| This dissertation describes our solution to four problems in quantum chaos. We first study how Berry's formula for the spatial correlations of chaotic eigenfunctions needs to be modified, when the separation is large compared to any relevant classical distance scales in the problem.;We show how to reconcile two methods in literature to calculate the average root-mean-square value of off-diagonal matrix elements of smooth operators in chaotic systems, using our previous result.;We derive, analytically, a trace formula for products of diagonal matrix elements in chaotic systems, which was first conjectured by Main and Wunner, based on their numerical studies.;We also find energy thresholds for the onset of quantum chaos in a gas of weakly interacting particles, when the particles are fermions and when they are bosons. |
