Nuclear Theory·nucl-th

Friday·April 28, 2023

7 papers—2 primary·5 cross-listed

03
Robust formulation of Wick's theorem for computing matrix elements between Hartree-Fock-Bogoliubov wavefunctions
Guo P. Chen · Gustavo E. Scuseria
Numerical difficulties associated with computing matrix elements of operators between Hartree-Fock-Bogoliubov (HFB) wavefunctions have plagued the development of HFB-based many-body theories for decades. The problem arises from divisions by zero in the standard formulation of the nonorthogonal Wick's theorem in the limit of vanishing HFB overlap. In this paper, we present a robust formulation of Wick's theorem that stays well-behaved regardless of whether the HFB states are orthogonal or not. This new formulation ensures cancellation between the zeros of the overlap and the poles of the Pfaffian, which appears naturally in fermionic systems. Our formula explicitly eliminates self-interaction, which otherwise causes additional numerical challenges. A computationally efficient version of our formalism enables robust symmetry-projected HFB calculations with the same computational cost as mean-field theories. Moreover, we avoid potentially diverging normalization factors by introducing a robust normalization procedure. The resulting formalism treats even and odd number of particles on equal footing and reduces to Hartree-Fock as a natural limit. As proof of concept, we present a numerically stable and accurate solution to a Jordan-Wigner-transformed Hamiltonian, whose singularities motivated the present work. Our robust formulation of Wick's theorem is a most promising development for methods using quasiparticle vacuum states.
↳ physics.chem-phcond-mat.str-elnucl-thJ.Chem.Phys.(2023)·7 citations
04
Sound velocity peak and conformality in isospin QCD
Ryuji Chiba🇯🇵 · Toru Kojo🇯🇵
We study zero temperature equations of state (EOS) in isospin QCD within a quark-meson model which is renormalizable and hence eliminates high density artifacts in models with the ultraviolet cutoff (e.g., NJL models). The model exhibits a crossover transition of pion condensations from the Bose-Einstein-Condensation regime at low density to the Bardeen-Cooper-Schrieffer regime at high density. The EOS stiffens quickly and approaches the quark matter regime at density significantly less than the density for pions to spatially overlap. The sound velocity develops a peak in the crossover region, and then gradually relaxes to the conformal value $1/3$ from above, in contrast to the perturbative QCD results which predicts the approach from below. In the context of QCD computations, this opposite trend is in part due to the lack of gluon exchanges in our model, and also due to the non-perturbative power corrections arising from the condensates. We argue that with large power corrections the trace anomaly can be negative. In quantitative level, our EOS is consistent with the lattice results in the BEC regime but begins to get stiffer at higher density. The sound velocity peak also appears at higher density. The BCS gap in our model is $Δ ≃ 300$ MeV in the quark matter domain, and naive application of the BCS relation for the critical temperature $T_{c} ≃ 0.57Δ$ yields the estimate $T_{c} ≃ 170$ MeV, in good agreement with the lattice data.
↳ hep-phhep-thnucl-thPRD(2024)·43 citations
05
First study of reaction $Ξ^{0} n \to Ξ^{-} p$ using $Ξ^{0}$ -nucleus scattering at an electron-positron collider
BESIII Collaboration: M. Ablikim · M. N. Achasov · P. Adlarson · R. Aliberti · A. Amoroso · M. R. An · Q. An · Y. Bai · O. Bakina · I. Balossino · Y. Ban · V. Batozskaya and 605 other authors
Using $(1.0087 \pm 0.0044) \times 1 0^{10}$ $J / ψ$ events collected with the BESIII detector at the BEPCII storage ring, the process $Ξ^{0} n \to Ξ^{-} p$ is studied, where the $Ξ^{0}$ baryon is produced in the process $J / ψ \to Ξ^{0} Ξ ˉ^{0}$ and the neutron is a component of the $^{9} Be$ , $^{12} C$ and $^{197} Au$ nuclei in the beam pipe. A clear signal is observed with a statistical significance of $7.1 σ$ . The cross section of the reaction $Ξ^{0} +^{9} Be \to Ξ^{-} + p +^{8} Be$ is determined to be $σ (Ξ^{0} +^{9} Be \to Ξ^{-} + p +^{8} Be) = (22.1 \pm 5. 3_{stat} \pm 4. 5_{sys})$ mb at the $Ξ^{0}$ momentum of $0.818$ GeV/ $c$ , where the first uncertainty is statistical and the second is systematic. No significant $H$ -dibaryon signal is observed in the $Ξ^{-} p$ final state. This is the first study of hyperon-nucleon interactions in electron-positron collisions and opens up a new direction for such research.
↳ hep-exhep-phnucl-exnucl-thPRL(2023)·41 citations
06
U(1) quasi-hydrodynamics: Schwinger-Keldysh effective field theory and holography
Matteo Baggioli🇨🇳 · Yanyan Bu🇨🇳 · Vaios Ziogas🇫🇷
We study the quasi-hydrodynamics of a system with a softly broken $U (1)$ global symmetry using effective field theory (EFT) and holographic methods. In the gravity side, we consider a holographic Proca model in the limit of small bulk mass, which is responsible for a controllable explicit breaking of the $U (1)$ global symmetry in the boundary field theory. We perform a holographic Schwinger-Keldysh analysis, which allows us to derive the form of the boundary effective action in presence of dissipation. We compare our results with the previously proposed EFT and hydrodynamic theories, and we confirm their validity by computing the low-energy quasi-normal modes spectrum analytically and numerically. Additionally, we derive the broken holographic Ward identity for the $U (1)$ current, and discuss the recently proposed novel transport coefficients for systems with explicitly broken symmetries. The setup considered is expected to serve as a toy model for more realistic situations where quasi-hydrodynamics is at work, such as axial charge relaxation in QCD, spin relaxation in relativistic systems, electric field relaxation in magneto-hydrodynamics, or momentum relaxation in condensed matter systems.
↳ hep-thcond-mat.str-elnucl-thJHEP(2023)·37 citations
07
Hexadecapole strength in the rare isotopes $^{74, 76}$ Kr
M. Spieker · S.E. Agbemava · D. Bazin · S. Biswas P.D. Cottle · P.J. Farris · A. Gade · T. Ginter · S. Giraud · K.W. Kemper · J. Li · W. Nazarewicz · S. Noji and 5 other authors
In the Ge-Sr mass region, isotopes with neutron number $N \leq 40$ are known to feature rapid shape changes with both nucleon number and angular momentum. To gain new insights into their structure, inelastic proton scattering experiments in inverse kinematics were performed on the rare isotopes $^{74, 76}$ Kr. This work focuses on observables related to the $J^{π} = 4_{1}^{+}$ states of the Kr isotopes and, in particular, on the hexadecapole degree of freedom. By performing coupled-channels calculations, hexadecapole deformation parameters $β_{4}$ were determined for the $J^{π} = 4_{1}^{+}$ states of $^{74, 76}$ Kr from inelastic proton scattering cross sections. Two possible coupled-channels solutions were found. A comparison to predictions from nuclear energy density functional theory, employing both non-relativistic and relativistic functionals, clearly favors the large, positive $β_{4}$ solutions. These $β_{4}$ values are unambiguously linked to the well deformed prolate configuration. Given the $β_{2} - β_{4}$ trend, established in this work, it appears that $β_{4}$ values could provide a sensitive measure of the nuclear shell structure.
↳ nucl-exnucl-thPLB(2023)·12 citations

Affiliations

first authorsco-authorsvia INSPIRE

Robust formulation of Wick's theorem for computing matrix elements between Hartree-Fock-Bogoliubov wavefunctions

Sound velocity peak and conformality in isospin QCD

First study of reaction Ξ0n→Ξ−p using Ξ0-nucleus scattering at an electron-positron collider

U(1) quasi-hydrodynamics: Schwinger-Keldysh effective field theory and holography

Hexadecapole strength in the rare isotopes 74,76Kr

Affiliations

First study of reaction $Ξ^{0} n \to Ξ^{-} p$ using $Ξ^{0}$ -nucleus scattering at an electron-positron collider

Hexadecapole strength in the rare isotopes $^{74, 76}$ Kr