Type II quantum chaos

As discussed in Section 4.2 type II systems (Bliimel and Esser (1995)) show exponential sensitivity in the quantum subsystem. This allows the possibility of investigating the characteristics of true quantum chaos (type III quantum chaos) using the quantum subsystems of type II systems as a model. Apart from these new possibilities for fundamental research, type II systems have already found an important application. The mixed classical/quantum description, the basis of type II chaos, is a natural starting point for the investigation of the physics of dimers. In these systems chaos may result when electronic and vibronic degrees of freedom are coupled (Hennig and Esser (1992), Esser and Schanz (1995)). 

The above arguments show that type II wave chaos is a genuine wave phenomenon in classical wave systems. In the context of quantum mechanics, however, type II quantum chaos is only an approximation. This is because classical walls or dynamic boundaries do not exist in quantum mechanics. The dynamical degrees of freedom of the walls, or boundaries, have to be quantized too, resulting in a higher-dimensional, but purely quantum, system, usually of type I. This fact leads us to a promising 

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Type II quantum chaos is discussed in Section 4.2. It arises naturally in molecular physics in the form of the dynamic Born-Oppenheimer approximation (Bliimel and Esser (1994)). In the dynamic Born-Oppenheimer approximation chaos may occur in both the classical and the quantum subsystem, although neither the classical nor the quantum systems by themselves are chaotic. Type II quantum chaos was also identifled in a nuclear physics context (Bulgac (1991)). 

In summary, we have shown in this section that even in one of the simplest conceivable models for a diatomic molecule, the coupling of classical and quantum degrees of freedom can lead to genuine chaos in both the quantum and the classical subsystems. This proves the existence of type II quantum chaos. This result is of general importance since type II quantum chaos may occur in any system that divides in a natural way into a... 

In Section 11.1 we discuss recent advances in quantum chaology, i.e. the semiclassical basis for the analysis of atomic and molecular spectra in the classically chaotic regime. In Section 11.2 we discuss some recent results in type II quantum chaos within the framework of the dynamic Born-Oppenheimer approximation. Recent experimental and theoretical results of the hydrogen atom in strong microwave and magnetic fields are presented in Sections 11.3 and 11.4, respectively. We conclude this chapter with a brief review of the current status of research on chaos in the helium atom. 

Bliimel, R. and Esser, B. (1995). Type II quantum chaos, Zeit. Physik B98, 119-131. 

Given the abovementioned bewildering cornucopia of quantum systems that in one way or another all invoke the notion of chaos, we have to ask the question what exactly is quantum chaos We think that quantum chaos comes in three varieties (I) quantized chaos, (II) semi-quantum chaos and (III) quantum chaos. We refer to these three categories as type I, II and III quantum chaos. The division of quantum chaos into these three types arises naturally if quantum systems are characterized according to whether they do or do not show exponential sensitivity and chaos. The three different types of quantum systems are discussed in Sections 4.1, 4.2 and 4.3, respectively. A short preview of the three different types of quantum chaos follows. 

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