https://doi.org/10.1140/epja/s10050-025-01606-5
Review
Equation of state of quantum cluster matter
1
Department of Physics, Osaka Metropolitan University, 3-3-138, 558-8585, Sugimoto-cho, Sumiyoshi-ku, Osaka, Japan
2
Department of Physics, Keio University, 3-14-1, 223-8522, Hiyoshi, Kohoku-ku, Yokohama, Japan
3
Department of Physics, Chuo University, 1-13-27, Kasuga, Bunkyo-ku, 112-8551, Tokyo, Japan
4
Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138, Sugimoto-cho, Sumiyoshi-ku, 558-8585, Osaka, Japan
Received:
3
March
2025
Accepted:
30
May
2025
Published online:
19
June
2025
This review article deals with the role of quantum clusters in the hierarchical structure of quantum many-body systems, especially focusing on a two-component spin-1/2 ultracold Fermi gas. Quantum clusters, which are loosely bound states with both atomic and molecular properties, play a key role in hierarchical transitions. We explain how an atom-molecule transition continuously occurs by using a Feshbach resonance. We also explain how this hierarchy is reflected in the so-called BCS-BEC crossover phase diagram, where a normal Fermi gas phase and a normal Bose gas phase form a hierarchy structure, and the pseudogap phase appears between them as an intermediate “semi-hierarchy.” The crossover region is shown to be conveniently determined by using the specific heat at constant volume, as well as the spin susceptibility. We also point out that the isothermal compressibility is a useful quantity to see how an atomic interaction gives rise to an intermolecular one. Future experiments on thermodynamic quantities would be crucial for the assessment of these theoretical results, as well as the further understanding of hierarchical many-body systems.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
