Spatiotemporal linear instability analysis for arbitrary dispersion relations on the Lefschetz thimble in multidimensional spacetime

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Spatiotemporal linear instability analysis for arbitrary dispersion relations on the Lefschetz thimble in multidimensional spacetime

Taiki Morinaga and Shoichi Yamada

Phys. Rev. Research 2, 013045 – Published 14 January 2020

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 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.

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Received 24 May 2019

DOI:https://doi.org/10.1103/PhysRevResearch.2.013045

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society