Neutron matter: a superfluid gas

Chang, Sang‐Yoon; Morales, J. R.; Pandharipande, V.R.; Ravenhall, D. G.; Carlson, J.; Pieper, Steven C.; Wiringa, R. B.; Schmidt, Kevin

doi:10.1016/j.nuclphysa.2004.09.119

Cited by 30 publications

(31 citation statements)

References 17 publications

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“…There have been a number of Green's Function Monte Carlo simulations of light nuclei based on AV18 as well as other phenomenological potentials, see for example [15,28,29,30,31,32,33]. A related technique implementing diffusion Monte Carlo with auxiliary fields has been used to study the ground state of neutron matter and neutron droplets [34,35,36,37]. The No-Core Shell Model (NCSM) is a different approach to light nuclei which uses basis-truncated eigenvector methods.…”

Section: Introductionmentioning

confidence: 99%

Lattice simulations for light nuclei: Chiral effective field theory at leading order

et al. 2007

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We discuss lattice simulations of light nuclei at leading order in chiral effective field theory. Using lattice pion fields and auxiliary fields, we include the physics of instantaneous one-pion exchange and the leading-order S-wave contact interactions. We also consider higher-derivative contact interactions which adjust the S-wave scattering amplitude at higher momenta. By construction our lattice path integral is positive definite in the limit of exact Wigner SU(4) symmetry for any even number of nucleons. This SU(4) positivity and the approximate SU(4) symmetry of the low-energy interactions play an important role in suppressing sign and phase oscillations in Monte Carlo simulations. We assess the computational scaling of the lattice algorithm for light nuclei with up to eight nucleons and analyze in detail calculations of the deuteron, triton, and helium-4.

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Section: Introductionmentioning

confidence: 99%

Lattice simulations for light nuclei: Chiral effective field theory at leading order

et al. 2007

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“…The function Ψ(R) ≡ Ψ(R, τ → ∞), which is the lowest energy state of the system having the nodes of ψ T (R), is obtained from the large-time evolution of f (R, τ ). The trial wave function we consider has the general form [11,13] …”

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confidence: 99%

“…Any residual bias in the extrapolated estimator is reduced if the trial function ψ T (R) has a large overlap with Ψ(R). Consequently, compared to the calculation of the eigenenergies, the optimization of ψ T is a more important issue in the calculation of observables like the OBDM and TBDM [13].…”

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confidence: 99%

Momentum Distribution and Condensate Fraction of a Fermion Gas in the BCS-BEC Crossover

et al. 2005

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By using the diffusion Monte Carlo method we calculate the one-and two-body density matrix of an interacting Fermi gas at T = 0 in the BCS-BEC crossover. Results for the momentum distribution of the atoms, as obtained from the Fourier transform of the one-body density matrix, are reported as a function of the interaction strength. Off-diagonal long-range order in the system is investigated through the asymptotic behavior of the two-body density matrix. The condensate fraction of fermionic pairs is calculated in the unitary limit and on both sides of the BCS-BEC crossover. PACS numbers:The physics of the crossover from Bardeen-CooperSchrieffer (BCS) superfluids to molecular Bose-Einstein condensates (BEC) in ultracold Fermi gases near a Feshbach resonance is a very exciting field that has recently attracted a lot of interest, both from the experimental [1,2] and the theoretical side [3]. An important experimental achievement is the observation of a condensate of pairs of fermionic atoms on the side of the Feshbach resonance where no stable molecules would exist in vacuum [4,5]. Although the interpretation of the experiment is not straightforward, as it involves an out-of-equilibrium projection technique of fermionic pairs onto bound molecules [6], it is believed that these results strongly support the existence of a superfluid order parameter in the strongly correlated regime on the BCS side of the resonance [5].The occurrence of off-diagonal long-range order (ODLRO) in interacting systems of bosons and fermions was investigated by C.N. Yang in terms of the asymptotic behavior of the one-and two-body density matrix [7]. In the case of a two-component Fermi gas with N ↑ spin-up and N ↓ spin-down particles, the one-body density matrix (OBDM) for spin-up particles, defined asdoes not possess any eigenvalue of order N ↑ . This behavior implies for homogeneous systems the asymptotic condition ρ 1 (rIn the above expression ψ † ↑ (r) (ψ ↑ (r)) denote the creation (annihilation) operator of spin-up particles. The same result holds for spin-down particles. ODLRO may occur instead in the two-body density matrix (TBDM), that is defined asFor an unpolarized gas with N ↑ = N ↓ = N/2, if ρ 2 has an eigenvalue of the order of the total number of particles N , the TBDM can be written as a spectral decomposition separating the largest eigenvalue,2 containing only eigenvalues of order one. The parameter α ≤ 1 in Eq. (3) is interpreted as the condensate fraction of pairs, in a similar way as the condensate fraction of single atoms is derived from the OBDM.The spectral decomposition (3) yields for homogeneous systems the following asymptotic behavior of the TBDMThe complex function ϕ is proportional to the order parameter ψ ↑ (r 1 )ψ ↓ (r 2 ) = αN/2ϕ(|r 1 − r 2 |), whose appearance distinguishes the superfluid state of the Fermi gas. Equation (4) should be contrasted with the behavior of Bose systems with ODLRO, where ρ 1 has an eigenvalue of order N [8], and consequently the largest eigenvalue of ρ 2 is of the order of N 2 . In thi...

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“…Some recent work includes the no-core shell model [1][2][3][4][5], constrained-path [6][7][8][9] and fixed-node [10,11] Green's function Monte Carlo calculations, auxiliary-field diffusion Monte Carlo calculations [12][13][14], and coupled cluster methods [15][16][17]. The diversity of methods is useful since each technique has its own computational scaling, systematic errors, and range of accessible problems.…”

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confidence: 99%