Details

Autor(en) / Beteiligte

• Chang, Robert

Titel

Random and Small-scale Quantum Ergodicity

Ort / Verlag

ProQuest Dissertations & Theses

Erscheinungsjahr

2019

Link zum Volltext

• ProQuest

Quelle

ProQuest Dissertations & Theses A&I

Beschreibungen/Notizen

• This thesis contains results in mathematical quantum ergodicity in a probabilistic or a complex analytic setting. For the former, we show that a random orthonormal basis of spherical harmonics is almost surely quantum ergodic, in which the randomness is induced by the generalized Wigner ensemble. For the latter, we show that small-scale quantum ergodicity holds on a compact Kahler manifold equipped with a prequantum line bundle, or the Grauert tube of a compact, negatively curved, real analytic manifold. Furthermore, the nodal sets of the eigensections or the complexified eigenfunctions are also equidistributed on small scales.