Quantum theory of light propagation in a fluctuating laser-active medium

The basic equations are derived which describe the propagation of an electromagnetic field in a fluctuating laser-active medium. The well-known methods of Langevinequations and master-equation for a few discrete modes are generalized to meet also the case of a radiation field with continuous spectrum. The medium is described by two-level atoms which are embedded in a merely passive solid matrix and homogeneously distributed over space. They have an inversion which is kept constant by an externally applied pump. The atomic line may be homogeneously or inhomogeneously broadened. We obtain a complete set of partial differential equations for the field operators with damping terms and fluctuating forces homogeneously distributed over the material. The telegraph equation with a fluctuating force occurs as a special case. After the exact elimination of the atomic variables we obtain a nonlinear field equation for the radiation field alone. By means of a pseudo-Hamiltonian and by a simple one-dimensional example we show that in a certain sense there exists a close formal analogy between the present theory and the theory of an interacting Bose gas. The characteristic differences between the two theories are also discussed. We find, that there occurs a phase transition of the radiation field because above a certain threshold of the pump the photons condense into a single mode and establish an “offdiagonal-long-range order”. The amplitude fluctuations and the phase fluctuations, which restore the broken phase symmetry, are calculated in detail. A new condition for the occurrence of undamped spiking (pulse formation) for a continuum of modes is derived.     

A theorem on the calculation of multi-time-correlation functions by the single-time density matrix

For the case of a laser systemS as well as for more general cases we show that multi-time correlation functions may be easily calculated by use of a slightly generalized density matrix ofS satisfying the usual master-equation with some additional terms in it.     

Some exact results on discrete noisy maps

Using the Chapman-Kolmogorov type equation introduced by H. Haken and G. Mayer-Kress for discrete time processes we derive forward and backward equations for the corresponding transition probability and obtain an integral equation for the conditional first passage time. In the case of linear dynamics with Gaussian noise we present the exact solution of the Chapman-Kolmogorov equation.     

Generalized Onsager-Machlup function as solution of a multi-dimensional Fokker-Planck equation

The multi-dimensional Fokker-Planck equation is solved by Feynman path integrals. The solution may be interpreted as generalized Onsager-Machlup function.     

Quantum theory of the two-photon laser

We start from a master equation for the density operator of the atoms and the field mode, and apply the operator method of adiabatic elimination of the atomic variables, recently developed by Haake and Lewenstein for the usual single mode laser, to the case of a degenerate two-photon laser. A Fokker-Planck equation for the Wigner distribution function of the lightfield and its steady state solution are derived. With a Gaussian approximation to the solution, analytical and numerical results on the photon statistics are calculated.     

Slaving principle for stochastic differential equations with additive and multiplicative noise and for discrete noisy maps

We first treat multidimensional nonlinear noisy maps. We assume that the variables can be split into two classes of variablesu ands so that the linearized equations would give rise to growth or decay foru ands, respectively. We show how the slaved variabless can be explicitly expressed by the order parametersu by making use of the fully nonlinear equations. By taking the limit of vanishing time steps and using a Wiener process and the Îto calculus we derive the corresponding formulas for stochastic differential equations (including multiplicative noise). In this way a high-dimensional problem can be reduced to a problem of much lower dimensions described again by stochastic equations of theÎto type. A similar procedure holds for theStratonovich calculus.     

An approach to the analysis of crosslinked epoxy systems

Summary The most widely use epoxy resins are the diglycidylethers of bisphenol A which in both the uncured and curd states posses functional groups that are theoretically amenable to cleavage using the vigorous conditions possible with acid or alkaline fusion chromatography.The cleavage of the simple oligomeric epoxy resins has been investigated together with their crosslinked products with diprimary amines of increasing molecular weight, several polyamines and dimer fatty polyamides. The results are discussed with regard to other polymer systems incorporating bisphenol A.Dedicated to Professor Leslie S. Ettre on the occasion of his 70th birthday.