Year: 2019
Type: preprint
Abstract: Motivated by the work of Colin de Verdière and Saint-Raymond on spectral theory 0th order pseudodifferential operators on tori we consider viscosity limits in which 0th order operators $ P $ are replaced by $ P + i νΔ$, $ ν> 0 $. By adapting the Helffer--Sjöstrand theory of scattering resonances we show that in a complex neighbourhood of the continuous spectrum eigenvalues of $ P + i νΔ$ have limits as viscosity $ ν$ goes to 0. In the simplified setting of tori this justifies claims made in the physics literature.
Source: arXiv (Cornell University)
Authors: Galkowski, Jeffrey, Zworski, Maciej
Institutions: University College London, University of California, Berkeley
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2995002498