Ideal Bosons and Fermions

H. A. Buchdahl

Malte C. Tichy, Peter Alexander Bouvrie, Klaus Mølmer

The composite character of two-fermion bosons manifests itself in the interference of many composites as a deviation from the ideal bosonic behavior. A state of many composite bosons can be represented as a superposition of different numbers of perfect bosons and fermions, which allows us to provide the full Hong-Ou-Mandel-like counting statistics of interfering composites. Our theory quantitatively relates the deviation from the ideal bosonic interference pattern to the entanglement of the fermions within a single composite boson.

Antônio Sérgio Teixeira Pires

Jutta Meyer

Recently, the mathematical formalism of the Dyson boson mapping has been extended to a system of 3n fermions, leading to the boson–fermion and the baryon mapping. In the present paper, the case of a restriction to a subset of three-fermion quantum numbers, the collective indices, is discussed. A theory is developed for the representation of fermionic states and operators in a truncated ideal space where only collective boson–fermion pairs or collective ideal baryons are allowed. An exact reproduction of physical properties is proved to be possible provided that the original fermionic problem can be solved in a subspace where all three-fermion subsystems carry collective indices. Examples of simple applications are presented in the two subsequent papers of this series.

Javid A. Sheikh

The nature of the appearance of the spurious states in the ideal boson basis states is investigated. It is shown that the occurrence of the spurious states can be mainly attributed to the orthogonality of the boson basis states. It is further observed that the matrix element of the pairing interaction between the ideal boson basis is identical to the corresponding fermion matrix element.