We determine the dispersion law of the carrier wave of an exciton-photon pulse which propagates as a solitary wave. For short pulses, four branches $\ensuremath{\Omega}=\ensuremath{\Omega}$ ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}$) appear: a branch which goes through the intersection point $\ensuremath{\hbar}cK={E}_{o}+\frac{{\ensuremath{\hbar}}^{2}{K}^{2}}{2M}$ of the uncoupled modes of the free exciton and the free light field, two polaritonlike branches and an excitonlike branch. The polaritonlike branches have a normal dispersion, whereas the branch which goes through the intersection point of the free modes has an anomalous dispersion for sufficiently short pulse width. This branch contains the solution of McCall and Hahn as a special case. For very short pulses the branch with anomalous dispersion continues into the two polaritonlike branches. For increasing pulse width a forbidden energy gap appears at $\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}=0$. For long pulses, only the two polaritonlike solutions exist.
We demonstrate the effects of an induced disorder (or a free-orientation :
θ which is related to the relative direction of scattering of particles w.r.t. to the normal of the propagating plane-wave front) upon the possible resonance of the plane (sound) wave propagating in Bose gases by using the quantum kinetic equations. We firstly present the diverse dispersion relations obtained by the relevant Pauli-blocking parameter
B (which describes the Bose particles when
B is positive) and the free-orientation
θ and then, based on the acoustic analog, address the possible resonant states.
Local observables of an infinite system are described by a quasilocal C*-algebra A. Traditionally classical observables are introduced as parameters that can be assigned to certain states on the local observables. As fundamental theories should be essentially free of parameters this can hardly be regarded as satisfactory. In the present paper classical observables are introduced explicitly as operators by a transitive system of imprimitivity of a kinematical group in the center of the W*-algebra π(A)″ belonging to a representation π of A. The states of the system are represented by linear functionals on π(A)″, which are dispersion-free on the center of π(A)″. For classical observables related to a kinematical group a W*-description—with algebra π(A)″ and its associated linear functionals that are dispersion-free on the center and normal on the noncentral part of π(A)″—is equivalent to a C*-description—with algebra A and a distinguished family of linear functionals on A, determined uniquely by π. The implications of these results on the interpretation of quantum mechanics of infinite systems are discussed.