Low-Density Neutron Matter and the Unitary Limit

Vidaña, Isaac

doi:10.3389/fphy.2021.660622

Cited by 15 publications

(6 citation statements)

References 85 publications

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“…By investi- gating other Skyrme models, which perform rather well for the ground state of finite nuclei, we now explore more widely the Skyrme's uncertainties in the predictions for the properties of low-density NM. These properties are interesting since low-density NM is close to the unitary gas limit [37,38,39], which is universal from nuclear systems to cold atom gas [40]. From our previous analysis, we have concluded that the crust composition (A cl , Z cl ) depends mainly on the properties of SM, while NM influences mostly the energy per particle, the pressure and the sound-speed in non-uniform matter.…”

Section: Uniform Matter In the Core Of Neutron Starsmentioning

confidence: 83%

Confronting a set of Skyrme and $χ_{EFT}$ predictions for the crust of neutron stars

Grams,

Margueron,

Somasundaram

et al. 2022

Preprint

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With the improved accuracy of neutron star observational data, it is necessary to derive new equation of state where the crust and the core are consistently calculated within a unified approach. For this purpose we describe non-uniform matter in the crust of neutron stars employing a compressible liquid-drop model, where the bulk and the neutron fluid terms are given from the same model as the one describing uniform matter present in the core. We then generate a set of fifteen unified equations of state for cold catalyzed neutron stars built on realistic modelings of the nuclear interaction, which belongs to two main groups: the first one derives from the phenomenological Skyrme interaction and the second one from χEFT Hamiltonians. The confrontation of these model predictions allows us to investigate the model dependence for the crust properties, and in particular the effect of neutron matter at low density. The new set of unified equations of state is available at the CompOSE repository. Keywords neutron star • equation of state • crust • compressible liquid-drop model • Skyrme and chiral EFT interactions

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Section: Uniform Matter In the Core Of Neutron Starsmentioning

confidence: 83%

Confronting a set of Skyrme and $χ_{EFT}$ predictions for the crust of neutron stars

Grams,

Margueron,

Somasundaram

et al. 2022

Preprint

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“…The limit of very large effective coupling g is called the unitary Fermi gas [94]. Monte Carlo simulations for the case of g → ∞ [95,96] yield…”

Section: Fermi Gas: Unitary Limitmentioning

confidence: 99%

Optimized Self-Similar Borel Summation

Gluzman,

Yukalov

2023

Axioms

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The method of Fractional Borel Summation is suggested in conjunction with self-similar factor approximants. The method used for extrapolating asymptotic expansions at small variables to large variables, including the variables tending to infinity, is described. The method is based on the combination of optimized perturbation theory, self-similar approximation theory, and Borel-type transformations. General Borel Fractional transformation of the original series is employed. The transformed series is resummed in order to adhere to the asymptotic power laws. The starting point is the formulation of dynamics in the approximations space by employing the notion of self-similarity. The flow in the approximation space is controlled, and “deep” control is incorporated into the definitions of the self-similar approximants. The class of self-similar approximations, satisfying, by design, the power law behavior, such as the use of self-similar factor approximants, is chosen for the reasons of transparency, explicitness, and convenience. A detailed comparison of different methods is performed on a rather large set of examples, employing self-similar factor approximants, self-similar iterated root approximants, as well as the approximation technique of self-similarly modified Padé–Borel approximations.

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“…The limit of very large g corresponds to the unitary Fermi gas. Monte-Carlo numerical calculations in the case of g → ∞ [72,73] yield…”

Section: One-dimensional Antiferromagnet: Ground State Energymentioning

confidence: 99%

“…according to [72,75]. Let us consider the inverse of the truncated series (64), and apply to it various resummation procedures.…”

Section: One-dimensional Antiferromagnet: Ground State Energymentioning

confidence: 99%

Borel Transform and Scale-Invariant Fractional Derivatives United

Gluzman¹

2023

Symmetry

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The method of Borel transformation for the summation of asymptotic expansions with the power-law asymptotic behavior at infinity is combined with elements of scale-invariant fractional analysis with the goal of calculating the critical amplitudes. The fractional order of specially designed scale-invariant fractional derivatives u is used as a control parameter to be defined uniquely from u-optimization. For resummation of the transformed expansions, we employed the self-similar iterated roots. We also consider a complementary optimization, called b-optimization with the number of iterations b as an alternative fractional control parameter. The method of scale-invariant Fractional Borel Summation consists of three constructive steps. The first step corresponds to u-optimization of the amplitudes with fixed parameter b. When the first step fails, the second step corresponds to b-optimization of the amplitudes with fixed parameter u. However, when the two steps fail, the third step corresponds to the simplified, Borel-light technique. The marginal amplitude should be found by means of the self-similar iterated roots constructed for the transformed series, optimized with either of the two above approaches and corrected with a diagonal Padé approximants. The examples are given when the complementary optimizations,“horses-for-courses” approach outperforms other analytical methods in calculation of critical amplitudes.

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Low-Density Neutron Matter and the Unitary Limit

Cited by 15 publications

References 85 publications

Confronting a set of Skyrme and $χ_{EFT}$ predictions for the crust of neutron stars

Confronting a set of Skyrme and $χ_{EFT}$ predictions for the crust of neutron stars

Optimized Self-Similar Borel Summation

Borel Transform and Scale-Invariant Fractional Derivatives United

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