Quantum chaos systems

On the other hand, we know that some chemical reaction systems, especially when highly excited, exhibit quantum chaotic features [16] that is, statistical properties of eigenenergies and eigenvectors are very similar to those of random matrix systems [17]. We call such systems quantum chaos systems. Researchers have also studied how these quantum chaos systems behave under some external... 

This chapter is organized as follows. In Section II, we show how quantum chaos systems can be controlled under the optimal fields obtained by OCT. The examples are a random matrix system and a quantum kicked rotor. (The former is considered as a strong-chaos-limit case, and the latter is considered as mixed regular-chaotic cases.) In Section III, a coarse-grained Rabi state is introduced to analyze the controlled dynamics in quantum chaos systems. We numerically obtain a smooth transition between time-dependent states, which justifies the use of such a picture. In Section IV, we derive an analytic expression for the optimal field under the assumption of the CG Rabi state, and we numerically show that the field can really steer an initial state to a target state in random matrix systems. Finally, we summarize the chapter and discuss further aspects of controlling quantum chaos. 

We study optimal control problems of quantum chaos systems. Our goal of control is to obtain an optimal field s(t) that guides a quantum chaos system from an initial state target state (pj) at some specific time t = T. One such method is optimal control theory (OCT), which has been successfully applied to atomic and molecular systems [4]. 

In the following subsections, we numerically demonstrate to control multilevel-multilevel transition problems in quantum chaos systems One is a random matrix system, and the other is a quantum kicked rotor. 

The random matrix was first introduced by E. P. Wigner as a model to mimic unknown interactions in nuclei, and it has been studied to describe statistical natures of spectral fluctuations in quantum chaos systems [17]. Here, we introduce a random matrix system driven by a time-dependent external field E(t), which is considered as a model of highly excited atoms or molecules under an electromagnetic field. We write the Hamiltonian... 

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