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On the dynamical kernels of fermionic equations of motion in strongly-correlated media

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Abstract

Two-point fermionic propagators in strongly-correlated media are considered with an emphasis on the dynamical interaction kernels of their equations of motion (EOM). With the many-body Hamiltonian confined by a two-body interaction, the EOMs for the two-point fermionic propagators acquire the Dyson form and, before taking any approximation, the interaction kernels decompose into the static and dynamical (time-dependent) contributions. The latter translate to the energy-dependent and the former map to the energy-independent terms in the energy domain. We dwell particularly on the energy-dependent terms, which generate long-range correlations while making feedback on their short-range static counterparts. The origin, forms, and various approximations for the dynamical kernels of one-fermion and two-fermion propagators, most relevant in the intermediate-coupling regime, are discussed. Applications to the electromagnetic dipole response of \(^{68,70}\)Ni and low-energy quadrupole response of \(^{114,116,124}\)Sn are presented.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All data generated during this study are contained in this published article.]

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Acknowledgements

Illuminating discussions with Mark Spieker, Nadezhda Tsoneva, Enrico Vigezzi, and Horst Lenske are gratefully acknowledged. This work was supported by the GANIL Visitor Program, US-NSF Grant PHY-2209376, and US-NSF Career Grant PHY-1654379.

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  1. Department of Physics, Western Michigan University, 1903 W Michigan Ave, Kalamazoo, MI, 49008-5252, USA

    Elena Litvinova

  2. Facility for Rare Isotope Beams, Michigan State University, 640 S Shaw Lane, East Lansing, Michigan, 48824, USA

    Elena Litvinova

  3. GANIL, CEA/DRF-CNRS/IN2P3, Bd Henri Becquerel, Caen, 14076, Calvados, France

    Elena Litvinova

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Communicated by David Blaschke.

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Litvinova, E. On the dynamical kernels of fermionic equations of motion in strongly-correlated media. Eur. Phys. J. A 59, 291 (2023). https://doi.org/10.1140/epja/s10050-023-01198-y

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