Quantum-like model for classical random electromagnetic field

Abstract

Semiclassical models can be used, see e.g. Scully and Zubairy [Quantum Optics; Cambridge University Press: Cambridge, 1997], to simulate some distinguishing features of quantum optics. In this paper we show that one can also proceed successfully in the opposite direction. A quantum-like model for the classical random electromagnetic field is proposed. Averages with respect to classical random fields can be approximated by quantum-like averages given by the von Neumann trace-formula: . The operators ρ and can be easily determined as classical quantities. Here ρ is obtained by normalization of the covariance operator of the random field. It has all the features of the von Neumann density operator. Additionally an analogue of the quantum observable is given by the second derivative of a functional (‘classical variable’) f (E, B) of the classical electromagnetic field ψ = (E, B).