Bridging the quartet and pair pictures of isovector proton-neutron pairing

$α$-like quartetting in the excited states of proton-neutron pairing Hamiltonians

“…( 6) one can see that in this approximation the quartets contains only those 4-body correlations generated by the isospin coupling. We remark that it has been recently shown that the QCM state (5) results from the projection on the isospin T = 0 and the particle number of the BCS-type function e Γ + 0 |− [20].…”

Biexciton-like quartet condensates in an electron-hole liquid

“…We note that while more sophisticated variational wave functions with the use of Hubbard-Stratonovich transformation are proposed in the studies of finite nuclei [13,14], the present wave function has an advantage in the practical numerical calculation of the physical quantities at the thermodynamic limit because of its natural extension of the BCS wave function.…”

“…While it is known that superconductors and fermionic superfluids are triggered by the formation of two-body loosely-bound states called Cooper pairs as a result of the Fermi-surface instability in the presence of twobody attractions [2], it is an interesting problem to explore condensation phenomena accompanying more than two-body bound states. While spin-1/2 fermions with s-wave interaction tend to form two-body Cooper pairs because of its spin degree of freedom and Pauli's exclusion principles, multi-body counterparts such as Cooper triples [3][4][5][6] and quartets [7][8][9][10][11][12][13][14][15] can be formed in the presence of larger degrees of freedom for fermions (e.g., isospin, color, atomic hyperfine states).…”

“…Nuclear equation of state and their droplet properties are associated with strongly attractive nuclear forces leading to the formation of bound states such as deuteron, alpha particle, and heavier nuclei in the low-density region [42], and the Fermi degenerate pressure of nucleons and multi-body forces in the high-density region [43]. Since alpha particle consisting of two neutrons and two protons is a stable cluster state with a large binding energy, the socalled alpha-particle condensation has been extensively studied in the context of Cooper quartets [7][8][9][10][11][12][13][14][15]. Note that fluctuation-driven quartet formations have also been investigated in unconventional superconductors [44,45].…”

“…(Note that we call it "biexciton-like" since a Cooper quartet considered here is a loosely-bound quantum state, unlike usual point-like bound states.) Recently, such a framework has been employed to study pair and quartet correlations in nuclear systems [10,[13][14][15]. Effects of Fermi degenerate pressure are automatically considered in this framework as in the usual BCS theory.…”