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Center for Nonlinear Studies |
A many-body formalism appropriate to describe composite bosons exists for a decade only. The difficulty has been to handle the particles as entities while treating the Pauli exclusion principle between their fermionic constituents in an exact way. This cannot be done through Green functions - which are scalar - but requires an operator algebra based on commutators: four commutators are necessary and sufficient to properly describe the physics of two-fermion particles. The major breakthrough revealed by this formalism is the existence of a many-body interaction induced by fermion exchange, which is missed by all effective Hamiltonians because it is dimensionless. Shiva diagrams have been proposed to visualize these exchanges and calculate composite boson many-body effects in a transparent way. Extension to composite fermions and the associated Kali diagrams will also be presented. Originally designed for semiconductor excitons and non-linear optical effects, this formalism has already proved useful in other fields like cold atomic gases and quantum information, with major hopes for the composite fermion part, in the physics of quarks and the possible quantum discussions between "Alice, Bob and Clara”.
Host: Aurelia Chenu