New operator identities with regard to the two-variable Hermite polynomial by virtue of entangled state representation

Abstract

By virtue of the entangled state representation we concisely derive some new operator identities with regard to the two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP) of operators we further derive new generating function formulas of the TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.

Damping of displaced chaotic light field in amplitude dissipation channel*

“…where k is the damping rate. By using the entangled state representation, [22][23][24] one can directly derive the infinitive-sum solution to Eq. ( 11), i.e.,…”

“…In this paper we explore how a displaced chaotic light behaves in an amplitude dissipation channel, and how its photon number decreases; in another word, we shall deduce a photon distribution formula (with time evolution) for DCL. With the use of the method of integration (summation) within ordered product of operator [9][10][11][12] and the new binomial theorem involving two-variable Hermite polynomials, [13][14][15] we obtain the evolution law of DCL in the channel.…”

Time evolution law of a two-mode squeezed light field passing through twin diffusion channels

“…Photon diffusion and photon dissipation are two processes in optical communications [1][2][3][4] in which decoherence usually happens. [5,6] In previous works, the diffusion and dissipation of photons have been investigated using different methods.…”

Some new generating function formulae of the two-variable Hermite polynomials and their application in quantum optics

“…In this work we shall extend Ref. [1] to derive some generating function of even-and odd-Hermite polynomials for the two-variable case, the twovariable Hermite polynomial H n,m (x) [2][3][4][5][6] can also be defined by its generating function exp…”