Time evolution law of the Laguerre-polynomial-weighted chaotic photon field in an amplitude-damping channel

We examine how a Laguerre-polynomial-weighted chaotic photon field (LPWCPF), whose density operator is λ(1 - λ)^l : L_l[-λ²a^†a/(1 - λ)]e^-λa†a :, evolves in an amplitude-damping channel. By using a newly derived generating function of two variable Hermite polynomials we obtain the evolution law of LPWCPF, which turns out to be a new LPWCPF with a new parameter, depending on 1 - e^-2κt, where κ represents decay rate. The technique of integration (summation) within an ordered product of operators is used in our discussions. (author)