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Coherent and Incoherent States of the Radiation Field

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Abstract

Methods are developed for discussing the photon statistics of arbitrary fields in fully quantum-mechanical terms. In order to keep the classical limit of quantum electrodynamics plainly in view, extensive use is made of the coherent states of the field. These states, which reduce the field correlation functions to factorized forms, are shown to offer a convenient basis for the description of fields of all types. Although they are not orthogonal to one another, the coherent states form a complete set. It is shown that any quantum state of the field may be expanded in terms of them in a unique way. Expansions are also developed for arbitrary operators in terms of products of the coherent state vectors. These expansions are discussed as a general method of representing the density operator for the field. A particular form is exhibited for the density operator which makes it possible to carry out many quantum-mechanical calculations by methods resembling those of classical theory. This representation permits clear insights into the essential distinction between the quantum and classical descriptions of the field. It leads, in addition, to a simple formulation of a superposition law for photon fields. Detailed discussions are given of the incoherent fields which are generated by superposing the outputs of many stationary sources. These fields are all shown to have intimately related properties, some of which have been known for the particular case of blackbody radiation.
... Since then, this problem has been revisited recurrently in different contexts either in physics or in engineering. Examples are abundant in condensed matter, statistical mechanics and quantum field theory among others [3][4][5][6]. ...
... Each cell k of size accounts for a lattice site, where radiation is locally at thermal equilibrium with surrounding walls. The three processes (1,2,3) namely, in-cell creation and annihilation (red), bulk (green) and boundaries (purple) inter-cell exchanges are indicated. ...
... where L ⊥ accounts for process (1) and L ≡ L bulk + L boundary accounts for processes (2) and (3). Expressions of these generators are given in the Supplementary Material S IV in [20]. ...
Preprint
Non-equilibrium radiation is addressed theoretically by means of a stochastic lattice-gas model. We consider a resonating transmission line composed of a chain of radiation resonators, each at a local equilibrium, whose boundaries are in thermal contact with two blackbody reservoirs at different temperatures. In the long chain limit, the stationary state of the non-equilibrium radiation is obtained in a closed form. The corresponding spectral energy density departs from the Planck expression, yet it obeys a useful scaling form. A macroscopic fluctuating hydrodynamic limit is obtained leading to a Langevin equation whose transport parameters are calculated. In this macroscopic limit, we identify a local temperature which characterises the spectral energy density. The generality of our approach is discussed and applications for the interaction of non-equilibrium radiation with matter are suggested.
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... The associated Glauber first order correlation function [21,22] then reads ...
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DOI:https://doi.org/10.1103/PhysRevLett.10.276
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