We develop a semiclassical theory for the spectral statistics of quasi-one-dimensional systems that show chaotic diffusion on the classical level and Anderson-localized quantal eigenstates. It relates the spectral two-point correlations to the classical probability for periodic motion. We obtain analytical expressions for the spectral form factor, defining a novel, one-parameter spectral universality class which spans the transition from Poissonian spectra in the limit corresponding to disordered systems in the isolating regime, to GOE statistics in the opposite (ballistic) regime. Our analytical predictions are confirmed by a numerical study of quasi-one-dimensional billiard chains.

We study spectral properties of quasi-one-dimensional extended systems that show deterministic diffusion on the classical level and Anderson localization in the quantal description. Using semi-classical arguments we relate universal aspects of the spectral fluctuations to features of the set of classical periodic orbits, expressed in terms of the probability to perform periodic motion, which are likewise universal. This allows us to derive an analytical expression for the spectral form factor which reflects the diffusive nature of the corresponding classical dynamics. It defines a novel spectral universality class which covers the transition between GOE statistics in the limit of a small ratio of the system size to the localization length, corresponding to the ballistic regime of disordered systems, to Poissonian level fluctuations in the opposite limit. Our semi-classical predictions are illustrated and confirmed by a numerical investigation of aperiodic chains of chaotic billiards.

We study the long-time behavior of the quantized baker's map in the semiclassical approximation. Our main object of investigation is the trace of the (n-step) time-evolution operator. We express this trace as a phase-space integral which equals the semiclassical expression in terms of periodic orbits. This enables us to follow the evolution explicitly up to the time at which the semiclassical traces start to diverge exponentially from the quantum ones. Our data indicate that this breakdown time scales with h in a way close to h-1/2.

We discuss two-point correlations of the actions of classical periodic orbits in chaotic systems. For systems where the semiclassical trace formula is exact and the spectral statistics follow random matrix theory, there exist nontrivial correlations between actions, which we express in a universal form. We illustrate this result with the analogous problem of the pair correlations between prime numbers. We also report on numerical studies of three chaotic systems where the semiclassical trace formula is only approximate, but nevertheless these unexpected action correlations are observed.

Existing semantic theories are charged with oversimplification by identifying point of view with utterance; educated speakers, however, easily interpret free indirect discourse in stream-of-consciousness novels by distinguishing between the narrator's perspective & that of a character despite alternations of perspective within the same paragraph. Free indirect discourse sentences, though unembedded, contain shifted tenses anchored to the narrator while deictic expressions are anchored to the subject of consciousness. Definite descriptions are related to the narrator in referential use & to the subject of consciousness in attributive uses. Free indirect discourse is also characterized semantically by logophoric third person pronouns & stylistically by exclamations typical of direct speech & use of a character's metaphors & speech mannerisms. A formalization of free indirect discourse is developed in the framework of situation semantics to represent the distribution of perspectival sensitivities of deictic elements, including third person pronouns & tenses, & the duality of definite descriptions. 9 References. J. Hitchcock

Situation semantics sees the meaning of sentences as a relationship between the discourse situation & the described situation. Advantages to such an approach in solving many problems in semantics are described by the originators of the theory, J. Barwise & J. Perry (Situations and Attitudes, Cambridge: MIT Press, 1983). The phenomenon referred to as "complex discourse" clearly indicates the need to add a third factor to this relationship: point of view. The analysis presented here shows that there is no upper limit on the number of points of view that may affect the meaning of the sentence. Addition of this factor increases the flexibility of situation meaning of a given sentence & makes clarification of problems of reference in complex discursive sentences possible. Examples are taken from modern Israeli literature. It is suggested that this approach is also a contribution to literary analysis. 8 References. A. Paris