Quasi-Normal Modes, Non-Selfadjoint Operators and Pseudospectrum: an Interdisciplinary Approach

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About this Research Topic

Submission closed

  1. Manuscript Extension Submission Deadline 31 May 2025

Background

Quasi-normal modes, namely the complex frequencies encoding the linear response of resonators under tiny perturbations, have acquired major importance in recent years in different settings of physics, ranging from astrophysical and theoretical problems in gravitational physics to the study of scattering properties of optical nanoresonators. Beyond physics, the subject makes direct contact with the study of the spectral and dynamical properties of non-selfadjoint operators, a very active area of current research in applied and fundamental mathematics with direct applications in physics, from hydrodynamics and turbulence to non-Hermitian quantum mechanics. In spite of these converging complementary interests and “working knowledge”, research interchanges among the involved subcommunities seem quite scarce. In this setting, the central notion of Pseudospectrum provides a systematic framework furnishing a common arena to this interdisciplinary field of research, namely a crossroad in the physics and mathematics of open non-conservative systems.

The general goal of this Research Topic is to bring to the front line of physics research the qualitative and quantitative features that are specific to systems whose dynamics is governed by non-selfadjoint operators. This generic goal is concretely articulated around the Pseudospectrum notion, a key concept in the spectral theory of non-selfadjoint (more generally, non-normal) operators. In this context, the main focus will be placed on the study of the structural stability of the spectrum of non-selfadjoint operators. In particular, the calculation of quasi-normal modes in a variety of physical scenarios provides a singularly timely problem. Indeed, the recent introduction of the Pseudospectrum in gravitation physics, namely in the study of the spectral instability of quasi-normal modes of black holes, has raised a number of questions that remain open and are urgent to answer in the context of astrophysical compact objects as sources of gravitational waves. Crucially, this research problem transcends the gravitational context making contact with other disciplines,
such as optics. Complementary to this main spectral instability focus, and taking the Pseudospectrum as a bridge to the broader setting of non-modal analysis largely developed in fluid and turbulence physics, attention will be placed to dynamical transients and pseudo-resonances. The ultimate goal is the threading of an interdisciplinary research community framed around the application of non-selfadjoint operator concepts and tools in physics.

Contributions to this Research Topic are expected to address a question directly related or motivated by the physics and/or mathematics of non-selfadjoint operators. Among the possible topics to be covered we can mention:

i) Formulations of quasi-normal modes as a spectral non-selfadjoint problem with particular attention
to hyperboloidal methods and spectral instability
ii) Mathematical and physical aspects of other non-selfadjoint spectral problems
iii) Application of the Pseudospectrum in spectral/dynamical settings in physics (gravitation, optics, fluids, quantum mechanics...) or applied mathematics
iv) Resonant (quasi-normal mode) expansions of scattered fields and interplay with spectral instability
v) Implications of the latter point on the data analysis of exponentially damped oscillating signals.

This list is not exhaustive, but only indicative and open to consideration of affine subjects. Contributions can be in the form of an original research article but, given the need of building a common research framework, contribution in the form of “ mini reviews”, and “perspectives” are particularly welcome.

Please note that the Topic Editors will accept only B-Type Articles: Mini Review, Perspective and Brief Research Report.

Keywords: Quasi-normal Modes, Non-selfadjoint Operators, Pseudospectrum, Non-normal Dynamics, Hyperboloidal Approach, Spectral Instability, Transients, Pseudo-resonances, Black Hole Spectroscopy

Important note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.

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