Abstract.
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.
Similar content being viewed by others
References
T.A. Weaver, S.E. Woosley, Phys. Rep. 227, 65 (1993)
E.G. Adelberger et al., Rev. Mod. Phys. 83, 195 (2011) arXiv:1004.2318 [nucl-ex]
A.D. Leva, L. Gialanella, F. Strieder, J. Phys. Conf. Ser. 665, 012002 (2016)
K.M. Nollett, S.C. Pieper, R.B. Wiringa, J. Carlson, G.M. Hale, Phys. Rev. Lett. 99, 022502 (2007) arXiv:nucl-th/0612035
P. Navratil, S. Quaglioni, Phys. Rev. Lett. 108, 042503 (2012) arXiv:1110.0460 [nucl-th]
G. Hagen, N. Michel, Phys. Rev. C 86, 021602 (2012) arXiv:1206.2336 [nucl-th]
S. Quaglioni, C. Romero-Redondo, P. Navratil, Phys. Rev. C 88, 034320 (2013) 94
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]
P. Navratil, S. Quaglioni, G. Hupin, C. Romero-Redondo, A. Calci, Phys. Scr. 91, 053002 (2016) arXiv:1601.03765 [nucl-th]
J. Dohet-Eraly, P. Navratil, S. Quaglioni, W. Horiuchi, G. Hupin, F. Raimondi, Phys. Lett. B 757, 430 (2016) arXiv:1510.07717 [nucl-th]
T.A. Lähde, U.-G. Meißner, Lect. Notes Phys. 957, 1 (2019)
G. Rupak, D. Lee, Phys. Rev. Lett. 111, 032502 (2013) arXiv:1302.4158 [nucl-th]
M. Pine, D. Lee, G. Rupak, Eur. Phys. J. A 49, 151 (2013) arXiv:1309.2616 [nucl-th]
S. Elhatisari, D. Lee, Phys. Rev. C 90, 064001 (2014) arXiv:1407.2784 [nucl-th]
G. Rupak, P. Ravi, Phys. Lett. B 741, 301 (2015) arXiv:1411.2436 [nucl-th]
A. Rokash, M. Pine, S. Elhatisari, D. Lee, E. Epelbaum, H. Krebs, Phys. Rev. C 92, 054612 (2015) arXiv:1505.02967 [nucl-th]
S. Elhatisari, D. Lee, Ulf-G. Meißner, G. Rupak, Eur. Phys. J. A 52, 174 (2016) arXiv:1603.02333 [nucl-th]
S. Elhatisari et al., Phys. Rev. Lett. 117, 132501 (2016) arXiv:1602.04539 [nucl-th]
B.N. Lu, T.A. Lähde, D. Lee, Ulf-G. Meißner, Phys. Rev. D 90, 034507 (2014) arXiv:1403.8056 [nucl-th]
G. Stellin, S. Elhatisari, Ulf-G. Meißner, Eur. Phys. J. A 54, 232 (2018) arXiv:1809.06109 [nucl-th]
B.N. Lu, T.A. Lähde, D. Lee, Ulf-G. Meißner, Phys. Lett. B 760, 309 (2016) arXiv:1506.05652 [nucl-th]
B. Borasoy, E. Epelbaum, H. Krebs, D. Lee, Ulf-G. Meissner, Eur. Phys. J. A 34, 185 (2007) arXiv:0708.1780 [nucl-th]
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by V. Somà
Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Author’s comment: All data generated during this study are contained in this published article.]
Publisher’s Note
The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Elhatisari, S. Adiabatic projection method with Euclidean time subspace projection. Eur. Phys. J. A 55, 144 (2019). https://doi.org/10.1140/epja/i2019-12844-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epja/i2019-12844-9