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Nonlinear Gamow vectors, shock waves and irreversibility in optically nonlocal media | | Silvia Gentilini
; Maria Chiara Braidotti
; Giulia Marcucci
; Eugenio DelRe
; Claudio Conti
; | | Date: |
Tue, 4 Aug 2015 08:07:20 GMT (1860kb) | | Abstract: | Dispersive shock waves dominate wave-breaking phenomena in Hamiltonian
systems. In the absence of loss, these highly irregular and disordered waves
are potentially reversible. However, no experimental evidence has been given
about the possibility of inverting the dynamics of a dispersive shock wave and
turn it into a regular wave-front. Nevertheless, the opposite scenario, i.e., a
smooth wave generating turbulent dynamics is well studied and observed in
experiments. Here we introduce a new theoretical formulation for the dynamics
in a highly nonlocal and defocusing medium described by the nonlinear
Schroedinger equation. Our theory unveils a mechanism that enhances the degree
of irreversibility. This mechanism explains why a dispersive shock cannot be
reversed in evolution even for an arbitrarirly small amount of loss. Our theory
is based on the concept of nonlinear Gamow vectors, i.e., power dependent
generalizations of the counter-intuitive and hereto elusive exponentially
decaying states in Hamiltonian systems. We theoretically show that nonlinear
Gamow vectors play a fundamental role in nonlinear Schroedinger models: they
may be used as a generalized basis for describing the dynamics of the shock
waves, and affect the degree of irreversibility of wave-breaking phenomena.
Gamow vectors allow to analytically calculate the amount of breaking of
time-reversal with a quantitative agreement with numerical solutions. We also
show that a nonlocal nonlinear optical medium may act as a simulator for the
experimental investigation of quantum irreversible models, as the reversed
harmonic oscillator. | | Source: | arXiv, 1508.0692 | | Services: | Forum | Review | PDF | Favorites | |
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