nuclear many-body theory is at a great disadvantage when compared to condensed matter and atomic theories or chemistry, where the dominant role of the Coulomb interaction and the link to Quantum Electrodynamics were clarified a long time ago. There is a general consensus by now however, that in order to describe nuclear many-body systems one probably can get away with the use of one set or another of reasonably well established two-and three-nucleon potentials (if only one would manage to use them in a convincing implementation) and that a non-relativistic approach is likely sufficient for now. The best example we have so far that such an ab initio approach can be brought to fruition is the Green Function Monte-Carlo (GFMC) approach implemented so successfully by V.R. Pandharipande and his many students and collaborators J. Carlson (truly the author of GFMC), S.C. Pieper, R. Schiavilla, K.E. Schmidt, R.B. Wiringa, and many others [1]. One of the most frustrating limitations of the GFMC approach is the relatively low particle number this method can deal with. Presently one cannot envision the study of nuclei heavier than oxygen within a GFMC framework. The Coupled-Cluster (CC) method [2] looks very promising in this respect, as it might be applied to medium size closed shell nuclei in the near future. The No-Core-Shell Model (NCSM) [3] will likely be successfully applied to light and medium size nuclei in the foreseeable future with a reasonable degree of accuracy.Heavy-nuclei seem out of reach from a direct frontal ab initio attack and th...

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“…Both of these concepts became cornerstone tools to study atomic physics phenomena and in particular were well suited for the physics studied with ion and atom traps [81]. ERE is now a standard tool used to understand many features in optical lattices [82], Bose-Einstein condensates [83,84], or the unitary Fermi gases [85][86][87][88].…”

Section: B Gluons Quarks and Nucleonsmentioning

confidence: 99%

Current Status of Nuclear Physics Research

Bertulani

Hussein

2015

Braz J Phys

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In this review we discuss the current status of research in nuclear physics which is being carried out in different centers in the World. For this purpose we supply a short account of the development in the area which evolved over the last 9 decades, since the discovery of the neutron. The evolution of the physics of the atomic nucleus went through many stages as more data become available. We briefly discuss models introduced to discern the physics behind the experimental discoveries, such as the shell model, the collective model, the statistical model, the interacting boson model, etc., some of these models may be seemingly in conflict with each other, but this was shown to be only apparent.The richness of the ideas and abundance of theoretical models attests to the important fact that the nucleus is a really singular system in the sense that it evolves from two-body bound states such as the deuteron, to few-body bound states, such as 4 He, 7 Li, 9 Be etc. and up the ladder to heavier bound nuclei containing up to more than 200 nucleons. Clearly statistical mechanics, usually employed in systems with very large number of particles, would seemingly not work for such finite systems as the nuclei, neither do other theories which are applicable to condensed matter. The richness of nuclear physics stems from these restrictions. New theories and models are presently being developed. Theories of the structure and reactions of neutron-rich and proton-rich nuclei, called exotic nuclei, halo nuclei, or Borromean nuclei, deal with the wealth of experimental data that became available in the last 35 years. Further, nuclear astrophysics and stellar and Big Bang nucleosynthesis have become a more mature subject. Due to limited space, this review only covers a few selected topics, mainly those with which the authors have worked on. Our aimed potential readers of this review are nuclear physicists and physicists in other areas, as well as graduate students interested in pursuing a career in nuclear physics.

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Local-density-functional theory for superfluid fermionic systems: The unitary gas

Cited by 139 publications

References 34 publications

Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction

Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction

The long journey fromab initiocalculations to density functional theory for nuclear large amplitude collective motion

Current Status of Nuclear Physics Research

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