Quantum limits of Eisenstein series and scattering states. (English) Zbl 1343.11055
Can. Math. Bull. 56, No. 4, 814-826 (2013); erratum 56, No. 4, 827-828 (2013).
Summary: We identify the quantum limits of scattering states for the modular surface. This is obtained through the study of quantum measures of non-holomorphic Eisenstein series away from the critical line. We provide a range of stability for the quantum unique ergodicity theorem of W. Luo and P. Sarnak [Publ. Math., Inst. Hautes Étud. Sci. 81, 207–237 (1995; Zbl 0852.11024)].
MSC:
| 11F72 | Spectral theory; trace formulas (e.g., that of Selberg) |
| 35P25 | Scattering theory for PDEs |
| 58J51 | Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity |
| 81Q50 | Quantum chaos |
