1 / 27

高エネルギー加速器研究機構 素粒子原子核研究所 Nov. 20, 2007

KEK 　研究会　「原子核・ハドロン物理：横断研究会」. Thermal properties of neutron matter by lattice calculation with NN effective field theory at the next-to-leading order. T. Abe (CNS, U. of Tokyo) in collaboration with R. Seki (CSUN & KRL, Caltech). 高エネルギー加速器研究機構 素粒子原子核研究所 Nov. 20, 2007. Outline. Motivation

cicely
Télécharger la présentation

高エネルギー加速器研究機構 素粒子原子核研究所 Nov. 20, 2007

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. KEK　研究会　「原子核・ハドロン物理：横断研究会」KEK　研究会　「原子核・ハドロン物理：横断研究会」 Thermal properties of neutron matter by lattice calculation with NN effective field theory at the next-to-leading order T. Abe (CNS, U. of Tokyo) in collaboration with R. Seki (CSUN & KRL, Caltech) 高エネルギー加速器研究機構 素粒子原子核研究所 Nov. 20, 2007

  2. Outline • Motivation • Formulation: NN EFT on the Lattice • LO calc. (c0 only): • 1S0 Pairing Gap @ T ~ 0 in Thermodynamic & Continuum Limits • Phase Diagram of Low-Density Neutron Matter in Thermodynamic & Continuum Limits • NLO calc. (c0 & c2): Preliminary Results & Comparisons w/ LO calc. • 1S0 Pairing Gap @ T ~ 0 in Ns = 43 & n = 1/4 • Phase Diagram of Neutron Matter in Ns = 43 & n = 1/4 • Summary & Outlook

  3. 1S0 Pairing gap △ (Neutron Matter) Motivation BCS gap equation BCS calc kF ~ 1.68 fm-1 (ρ ~ 0.16 fm-3) for neutron matter Polarization effects • D. J. Dean & M. Hjorth-Jensen, Rev. Mod. Phys. 75, 607 (2003)

  4. Motivation • Thermal Properties (Low-density Neutron Matter) - 1S0 Pairing Gap - Phase Diagram Normal-to-Superfluid Phase Transition △(T~0) Tc(ρ) • Calculation Method + Nucleon-Nucleon Effective Field Theory (NN EFT) Lattice Framework Quantum Monte Carlo (QMC) Hybrid Monte Carlo (HMC)

  5. Formulation: NN EFT on the Lattice - Effective Field Theory (EFT) low-energy physics long-distance dynamics - Nucleon-Nucleon Effective Field Theory (NN EFT) Symmetries of underlying theory (QCD) Low-energy theory with the relevant degrees of freedom (N, π, etc.) based on the relevant symmetries of the underlying theory (QCD) in low-energy physics (Lorentz, parity, time-reversal etc.) - Power counting Systematic expansion in powers of p / Q (p: long-distance scale, Q: short-distance scale) Coupling constants Experimental data (phase shift …) connection to the underlying theory (QCD) systematic improvement of the calculations

  6. Formulation • Non-relativistic Hamiltonian w/ • Non-relativistic Lattice Hamiltonian c.f.) Attractive Hubbard Model Extended Attractive Hubbard Model c0 (LO) c0 & c2 (NLO)

  7. R. Seki, & U. van Kolck, Phys. Rev. C 73, 044006 (2006) Effective Range Expansion on the Lattice • Potential Terms • K (reaction) Matrix Luscher’s method ~ K matrix with asymptotically standing-wave boundary condition

  8. Observables (a0, r0) Coupling Constants & Regularization Scale (c0, c2, …, Λ(~π/a)) where R. Seki, & U. van Kolck, Phys. Rev. C 73, 044006 (2006).

  9. LO calc. (c0 only)

  10. Set up • Calculation Methods - Detarminantal Quantum Monte Carlo (DQMC) w/ MDS technique - Hybrid Monte Carlo (HMC) • Parameter set up - kF = 15, 30, 60 MeV - Nt = 2 – 128 (for observing the phase transition) - Ns = 43, 63, 83 (DQMC), & 103 (HMC) (for taking the thermodynamic limit) - n = 1/16, 1/8, 3/16 1/4, 3/8, & 1/2 (for taking the continuum limit) sample # ~ 2,000 – 10,000 with 50 – 100 thermalization steps Performed @ NERSC Seaborg, Bassi & Titech GRID, TSUBAME

  11. Results & Discussions a. 1S0 Pairing Gap @ T ~ 0 kF = 0.15 fm-1(30 MeV) a = 12.82 fm t = 0.1261 MeV Ns = 83 • S-wave Pair Correlation Function w/ S-wave pair field & # of spatial lattice sites • Estimation of Δ • Matrix-decomposition Stabilization Method M. Guerrero, G. Ortiz, & E. Gubernatis, Phys. Rev. B 62, 600 (2000)

  12. 1S0 pairing gap △ in thermodynamic & continuum limits thermodynamic limit continuum limit N -> ∞ n -> 0 (a -> 0) kF = 0.3 fm-1(60 MeV) Ns = 63

  13. 1S0 pairing gap △ in thermodynamic & continuum limits T. Abe & R. Seki, arXiv:07082523 BCS calc w/ polarization effects Ø. Elgarøy, L. Engvik, M. Hjorth-Jensen & E. Osnes, Nucl. Phys. A 604, 446 (1996) J. Wambach, T. L. Ainsworth & D. Pines, Nucl. Phys. A 555, 128 (1993)

  14. Discussions about 1S0 pairing gap △ • the size of △ no evidence of significant suppression of △ • ratio of △MC to △MF noticeable reduction of △MCfrom △MFby ~ 30 % • importance of pairing correlation induced by many-body effects even at low density ρ ~ 10-4ρ0– 10-2ρ0 (ρ0 = 0.16 fm-3)

  15. b. Phase Diagram: 1S0 Superfluid Phase Transition • Results & Discussions • S-wave Pair Correlation Function w/ Tc kF = 0.15 fm-1(30 MeV) a = 12.82 fm t = 0.1261 MeV N = 83 • Determination of Tc Tc is given by the inflexion point of

  16. Results & Discussions b. Phase Diagram: Pseudo Gap kF = 0.15 fm-1(30 MeV) a = 12.82 fm t = 0.1261 MeV N = 83 • Pauli Spin Susceptibility T* • Determination of T* T*is identified with the maximum position of (BCS limit) (BEC limit) • A. Sewer, X. Zotos & H. Beck, Phys. Rev. B66,140504 (2002)

  17. BCS-BEC Crossover BEC BCS (BCS limit) (BEC limit) |c0|/(a3t) = 0, 2, 4, 6, 8, 10, 12 (from top to bottom) A. Sewer, X. Zotos & H. Beck, Phys. Rev. B66,140504 (2002)

  18. Finite-size Scaling for Tc & T* continuum limit kF = 60 MeV kF = 30 MeV kF = 15 MeV thermodynamic limit E. Burovski, N. Prokofev, B. Svistunov, & M. Troyer, Phys. Rev. Lett. 96, 160402 (2006)

  19. Phase Diagram in thermodynamic & continuum limits T. Abe & R. Seki, arXiv:07082523 T* normal pseudo gap Tc 1S0 superfluid

  20. Discussions about Phase Diagram • phase diagram of low-density neutron matter - drawn for the first time in a sense of ab initio calculation - existence of pseudo gap phase induced by the strong short-range correlation • △/T - approach the BCS value (△MF/Tc ~ 1.76) as the density decreases • evidence of the deviation from BCS weak-coupling approx. even at low density rangingρ ~ 10-4ρ0 – 10-2ρ0

  21. NLO calc. (c0 & c2)

  22. Determinantal Quantum Monte Carlo (DQMC) Method • Lattice Hamiltonian c0 (LO) c0 & c2 (NLO)

  23. Set up • Calculation Methods - Detarminantal Quantum Monte Carlo (DQMC) w/ MDS technique All orders in c0 included, c2 treated perturbatively • Parameter set up - kF = 60, 90, 120 MeV - Temporal lattice: Nt = 4 – 128 (for observing the phase transition) - Spatial lattice: Ns = 43 - Lattice filling: n = 1/4 sample # ~ 1,000 – 10,000 with 10 – 100 thermalization steps Performed @ NERSC Seaborg, Bassi & Titech GRID, TSUBAME • Comparison w/ one-parameter calc. @ Ns = 43 & kF = 60, 90, 120 MeV

  24. 4. Preliminary Result & Comparison: △ @ Ns = 43 & n = 1/4 (w/o taking thermodynamic & continuum limits) BCS calc preliminary LO (c0 only) NLO (c0 & c2) w/ polarization effects ρ ~ 0.05ρ0 ρ ~ 0.02ρ0 Ø. Elgarøy, L. Engvik, M. Hjorth-Jensen & E. Osnes, Nuclear Phys. A 604, 446 (1996) J. Wambach, T. L. Ainsworth & D. Pines, Nuclear Phys. A 555, 128 (1993)

  25. 4. Preliminary Result & Comparison: Phase Diagram @ Ns = 43 & n = 1/4 (w/o taking thermodynamic & continuum limits) T* preliminary Tc normal pseudo gap 1S0 superfluid

  26. Summary LO calc. (c0 only) • LO calc. @ T≠0 in Ns = 43, 63, 83 (DQMC), 103 (HMC) & Nt =2 – 128 • NLO calc. @ T≠0 in Ns = 43 & Nt =4 – 128 (DQMC) • 1S0 pairing gap @ T ~ 0 - Reduction of △ by ~ 30 % from BCS weak-coupling approx. • Phase diagram - Existence of Pseudo gap • Importance of neutron-neutron pairing correlation even at low density NLO calc. (c0 & c2)preliminary • 1S0 pairing gap @ T ~ 0 & phase diagram @ Ns = 43, n = 1/4 & kF = 60, 90, 120 MeV - △ decreased - Tc & T* unaltered btw LO & NLO calc. -> thermodynamics controlled by LO ?? • Feasible approach for the consistent calculation w/ NN EFT up to ~ the pion mass (at least @ T~ 0)

  27. Outlook • Completion of NLO calc. in thermodynamic & continuum limits • Calculation @ higher density by includingpions, … • Other partial waves 3P-F2, … <- astrophysical interest from internal structure of NS • Nuclear matter enhancement of △ by polarization effects??, … • Application to the finite nuclei di-neutron correlation in halo nuclei (dimer), neutron nugget, … ρ0 = 0.16 fm-3

More Related