Random and Small-scale Quantum Ergodicity
Abstract
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.
- Publication:
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Ph.D. Thesis
- Pub Date:
- 2019
- Bibcode:
- 2019PhDT........74C
- Keywords:
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- Mathematics;Quantum physics;Plasma physics