Chaotic eigenfunctions in momentum space

We study eigenstates of chaotic billiards in the momentum representation an d propose the radially integrated momentum distribution as a useful measure to detect localization effects. For the momentum distribution, the radiall y integrated momentum distribution, and the angular integrated momentum dis tribution explicit formulae in terms of the normal derivative along the bil liard boundary are derived. We present a detailed numerical study for the s tadium and the cardioid billiard, which shows iii several cases that the ra dially integrated momentum distribution is a good indicator of localized ei genstates; such as scars, or bouncing ball modes. We also find examples, wh ere the localization is more strongly pronounced in position space than in momentum space, which we discuss in detail. Finally, applications and gener alizations are discussed.