Stable and metastable states and the formation and destruction of breathers in the discrete nonlinear Schrödinger equation

Rumpf, Benno

doi:10.1016/j.physd.2009.08.006

Cited by 38 publications

(40 citation statements)

References 22 publications

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“…The reported dynamical regimes in the Gibbsean and nonGibbsean are remarkably different [7,8,9,10,11,12]. While the Gibbsean regime is characterized by a relatively quick decay into a thermal equilibrium on time scales which are presumably inverse proportional to the largest Lyapunov coefficient, the nonGibbsean regime is very different.…”

Section: Gibbsean and Nongibbsean Regimesmentioning

confidence: 99%

Spreading, Nonergodicity, and Selftrapping: A Puzzle of Interacting Disordered Lattice Waves

Flach

2015

Springer Proceedings in Physics

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Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transitions, the quantum Hall effect, light propagation in photonic crystals, and dynamics of ultra-cold atoms in optical arrays, to name just a few examples. Large intensity light can induce nonlinear response, ultracold atomic gases can be tuned into an interacting regime, which leads again to nonlinear wave equations on a mean field level. The interplay between disorder and nonlinearity, their localizing and delocalizing effects is currently an intriguing and challenging issue in the field of lattice waves. In particular it leads to the prediction and observation of two different regimes of destruction of Anderson localization -asymptotic weak chaos, and intermediate strong chaos, separated by a crossover condition on densities. On the other side approximate full quantum interacting many body treatments were recently used to predict and obtain a novel many body localization transition, and two distinct phases -a localization phase, and a delocalization phase, both again separated by some typical density scale. We will discuss selftrapping, nonergodicity and nonGibbsean phases which are typical for such discrete models with particle number conservation and their relation to the above crossover and transition physics. We will also discuss potential connections to quantum many body theories.

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Section: Gibbsean and Nongibbsean Regimesmentioning

confidence: 99%

Spreading, Nonergodicity, and Selftrapping: A Puzzle of Interacting Disordered Lattice Waves

Flach

2015

Springer Proceedings in Physics

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“…Here, the diffusive regime is preceded by jump-like increases of P which correspond to radiation of substantial parts of norm as small amplitude waves. It is expected that discrete breathers remain robust upon radiation of small amplitude waves [34] which can be treated as linear background of the high amplitude breather [35]. Consequently, when dephasing is only performed very rarely, new self-trapping may occur leading to a series of stepwise increases of P (Fig.4(a)) .…”

Section: Decohering and Delocalizingmentioning

confidence: 99%

Decohering localized waves

2013

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In the absence of confinement localization of waves takes place due to randomness or nonlinearity and relies on their phase coherence. We quantitatively probe the sensitivity of localized wave packets to random phase fluctuations and confirm the necessity of phase coherence for localization. Decoherence resulting from a dynamical random environment leads to diffusive spreading and destroys linear and nonlinear localization. We find that maximal spreading is achieved for optimal phase fluctuation characteristics which is a consequence of the competition between diffusion due to decoherence and ballistic transport within the mean free path distance.

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“…Its fame is also due to the so-called negativetemperature region [14,[26][27][28], where equipartition is violated due to the spontaneous emergence of breathers out of a noisy background. Statistical-mechanical arguments [29][30][31][32] show that the density of breathers should progressively decrease until a final state is reached where a single breather collects the excess energy from the background. Such relaxation process, induced by purely entropic forces, has been understood to be a condensation phenomenon [33][34][35] due to the existence of two conserved quantities, the mass and the energy.…”

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confidence: 99%

“…Conversely, for T > 0 (i.e. a 2 − 2a < h < 2a 2 [26]), breathers are entropically disadvantaged and must decay [26,[29][30][31][32]. In this Letter we probe the positive-temperature frozen dynamics by studying the relaxation of a single breather initially set at n = 0, with T and the chemical potential µ imposed by external reservoirs acting on both chain ends [39].…”

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confidence: 99%

Dynamical Freezing of Relaxation to Equilibrium

et al. 2019

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We provide evidence of an extremely slow thermalization occurring in the Discrete NonLinear Schrödinger (DNLS) model. At variance with many similar processes encountered in statistical mechanics -typically ascribed to the presence of (free) energy barriers -here the slowness has a purely dynamical origin: it is due to the presence of an adiabatic invariant, which freezes the dynamics of a tall breather. Consequently, relaxation proceeds via rare events, where energy is suddenly released towards the background. We conjecture that this exponentially slow relaxation is a key ingredient contributing to the non-ergodic behavior recently observed in the negative temperature region of the DNLS equation.

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Stable and metastable states and the formation and destruction of breathers in the discrete nonlinear Schrödinger equation

Cited by 38 publications

References 22 publications

Spreading, Nonergodicity, and Selftrapping: A Puzzle of Interacting Disordered Lattice Waves

Spreading, Nonergodicity, and Selftrapping: A Puzzle of Interacting Disordered Lattice Waves

Decohering localized waves

Dynamical Freezing of Relaxation to Equilibrium

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