Kicked-rotator model

The preceding considerations are essentially based on the model of random-matrix ensembles proposed by Dyson and others in the 1960s. Recent works, in particular by Casati and co-workers [89], have focused on band random matrices. Such matrices naturally arise in quantum systems with subspaces coupled only to next-neighboring subspaces such as for electronic states in a chain of atoms or in the kicked rotator. In such systems, localized states are observed that present a level statistics interme-... 

The plan of Chapter 5 is the following. In order to get a feeUng for the dynamics of the kicked molecule, we approximate it by a one-dimensional schematic model by restricting its motion to rotation in the x, z) plane and ignoring motion of the centre of mass. In this approximation the kicked molecule becomes the kicked rotor, probably the most widely studied model in quantum chaology. This model was introduced by Casati et al. in 1979. The classical mechanics of the kicked rotor is discussed in Section 5.1. Section 5.2 presents Chirikov s overlap criterion, which can be applied generally to estimate analytically the critical control parameter necessary for the onset of chaos. We use it here to estimate the onset of chaos in the kicked rotor model. The quantum mechanics of the kicked rotor is discussed in Section 5.3. In Section 5.4 we show that the results obtained for the quantum kicked rotor model are of immediate... 

To include the effects of collisions on the rotational motion part of any of the above C(t) functions, one must introduce a model for how such collisions change the dipole-related vectors that enter into C(t). The most elementary model used to address collisions applies to gaseous samples which are assumed to undergo unhindered rotational motion until struck by another molecule at which time a randomizing "kick" is applied to the dipole vector and after which the molecule returns to its unhindered rotational movement. 

The effects of such collisionally induced kicks are treated within the so-called pressure broadening (sometimes called collisional broadening) model by modifying the free-rotation correlation function through the introduction of an exponential damping factor exp( -Itl/x) ... 

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