Adiabatic projection method with Euclidean time subspace projection

  • Serdar ElhatisariEmail author
Regular Article - Theoretical Physics


Euclidean time projection is a powerful tool that uses exponential decay to extract the low-energy information of quantum systems. The adiabatic projection method, which is based on Euclidean time projection, is a procedure for studying scattering and reactions on the lattice. The method constructs the adiabatic Hamiltonian that gives the low-lying energies and wave functions of two-cluster systems. In this paper we seek the answer to the question whether an adiabatic Hamiltonian constructed in a smaller subspace of the two-cluster state space can still provide information on the low-lying spectrum and the corresponding wave functions. We present the results from our investigations on constructing the adiabatic Hamiltonian using Euclidean time projection and extracting details of the low-energy spectrum and wave functions by diagonalizing it. In our analyses we consider systems of fermion-fermion and fermion-dimer interacting via a zero-range attractive potential in one dimension, and fermion-fermion interacting via an attractive Gaussian potential in three dimensions. The results presented here provide a guide for improving the adiabatic projection method and for reducing the computational costs of large-scale calculations of ab initio nuclear scattering and reactions using Monte Carlo methods.


  1. 1.
    T.A. Weaver, S.E. Woosley, Phys. Rep. 227, 65 (1993)ADSCrossRefGoogle Scholar
  2. 2.
    E.G. Adelberger et al., Rev. Mod. Phys. 83, 195 (2011) arXiv:1004.2318 [nucl-ex]ADSCrossRefGoogle Scholar
  3. 3.
    A.D. Leva, L. Gialanella, F. Strieder, J. Phys. Conf. Ser. 665, 012002 (2016)CrossRefGoogle Scholar
  4. 4.
    K.M. Nollett, S.C. Pieper, R.B. Wiringa, J. Carlson, G.M. Hale, Phys. Rev. Lett. 99, 022502 (2007) arXiv:nucl-th/0612035ADSCrossRefGoogle Scholar
  5. 5.
    P. Navratil, S. Quaglioni, Phys. Rev. Lett. 108, 042503 (2012) arXiv:1110.0460 [nucl-th]ADSCrossRefGoogle Scholar
  6. 6.
    G. Hagen, N. Michel, Phys. Rev. C 86, 021602 (2012) arXiv:1206.2336 [nucl-th]ADSCrossRefGoogle Scholar
  7. 7.
    S. Quaglioni, C. Romero-Redondo, P. Navratil, Phys. Rev. C 88, 034320 (2013) 94ADSCrossRefGoogle Scholar
  8. 8.
    S. Elhatisari, D. Lee, G. Rupak, E. Epelbaum, H. Krebs, T.A. Lähde, T. Luu, Ulf-G. Meißner, Nature 528, 111 (2015) arXiv:1506.03513 [nucl-th]ADSCrossRefGoogle Scholar
  9. 9.
    P. Navratil, S. Quaglioni, G. Hupin, C. Romero-Redondo, A. Calci, Phys. Scr. 91, 053002 (2016) arXiv:1601.03765 [nucl-th]ADSCrossRefGoogle Scholar
  10. 10.
    J. Dohet-Eraly, P. Navratil, S. Quaglioni, W. Horiuchi, G. Hupin, F. Raimondi, Phys. Lett. B 757, 430 (2016) arXiv:1510.07717 [nucl-th]ADSCrossRefGoogle Scholar
  11. 11.
    T.A. Lähde, U.-G. Meißner, Lect. Notes Phys. 957, 1 (2019)CrossRefGoogle Scholar
  12. 12.
    G. Rupak, D. Lee, Phys. Rev. Lett. 111, 032502 (2013) arXiv:1302.4158 [nucl-th]ADSCrossRefGoogle Scholar
  13. 13.
    M. Pine, D. Lee, G. Rupak, Eur. Phys. J. A 49, 151 (2013) arXiv:1309.2616 [nucl-th]ADSCrossRefGoogle Scholar
  14. 14.
    S. Elhatisari, D. Lee, Phys. Rev. C 90, 064001 (2014) arXiv:1407.2784 [nucl-th]ADSCrossRefGoogle Scholar
  15. 15.
    G. Rupak, P. Ravi, Phys. Lett. B 741, 301 (2015) arXiv:1411.2436 [nucl-th]ADSCrossRefGoogle Scholar
  16. 16.
    A. Rokash, M. Pine, S. Elhatisari, D. Lee, E. Epelbaum, H. Krebs, Phys. Rev. C 92, 054612 (2015) arXiv:1505.02967 [nucl-th]ADSCrossRefGoogle Scholar
  17. 17.
    S. Elhatisari, D. Lee, Ulf-G. Meißner, G. Rupak, Eur. Phys. J. A 52, 174 (2016) arXiv:1603.02333 [nucl-th]ADSCrossRefGoogle Scholar
  18. 18.
    S. Elhatisari et al., Phys. Rev. Lett. 117, 132501 (2016) arXiv:1602.04539 [nucl-th]ADSCrossRefGoogle Scholar
  19. 19.
    B.N. Lu, T.A. Lähde, D. Lee, Ulf-G. Meißner, Phys. Rev. D 90, 034507 (2014) arXiv:1403.8056 [nucl-th]ADSCrossRefGoogle Scholar
  20. 20.
    G. Stellin, S. Elhatisari, Ulf-G. Meißner, Eur. Phys. J. A 54, 232 (2018) arXiv:1809.06109 [nucl-th]ADSCrossRefGoogle Scholar
  21. 21.
    B.N. Lu, T.A. Lähde, D. Lee, Ulf-G. Meißner, Phys. Lett. B 760, 309 (2016) arXiv:1506.05652 [nucl-th]ADSCrossRefGoogle Scholar
  22. 22.
    B. Borasoy, E. Epelbaum, H. Krebs, D. Lee, Ulf-G. Meissner, Eur. Phys. J. A 34, 185 (2007) arXiv:0708.1780 [nucl-th]ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of EngineeringKaramanoglu Mehmetbey UniversityKaramanTurkey

Personalised recommendations