Spatio-temporal linear instability analysis for arbitrary dispersion relations on the Lefschetz thimble in multidimensional spacetime
Mathematical Physics
2021-03-31 v1 High Energy Astrophysical Phenomena
High Energy Physics - Phenomenology
math.MP
Fluid Dynamics
Plasma Physics
Abstract
In linear stability analysis of field quantities described by partial differential equations, the well-established classical theory is all but impossible to apply to concrete problems in its entirety even for uniform backgrounds when the spatial dimension is more than 1. In this study, using the Lefschetz thimble method, we develop a new formalism to give an explicit expression to the asymptotic behavior of linear perturbations. It is not only more mathematically rigorous than the previous theory but also useful practically in its applications to realistic problems, and, as such, has an impact on broad subjects in physics.
Cite
@article{arxiv.1912.11177,
title = {Spatio-temporal linear instability analysis for arbitrary dispersion relations on the Lefschetz thimble in multidimensional spacetime},
author = {Taiki Morinaga and Shoichi Yamada},
journal= {arXiv preprint arXiv:1912.11177},
year = {2021}
}
Comments
10 pages, 18 figures, accepted for publication in Physical Review Research