The analysis of statistical properties of energy spectra is a very important research topic for understanding the dynamics of quantum and wave systems. It is established that the level fluctuations in the spectra of quantum systems whose classical analogs are chaotic follow the predictions of the random matrix theory (RMT), depending on the time-reversal invariance and spin. One-dimensional networks and two-dimensional quantum billiards simulated by microwave networks and flat resonators, respectively, are the proper systems for the study. I will report the applicability of correlation functions in terms of missing levels to obtain the information about the fundamental symmetry classes in the RMT and degree of chaoticity determined by the degree of level correlation [1].

               The second part includes the ultrashort time-resolved spectroscopy in THz domain. An electro-optical sampling (EOS), the pioneering construction in Poland, is applied as a powerful tool for characterizing ultra-high-speed optoelectronic devices. For the photo-excitation and EO sampling the femtosecond optical pulses are used, generated by the Ti:sapphire laser. The investigated LT GaAs photodetectors after neutron irradiation exhibit ultrafast response time with the FWHM of ~680 fs. At that time it corresponded to the fastest detectors in the world.

[1] M. Białous, V. Yunko, Sz. Bauch, M. Ławniczak, B. Dietz, L. Sirko,

Phys. Rev. Lett. 117, 144101 (2016).

Małgorzata Białous habilitation lecture