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David J. Dean ORNL

The Rare Isotope Accelerator and Nuclear Theory. David J. Dean ORNL. Outline Perspectives on RIA Ab initio coupled-cluster theory applied to 16 O The space and the Hamiltonian The CC method Ground- and excited state implementation: CCSD Triples Corrections: CR-CCSD(T)

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David J. Dean ORNL

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  1. The Rare Isotope Accelerator and Nuclear Theory David J. Dean ORNL • Outline • Perspectives on RIA • Ab initio coupled-cluster theory applied to 16O • The space and the Hamiltonian • The CC method • Ground- and excited state implementation: CCSD • Triples Corrections: CR-CCSD(T) • Conclusions

  2. Nuclei and RIA • Scientific Thrusts: • How do complex systems emerge from simple ingredients (interaction question)? • What are the simplicities and regularities in complex systems (shell/symmetries question)? • How are elements produced in the Universe (astrophysics question)? • Broad impact of neutron-rich nuclei: • Nuclei as laboratories for tests of ‘standard model physics’. • Nuclear reactions relevant to astrophysics. • Nuclear reactions relevant to Science Based Stockpile Stewardship. • Nuclear transportation, safety, and criticality issues.

  3. The opportunity: connection of nuclear structure and reaction theory and simulation to the Rare Isotope Accelerator • RIA: $1 billion facility, • near-term number-three priority • (first priority in Nuclear Physics) • CD-0 approved, moving to CD-1 • OSTP Report: • directs DOE and NSF to • ‘generate a roadmap for RIA’.

  4. Nanoscale Molecules ~10 nm Molecular scale: conductance through molecules. Delocalized conduction orbitals 2-d quantum dot in strong magnetic field. The field drives localization. Nuclei ~5 fm • Studies of the interaction • Degrees of freedom • Astrophysical implications Quantum many-body problem is everywhere • Quantum mechanics plays a role when • the size of the object is of the same order • as the interaction length. • Common properties • Shell structure • Excitation modes • Correlations • Phase transitions • Interactions with external probes

  5. Steps toward solutions Begin with a bare NN (+3N) Hamiltonian Bare (GFMC) Basis expansion • Basis expansions: • Choose the method of solution • Determine the appropriate basis • Generate Heff Oscillator single-particle basis states Many-body basis states Many-body problems

  6. The ORNL-Oslo-MSU collaboration on nuclear many-body problems David Dean (CC methods for nuclei and extensions to V3N) Thomas Papenbrock David Bernholdt (Computer Science and Mathematics) Trey White, Kenneth Roche (Computational Science) Research Plan -- Excited states (!) -- Observables (!) -- Triples corrections (!) -- Open shells -- V3N -- 50<A<100 -- Reactions -- TD-CCSD?? Piotr Piecuch (CC methods in chemistry and extensions) Karol Kowalski (to PNNL) Marta Wloch Jeff Gour Morten Hjorth-Jensen (Effective interactions) Maxim Kartamychev (3-body forces in nuclei) Gaute Hagen (effective interactions; to ORNL in May)

  7. = + +… h G h CC-ph p p Choice of model space and the G-matrix Q-Space P-Space ph intermediate states Use BBP to eliminate w-dependence below fermi surface.

  8. In the near future: similarity transformed H K. Suzuki and S.Y. Lee, Prog. Theor. Phys. 64, 2091 (1980) P. Navratil, G.P. Kamuntavicius, and B.R. Barrett, Phys. Rev. C61, 044001 (2000) • Advantage: no parameter dependence in the interaction • Current status • Exact deuteron energy obtained in P space • Working on full implementation in CC theory. • G-matrix + all folded-diagrams+… • Implemented, new results cooking….stay tuned.

  9. Fascinating Many-body approach: Coupled Cluster Theory • Some interesting features of CCM: • Fully microscopic • Size extensive: • only linked diagrams enter • Size consistent: • the energy of two non-interacting • fragments computed separately is the same as that • computed for both fragments simultaneously • Capable of systematic improvement • Amenable to parallel computing Computational chemistry: 100’s of publications in any year (Science Citation Index) for applications and developments.

  10. Coupled Cluster Theory Correlation operator Correlated Ground-State wave function Reference Slater determinant Energy Amplitude equations • Nomenclature • Coupled-clusters in singles and doubles (CCSD) • …with triples corrections CCSD(T); Dean & Hjorth-Jensen, PRC69, 054320 (2004); Kowalski, Dean, Hjorth-Jensen, Papenbrock, Piecuch, PRL92, 132501 (2004)

  11. Derivation of CC equations T1 amplitudes from: Note T2 amplitudes also come into the equation.

  12. T2 amplitudes from: Nonlinear terms in t2 (4th order) An interesting mess. But solvable….

  13. 2nd order 3rd order Correspondence with MBPT

  14. A few more diagrams + all diagrams of this kind (11 more) 4th order [replace t(2) and repeat above 3rd order calculation] + all diagrams of this kind (6 more) 4th order

  15. Calculations for 16O Reasonably converged (N3LO gives -6.95 MeV/A) • Idaho-A: No Coulomb • Coulomb: +0.7 MeV • Expt result is -8.0 MeV/A

  16. Nuclear Properties Also includes second-order corrections from the two-body density.

  17. Very preliminary investigations in 16O neighbors (N3LO, 6 shells, not converged) Calculated ground-state energy Experiment (E/A) 15O 6.0864 (PR-EOMCCSD) 7.4637 16O 6.9291 (CCSD) 7.9762 17O 6.6505 (PA-EOMCCSD) 7.7507

  18. Moving to larger model spaces always requires innovation • CCSD code written for IBM using MPI. • Performs at 0.18 Tflops on 100 processors RAM. • Requires further optimization for new science. • Problem size increases by about a factor of 5 for each major oscillator shell • Number of unknowns by a factor of 2 ( for each step in N) • Number of unknowns by a factor of 20 (for 4 times the particles)

  19. Correcting the CCSD results by non-iterative methods Goal: Find a method that will yield the complete diagonalization result in a given model space How do we obtain the triples correction? How do our results compare with ‘exact’ results in a given model space, for a given Hamiltonian? “Completely Renormalized Coupled Cluster Theory” P. Piecuch, K. Kowalski, P.-D. Fan, I.S.O. Pimienta, and M.J. McGuire, Int. Rev. Phys. Chem. 21, 527 (2002)

  20. Completely renormalized CC in one slide CC generating functional T(A) = model correlation Leading order terms in the triples equation Different choices of Y will yield slightly different triples corrections

  21. Extrapolations: EOMCCSD level Wloch, Dean, Gour, Hjorth-Jensen, Papenbrock, Piecuch, PRL, submitted (2005)

  22. CCSD CR-CCSD(T) Relationship between diagonalization and CC amplitudes “Disconnected quadruples” “Connected quadruples”

  23. Supercomputing of the 1960s 1964, CDC6600, first commercially successful supercomputer; 9 MFlops 1969, CDC7600, 40 Mflops 1965: The ion-channeling effect, one of the first materials physics discoveries made using computers, is key to the ion implantation used by current chip manufacturers to "draw" transistors with boron atoms inside blocks of silicon. 1967, Computer simulations used to calculate radiation dosages. 1969, early days of the internet.

  24. Office of Science Computing Today 2001, Dispersive waves in magnetic reconnection NERSC: IBM/RS6000 (9.1 TFlops peak) CRAY-X1 at ORNL Precursor to NLCF (300 TF, FY06) 2003, Turbulent flow in Tokomak Plasmas

  25. Today’s science on today’s computers Reacting flow science Accelerator design Type IA supernova explosion (BIG SPLASH) Multiscale model of HIV Atmospheric models Structure of deutrons and nuclei Fusion Stellarator Materials: Quantum Corral

  26. Conclusions and perspectives • Solution of the nuclear many-body problems requires extensive use of • computational and mathematical tools. Numerical analysis becomes • extremely important; methods from other fields (chemistry, CS) • invaluable. • Detailed investigation of triples corrections via CR-CCSD(T) • indicates convergence at the triples level (in small space) for • both He and O calculations. Promising result. • Excited states calculated for the first time using EOMCCSD in O-16 • O-16 nearly converged at 8 oscillator shells (shells, not Nhw). • Continuing work on the interaction; efforts to move to similarity • transformed G are underway. • Open shell systems is the next big algorithmic step; EOMCCSD for • larger model spaces underway; Ca-40 underway; V3N beginning • Time-dependent CC theory for reactions?

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