On coherent states description of exciton systems: NLSE equations and hydrodynamics

CIRILO-LOMBARDO, DIEGO JULIO

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS

WORLD SCIENTIFIC PUBL CO PTE LTD

Año: 2023

0219-8878

The exciton system is described by means of specially constructed coherent states (CS),according to an idea of L.V. Keldysh long ago. The system is analyzed from the geometricpoint of view and from the relevant symmetry group contained in the displacementoperator as generador of the CS system in the Klauder–Perelomov sense. Explicitlyimportant quantities involving the quantum statistics of the system (partition function,mean density n and the Yuen limit) are calculated and briefly discussed in relation tothe known case of pure bosons (e.g. photons). The Bogoliubov type transformations forthe field operators of the Wannier–Mott type exciton system are presented in an exactway (in sharp contrast with the case of [11] where only a rough approximation wasgiven) showing how these transformations induce nonlinearity (cubic at first order) inthe Schrodinger equation of the system. The conditions for a hydrodynamic descriptionof the original Keldysh model, as the possibility of a BEC (Bose–Einstein Condensation),are discussed.