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.

Creator

• Chang, Hsiang

DOI

• https://doi.org/10.21985/n2-4k82-an29

Subject

• Mathematics
• Quantum physics
• Plasma physics

Language

• en

Alternate Identifier

• http://dissertations.umi.com/northwestern:14574
• etdadmin_upload_658290

Keyword

• Eigenfunction
• Quantum ergodicity
• Microlocal analysis
• Grauert tube

Date created

• 2019-01-01

Resource type

• Dissertation

Rights statement

• In Copyright