This thesis falls naturally into four parts, which are relatively independent:
The first two parts form the main body of the thesis, and they are both devoted to the study of billiard systems (hard-walled cavities enclosing a region of free space) in which the classical motion is chaotic. The quantum mechanics of such systems has become known as the field of `quantum chaos'. The first part probably contains the most significant new physical results; this is reflected in the choice of thesis title. The second part can be viewed merely as a description of numerical quantum-mechanical calculations that play a supporting role in the first part. However, there will also turn out to be a surprising reciprocal connection, namely that results from the first part will provide a much-needed explanation for the success of a very efficient numerical technique in the second part. The intertwining of these two subject areas had turned out to be one of the most beautiful surprises in this body of research.
The third and fourth parts form essentially separate projects, and can therefore be read independently. However they do share with the rest of the thesis the common theme of wave mechanics: the third presents a new approach to the transport of quasiparticle waves in mesoscopic systems, and the fourth models confined electromagnetic waves to trap and guide atoms (which themselves can be treated as coherent matter waves).
The goals and subject matter of the four parts are sufficiently different to merit individual introductions and summaries, which now follow without further ado.