nucl-th digest · Jun 12, 2024

[Submitted on 10 Jun 2024] (cross-list from hep-th)

Transient dynamics of quasinormal mode sums

Quasinormal modes of spacetimes with event horizons are typically governed by a non-normal operator. This gives rise to spectral instabilities, a topic of recent interest in the black hole pseudospectrum programme. In this work we show that non-normality leads to the existence of arbitrarily long-lived sums of short-lived quasinormal modes, corresponding to localising packets of energy near the future horizon. There exist sums of $M$ quasinormal modes whose lifetimes scale as $lo g M$ . This transient behaviour results from large cancellations between non-orthogonal quasinormal modes. We provide simple closed-form examples for a massive scalar field in the static patch of dS $_{d + 1}$ and the BTZ black hole. We also provide numerical examples for scalar perturbations of Schwarzschild-AdS $_{d + 1}$ , and gravitational perturbations of Schwarzschild in asymptotically flat spacetime, using hyperboloidal foliations. The existence of these perturbations is linked to certain properties of black hole pseudospectra. We comment on implications for thermalisation times in holographic plasmas.

Comments:: 42 pages, 12 figures, 1 table. Added some comments and references. Matches published version
Subjects:: High Energy Physics — Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el); General Relativity and Quantum Cosmology (gr-qc); Nuclear Theory (nucl-th)
arXiv:: 2406.06685 [pdf]

JHEP(2024)·26 citations

Anomalous propagators and the particle-particle channel: Hedin's equations

Hedin's equations provide an elegant route to compute the exact one-body Green's function (or propagator) via the self-consistent iteration of a set of non-linear equations. Its first-order approximation, known as

G W

, corresponds to a resummation of ring diagrams and has shown to be extremely successful in physics and chemistry. Systematic improvement is possible, although challenging, via the introduction of vertex corrections. Considering anomalous propagators and an external pairing potential, we derive a new self-consistent set of closed equations equivalent to the famous Hedin equations but having as a first-order approximation the particle-particle (pp)

T

-matrix approximation where one performs a resummation of the ladder diagrams. This pp version of Hedin's equations offers a way to go systematically beyond the

T

-matrix approximation by accounting for low-order pp vertex corrections.

Comments:: 12 pages, 5 figures (Supp. Mat. available)
Subjects:: physics.chem-ph (physics.chem-ph); cond-mat.mtrl-sci (cond-mat.mtrl-sci); Strongly Correlated Electrons (cond-mat.str-el); Nuclear Theory (nucl-th)
arXiv:: 2406.07062 [pdf]

PRB(2024)·5 citations

Wednesday·June 12, 2024

Transient dynamics of quasinormal mode sums

Anomalous propagators and the particle-particle channel: Hedin's equations

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