Spatio-temporal linear instability analysis for arbitrary dispersion relations on the Lefschetz thimble in multidimensional spacetime

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.

arXiv comment10 pages, 18 figures, accepted for publication in Physical Review Research

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• Stabilization of Solitons Generated by a Supersonic Flow of Bose-Einstein Condensate Past an Obstacle
• Fast flavor conversions of supernova neutrinos: Classifying instabilities via dispersion relations
• The dispersion relation of the fast neutrino oscillation wave