We show that exponential instabilities and quantum chaos occur in a system with a mixed classical-quantum description. This type of chaos is of general importance and may occur in any quantum system which divides in a natural way into a fast (quantum) and a slow (classical) subsystem.PACS numbers: 05.45.+b Current research in quantum chaos is mainly focused on the classical-quantum correspondence in the semiclassical regime of classically chaotic dynamical systems [1 -3]. But yet another main avenue of quantum chaos research may derive from the observation that for some quantum systems of theoretical and practical importance the system divides in a natural way into two interacting subsystems, one of which is treated quantum mechanically, whereas the other is treated in the classical approximation.The mixed quantum-classical description of a dynamical system is justified whenever the quantum effects of one subsystem are negligible compared to the other or when the quantization of the whole system poses a severe challenge and the classical treatment of one part has to serve as a necessary guide in the further investigation. In fact, there are many examples in the physics literature where such a mixed description was already successfully applied. We mention the case of a two-level system interacting with the electromagnetic field of a laser cavity [4,5], the micromaser [6], nuclear collective motion [7], and the exciton transfer in a nonlinear molecular dimer perturbed by an intermolecular vibration [8]. It was demonstrated recently [9] that the number of photons in the electromagnetic maser field can be changed essentially in units of 1 from one photon (quantum limit) to a large number of photons (classical limit). Thus, the importance of quantum corrections in the "classical" subsystem (the cavity field) can be controlled to an astonishing degree. The molecular physics example of the nonlinear dimers is instructive because it provides an example for the justification of the division into a quantum and a classical subsystem. Describing the strong intramolecular interactions in the molecules constituting the dimer in the framework of the nonlinear discrete self-trapping equation (see, e.g. , [10,11]) one can use the weakness of the intermolecular forces between the molecules (and correspondingly small frequencies) to use a classical approximation for the intermolecular vibrations perturbing the transfer dynamics. In this case the density matrix dynamics for the exciton transfer of the quantum subsystem is characterized by a homoclinic structure on the Bloch sphere from which by perturbation with the classical oscillator a stochastic layer and chaos develops [8]. A further example is provided by a quantum system with a classical boundary moving in an anharmonic potential [12]. All the models discussed above are characterized by a mixed quantum-classical description. One of the main purposes of this Letter is to show that such systems can display quantum chaos and arise quite naturally within the framework of the Born...

Relative abundances of the various ionic charges resulting from photoionization of argon by monochromatked synchrotron radiation at energies between 3150 and 4900 eV have been measured with low statistical error. Despite the fact that already, right at the onset of K excitation (3203.5 eV), almost the full Is binding energy is deposited in the atom, the relative abundances change smoothly over the region of np excitation up to 6 eV above the limit. While this behaviour, caused by Rydberg shake-off (about 0.5 probability at the Is -4p resonance) and by recapture ofthephotoelectron via post-collision interaction, appeanta be undentoodthereinnoexplanation foragradualchange of relative abundances extending over tens of eV below the lowest K excitation. K + M and K + L single photon double excitations both show up as a smooth rise of the average ionic charge c j from the respective threshold to a plateau at considerably higher energy, the overall increase of being 0.206+0.02 and 0.13*0.01.

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CS 2 and OCS molecules were excited and fragmented by x-rays of variable energy around the sulphur 1s threshold (2478 eV). Coincident detection of three ionic fragments by a time-of-flight mass spectrometer enabled the determination of branching ratios for 18 dissociation channels with total ionic charges between 2 and 7. While the electronic de-excitation is similar in both molecules (see the preceding paper), the dissociation shows differences, notably a more asymmetric distribution of charge onto the fragments of OCS. Branching among channels of the same total charge is independent of photon energy although the dominant de-excitation cascades are not. This is interpreted as an indication of strong interchannel mixing. A simple, parameter-free Coulomb explosion model to simulate the dissociative kinematics is described. Detailed results based on this model give, contrary to opinions to be found in the literature, very good agreement with observed momentum correlations whereas maximum kinetic energies are somewhat overestimated for channels of higher total charge.

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