Efimov physics in a finite volume

Kreuzer, Simon; Hammer, H.-W.

doi:10.1016/j.physletb.2009.02.035

Cited by 85 publications

(111 citation statements)

References 41 publications

(47 reference statements)

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“…The methods of π /EFT have for some time been deployed in the study of reactions directly on the lattice [4,40]. Both two-nucleon elastic scattering [41] and neutron radiative capture on the proton [42] have been considered directly on the lattice.…”

Section: Introductionmentioning

confidence: 99%

Spectra and scattering of light lattice nuclei from effective field theory

et al. 2015

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An effective field theory is used to describe light nuclei, calculated from quantum chromodynamics on a lattice at unphysically large pion masses. The theory is calibrated at leading order to two available data sets on two-and three-body nuclei for two pion masses. At those pion masses we predict the quartet and doublet neutron-deuteron scattering lengths, and the alpha-particle binding energy. For mπ=510 MeV we obtain, respectively, 4 anD = 2.3 ± 1.3 fm, 2 anD = 2.2 ± 2.1 fm, and B α = 35 ± 22 MeV, while for mπ=805 MeV 4 anD = 1.6 ± 1.3 fm, 2 anD = 0.62 ± 1.0 fm, and B α = 94 ± 45 MeV are found. Phillips-and Tjon-like correlations to the triton binding energy are established. We find the theoretical uncertainty in the respective correlation bands to be independent of the pion mass. As a benchmark, we present results for the physical pion mass, using experimental two-body scattering lengths and the triton binding energy as input. Hints of subtle changes in the structure of the triton and alpha particle are discussed.

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Section: Introductionmentioning

confidence: 99%

Spectra and scattering of light lattice nuclei from effective field theory

et al. 2015

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“…We have extended our earlier studies of the Efimov spectrum in a cubic box with periodic boundary conditions [38]. The knowledge of the finite volume modifications of the spectrum is important in order to understand results from future 3-body lattice calculations.…”

Section: Conlusionsmentioning

confidence: 86%

“…3, the three datasets obtained for state II are plotted again, this time in comparison to the results from a calculation using the expansion of the kernel as in Ref. [38]. ates from the result of the full calculation.…”

Section: Positive Scattering Lengthmentioning

confidence: 99%

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Three-boson bound states in ﬁnite volume with EFT

Kreuzer

Hammer

2010

EPJ Web of Conferences

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Abstract. The universal properties of a three-boson system with large scattering length are well understood within the framework of Effective Field Theory. They include a geometric spectrum of shallow three-body bound states called "Efimov states" and log-periodic dependence of scattering observables on the scattering length. We investigate the modification of this spectrum in a finite cubic box using a partial wave expansion. The dependence of the binding energies on the box size is calculated for systems with positive and negative two-body scattering length. We compare the full results to results obtained using an expansion around the infinite volume binding energy. The renormalization of the Effective Field Theory in the finite volume is verified explicitly.

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“…Of course, a comprehension of such effects may also provide useful information for an analysis of data from Quantum Monte-Carlo studies [36] of the Tan relations [37]. Let us also mention that finite-volume effects in atomic few-body systems have been studied recently using an effective field theory approach [38][39][40]. Finally, we would like to add that a study of finite-size and particle-number effects arising from a given experimental setup may eventually allow us to make better contact between theory and experiment, see e. g. Refs.…”

Section: Introductionmentioning

confidence: 99%

Finite-size and particle-number effects in an ultracold Fermi gas at unitarity

2011

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We investigate an ultracold Fermi gas at unitarity confined in a periodic box V = L 3 using renormalization group (RG) techniques. Within this approach we can quantitatively assess the long range bosonic order parameter fluctuations which dominate finite-size effects. We determine the finite-size and particle-number dependence of universal quantities, such as the Bertsch parameter and the fermion gap. Moreover, we analyze how these universal observables respond to the variation of an external pairing source. Our results indicate that the Bertsch parameter saturates rather quickly to its value in the thermodynamic limit as a function of increasing box size. On the other hand, we observe that the fermion gap shows a significantly stronger dependence on the box size, in particular for small values of the pairing source. Our results may contribute to a better understanding of finitesize and particle-number effects present in Monte-Carlo simulations of ultracold Fermi gases.

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Efimov physics in a finite volume

Cited by 85 publications

References 41 publications

Spectra and scattering of light lattice nuclei from effective field theory

Spectra and scattering of light lattice nuclei from effective field theory

Three-boson bound states in ﬁnite volume with EFT

Finite-size and particle-number effects in an ultracold Fermi gas at unitarity

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