Universal level-spacing distribution in quantum systems

Classical counterparts of a great variety of quantum systems, from atomic physics to quantum wells and quantum dots, to optical, microwave, and acoustic resonators exhibit partially chaotic dynamics. Since it is often impossible to measure the temporal dynamics in qunatum systems, the main and probably the most dramatic manifestation of classical chaos in their phase space is seen in the distribution of spacing between the neighboring energy levels. While the mechanism leading to the onset of chaotic dynamics is different in every system, the level spacing distribution obeys the universal law, changing from Poissonian in the completely integrable systems to Wigner in completely chaotic ones.