Open AccessGamow vectors explain the shock profile
Author(s) -
Maria Chiara Braidotti,
Silvia Gentilini,
Claudio Conti
Publication year - 2016
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.24.021963
Subject(s) - physics , nonlinear system , shock wave , rigged hilbert space , shock (circulatory) , eigenvalues and eigenvectors , harmonic oscillator , classical mechanics , hilbert space , harmonic , optics , quantum mechanics , mechanics , reproducing kernel hilbert space , medicine
The description of shock waves beyond the shock point is a challenge in nonlinear physics and optics. Finding solutions to the global dynamics of dispersive shock waves is not always possible due to the lack of integrability. Here we propose a new method based on the eigenstates (Gamow vectors) of a reversed harmonic oscillator in a rigged Hilbert space. These vectors allow analytical formulation for the development of undular bores of shock waves in a nonlinear nonlocal medium. Experiments by a photothermal induced nonlinearity confirm theoretical predictions: the undulation period as a function of power and the characteristic quantized decays of Gamow vectors. Our results demonstrate that Gamow vectors are a novel and effective paradigm for describing extreme nonlinear phenomena.