Instabilities Appearing in Effective Field theories: When and How? - Archive ouverte HAL
Article Dans Une Revue Nonlinearity Année : 2023

Instabilities Appearing in Effective Field theories: When and How?

Résumé

Nonlinear partial differential equations appear in many domains of physics, and we study here a typical equation which one finds in effective field theories (EFT) originated from cosmological studies. In particular, we are interested in the equation $\partial_t^2 u(x,t) = \alpha (\partial_x u(x,t))^2 +\beta \partial_x^2 u(x,t)$ in $1+1$ dimensions. It has been known for quite some time that solutions to this equation diverge in finite time, when $\alpha >0$. We study the detailed nature of this divergence as a function of the parameters $\alpha>0 $ and $\beta\ge0$. The divergence does not disappear even when $\beta $ is very large contrary to what one might believe. But it will take longer to appear as $\beta$ increases when $\alpha$ is fixed. We note that there are two types of divergence and we discuss the transition between these two as a function of parameter choices. The blowup is unavoidable unless the corresponding equations are modified. Our results extend to $3+1$ dimensions.
Fichier principal
Vignette du fichier
Eckmann_2023_Nonlinearity_36_4844.pdf (521.89 Ko) Télécharger le fichier
Origine Fichiers éditeurs autorisés sur une archive ouverte
Licence

Dates et versions

hal-03873076 , version 1 (16-09-2024)

Licence

Identifiants

Citer

Jean-Pierre Eckmann, Farbod Hassani, Hatem Zaag. Instabilities Appearing in Effective Field theories: When and How?. Nonlinearity, 2023, 36 (9), pp.4844-4861. ⟨10.1088/1361-6544/ace769⟩. ⟨hal-03873076⟩
55 Consultations
3 Téléchargements

Altmetric

Partager

More