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Quantum Reports

Spectral Explanation for Statistical Odd-Even Staggering in Few Fermions Systems

Angelo Plastino, G.L. Ferri, Angel Ricardo Plastino

Published Feb 16, 2021• 5 citations
Publisher

Abstract

Odd-even statistical staggering in a Lipkin-like few fermions model has been recently encountered. Of course, staggering in nuclear binding energies is a well established fact. Similar effects are detected in other finite fermion systems as well, as for example, ultra small metallic grains and metal clusters. We work in this effort with the above-mentioned Lipkin-like, two-level fermion model and show that statistical staggering effects can be detailedly explained by recourse to a straightforward analysis of the associated energy-spectra.

DOI
10.3390/quantum3010010

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Odd-even statistical staggering in a Lipkin-like few fermions model has been recently encountered. Of course, staggering in nuclear binding energies is a well established fact. Similar effects are detected in other finite fermion systems as well, as for example, ultra small metallic grains and metal clusters. We work in this effort with the above-mentioned Lipkin-like, two-level fermion model and show that statistical staggering effects can be detailedly explained by recourse to a straightforward analysis of the associated energy-spectra.
Odd-even staggering of binding energies is studied in finite fermion systems with pairing correlations. We discuss contributions of the pairing and mean field to the staggering, and we construct the binding-energy indicators which measure the magnitude of pairing correlations and the effective single-particle spacings in a given system. The analysis is based on studying several exactly solvable many-body Hamiltonians as well as on the analytical formulas that can be applied in the weak and strong pairing limits.
Finite quantum many fermion systems are essential for our current understanding of Nature. They are at the core of molecular, atomic, and nuclear physics. In recent years, the application of information and complexity measures to the study of diverse types of many-fermion systems has opened a line of research that elucidates new aspects of the structure and behavior of this class of physical systems. In this work we explore the main features of information and information-based complexity indicators in exactly soluble many-fermion models of the Lipkin kind. Models of this kind have been extremely useful in shedding light on the intricacies of quantum many body physics. Models of the Lipkin kind play, for finite systems, a role similar to the one played by the celebrated Hubbard model of solid state physics. We consider two many fermion systems and show how their differences can be best appreciated by recourse to information theoretic tools. We appeal to information measures as tools to compare the structural details of different fermion systems. We will discover that few fermion systems are endowed by a much larger complexity-degree than many fermion ones. The same happens with the coupling-constants strengths. Complexity augments as they decrease, without reaching zero. Also, the behavior of the two lowest lying energy states are crucial in evaluating the system's complexity.
An effective boson Hamiltonian is derived from the original Hamiltonian of a many-fermion system. The results show that when the intrinsic motion of bosons is collective and the excitation energies of the system are small, the effective boson-boson interaction can be reduced to a two-body interaction while for odd systems or systems with uncorrelated fermions, there is an additional two-body boson-fermion interaction. Both these interactions can be calculated from the original fermion-fermion ones. Thus, the microscopic foundation of the interacting boson model is established without recourse to mapping procedures.NUCLEAR STRUCTURE Interacting boson model, boson fermion hybrid representation, microscopic foundation.