We introduce aspects of quantum chaos by analyzing the eigenvalues and the eigenstates of quantum many-body systems. The properties of quantum systems whose classical counterparts are chaotic differ from those whose classical counterparts are not chaotic. The spectrum of the first exhibits repulsion of the energy levels, which is one of the main signatures of quantum chaos. We show how level repulsion develops in one-dimensional systems of interacting spins 1/2 which are devoid of random elements and involve only two-body interactions. In addition to the statistics of the eigenvalues, we analyze how the structure of the eigenstates may indicate chaos. The programs used to obtain the data are available online.

We present a simple high school and university undergraduate laboratory setup, with which we are able to texture microscopic structures into polymer and dye films using a homemade UV nitrogen laser. We describe both the laser and the microstructuring setup and provide detailed information on the laser and its beam characteristics. Although this is a low-cost setup, we are able to directly write or texture high-quality patterns into thin films, either by manually controlling a positioning stage or by programming a desired sequence for an automated structuring process. We introduce several hands-on experiments for high school and university undergraduate students and present our first results.