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Statistical Behaviour of Three Boson Field Modes with Trilinear Interaction
Author(s) -
Trung T. V.,
Schütte F.J.
Publication year - 1978
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19784900306
Subject(s) - boson , physics , density matrix , coupling constant , operator (biology) , unitary state , unitary operator , fock state , coherent states , matrix (chemical analysis) , perturbation theory (quantum mechanics) , nonlinear system , quantum mechanics , perturbation (astronomy) , field (mathematics) , basis (linear algebra) , coupling (piping) , mathematical physics , quantum electrodynamics , photon , hilbert space , mathematics , pure mathematics , quantum , materials science , repressor , law , chemistry , composite material , biochemistry , political science , transcription factor , mechanical engineering , gene , engineering , geometry
The time variation of the density matrix for a system of three interacting boson field modes is described in the Schrödinger picture with the help of the unitary time development operator in coherent state basis. The nonlinear c ‐number equation for this operator is solved using a perturbation expansion in powers of the coupling constant. The explicit time dependence is obtained for the matrix elements of the total density matrix and of the particular density matrices of the individual modes. Photon number distributions and second order correlations are calculated for several initial situations.