We propose a new method that transcribes the fermion system to the boson-fermion system by introducing a unitary operator defined in the whole boson-fermion space. We obtain the boson-fermion expansion of the fermion pair operators such that only the collective pair modes are transformed into boson operators while the non-collective modes are unchanged in the lowest order approximation. The odd- A system is treated in the same formalism as the even-even nuclear system. We briefly discuss the relation between our method and the conventional boson expansion theory.We propose a new method that transcribes the fermion system to the boson-fermion system by introducing a unitary operator defined in the whole boson-fermion space. We obtain the boson-fermion expansion of the fermion pair operators such that only the collective pair modes are transformed into boson operators while the non-collective modes are unchanged in the lowest order approximation. The odd- A system is treated in the same formalism as the even-even nuclear system. We briefly discuss the relation between our method and the conventional boson expansion theory.

Progress of Theoretical PhysicsJul 1, 19914 citations

PAIRING IN ASYMMETRICAL FERMI SYSTEMS

Khandker Quader, Renyuan Liao

Sep 1, 20070 citations

Classification of states of single- j fermions with J -pairing interaction

Y. M. Zhao, A. Arima

In this paper we show that a system of three fermions is exactly solvable for the case of a single- $j$ in the presence of an angular momentum- $J$ pairing interaction. On the basis of the solutions for this system, we obtain new sum rules for six- $j$ symbols. When the Hamiltonian contains only an interaction between pairs of fermions coupled to spin $J={J}_{\mathrm{max}}=2j\ensuremath{-}1$, the ``non-integer'' eigenvalues of three fermions with angular momentum $I$ around the maximum appear as ``non-integer'' eigenvalues of four fermions if $I$ is around (or larger than) ${J}_{\mathrm{max}}$ . This pattern is also found in five and six fermion systems. A boson system with spin $l$ exhibits a similar pattern.In this paper we show that a system of three fermions is exactly solvable for the case of a single-$j$ in the presence of an angular momentum-$J$ pairing interaction. On the basis of the solutions for this system, we obtain new sum rules for six-$j$ symbols. When the Hamiltonian contains only an interaction between pairs of fermions coupled to spin $J={J}_{\mathrm{max}}=2j\ensuremath{-}1$, the ``non-integer'' eigenvalues of three fermions with angular momentum $I$ around the maximum appear as ``non-integer'' eigenvalues of four fermions if $I$ is around (or larger than) ${J}_{\mathrm{max}}$. This pattern is also found in five and six fermion systems. A boson system with spin $l$ exhibits a similar pattern.

arXiv:nucl-th/0404042Physical Review CSep 21, 200421 citations

Stable pair liquid phase in fermionic systems

P. E. Kornilovitch

We predict the existence of a pair-liquid phase in lattice fermion systems with finite-range attractive interactions. This exotic state competes on one side with a normal Fermi liquid of unpaired fermions and on the other side with a phase-separated state where all fermions are coupled into macroscopic clusters. We show that such a phase is absent in bosonic systems and therefore is protected by the exclusion principle. In contrast with zero-range attractive systems where clustering of more than two fermions is directly prohibited, here quantum statistics acts dynamically and in a more subtle way. Since a many-fermion wave function must have nodes, the cluster formation threshold is larger than the pair formation threshold. By directly solving a four-body Schr\"odinger equation on one- and two-dimensional lattices, we map the boundaries of pair stability. The pair liquid phase should be observable in cold-atom systems. We also discuss implications for the preformed-pair mechanism of high-temperature superconductivity.We predict the existence of a pair-liquid phase in lattice fermion systems with finite-range attractive interactions. This exotic state competes on one side with a normal Fermi liquid of unpaired fermions and on the other side with a phase-separated state where all fermions are coupled into macroscopic clusters. We show that such a phase is absent in bosonic systems and therefore is protected by the exclusion principle. In contrast with zero-range attractive systems where clustering of more than two fermions is directly prohibited, here quantum statistics acts dynamically and in a more subtle way. Since a many-fermion wave function must have nodes, the cluster formation threshold is larger than the pair formation threshold. By directly solving a four-body Schr\"odinger equation on one- and two-dimensional lattices, we map the boundaries of pair stability. The pair liquid phase should be observable in cold-atom systems. We also discuss implications for the preformed-pair mechanism of high-temperature superconductivity.

arXiv:2204.02214Physical review. B./Physical review. BMar 16, 20234 citations

Pairing interaction in finite Fermi-systems

Dieter Zawischa

The European Physical Journal AOct 1, 19723 citations

In this paper we show that a system of three fermions is exactly solvable for the case of a single-

j

in the presence of an angular momentum-

J

pairing interaction. On the basis of the solutions for this system, we obtain new sum rules for six-

j

symbols. When the Hamiltonian contains only an interaction between pairs of fermions coupled to spin $J={J}_{\mathrm{max}}=2j\ensuremath{-}1$, the ``non-integer'' eigenvalues of three fermions with angular momentum

I

around the maximum appear as ``non-integer'' eigenvalues of four fermions if

I

is around (or larger than)

{J}_{\mathrm{max}}

. This pattern is also found in five and six fermion systems. A boson system with spin

l

exhibits a similar pattern.