2born (2born) wrote,
2born
2born

Нелинейная динамика и хаос в разупорядоченных гамильтоновых системах: кандидатская из ЮАР

Nonlinear dynamics and chaos in multidimensional disordered Hamiltonian systems: https://arxiv.org/abs/2105.03685
Bertin Many Manda
We study the chaotic behavior of multidimensional Hamiltonian systems in the presence of nonlinearity and disorder. It is known that any localized initial excitation in a large enough linear disordered system spreads for a finite amount of time and then halts forever. This phenomenon is called Anderson localization (AL). What happens to AL when nonlinearity is introduced is an interesting question which has been considered in several studies over the past decades. However, the characteristics and the asymptotic fate of such evolutions still remain an issue of intense debate due to their computational difficulty, especially in systems of more than one spatial dimension. As the spreading of initially localized wave packets is a non-equilibrium thermalization process related to the ergodic and chaotic properties of the system, in our work we investigate the properties of chaos studying the behavior of observables related to the system's tangent dynamics. In particular, we consider the disordered discrete nonlinear Schrödinger (DDNLS) equation of one (1D) and two (2D) spatial dimensions. We present detailed computations of the time evolution of the system's maximum Lyapunov exponent (MLE--Λ), and the related deviation vector distribution (DVD). We find that although the systems' MLE decreases in time following a power law tαΛ with αΛ<0 for both the weak and strong chaos regimes, no crossover to the behavior Λ∝t−1 (which is indicative of regular motion) is observed. In addition, the analysis of the DVDs reveals the existence of random fluctuations of chaotic hotspots with increasing amplitudes inside the excited part of the wave packet, which assist in homogenizing chaos and contribute to the thermalization of more lattice sites.
Comments: PhD Thesis, 137 pages, University of Cape Town
Tags: Мегаучебник или Что я читал и похвалил, наука, разгребая arXiv'ы, хаос
Subscribe

  • Скворцы и дети

    10 июня в парке наблюдал, как четверо скворчат преследуют родителя, а он их кормит:)) Один скворченок при этом уже держался слегка самостоятельнее, а…

  • Для разнообразия - млекопитающее

    Прошлогоднее:) DSC_2117_soba.jpg © qedqed.iMGSRC.RU DSC_2121_soba.jpg © qedqed.iMGSRC.RU DSC_2128_soba.jpg © qedqed.iMGSRC.RU…

  • А я сегодня видел куницу!!!

    Пересекла дорожку из левых зарослей в правые:))) Увы, сфотографировать не было ни малейших шансов, но хоть полюбовался, она офигительная! А…

  • Post a new comment

    Error

    default userpic

    Your reply will be screened

    Your IP address will be recorded 

    When you submit the form an invisible reCAPTCHA check will be performed.
    You must follow the Privacy Policy and Google Terms of use.
  • 0 comments