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Register a new userSpreading of wave packets in disordered systems with tunable nonlinearity
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We study the spreading of single-site excitations in one-dimensional disordered Klein-Gordon chains with tunable nonlinearity $|u_{l}|^{sigma} u_{l}$ for different values of $sigma$. We perform extensive numerical simulations where wave packets are evolved a) without and, b) with dephasing in normal mode space. Subdiffusive spreading is observed with the second moment of wave packets growing as $t^{alpha}$. The dependence of the numerically computed exponent $alpha$ on $sigma$ is in very good agreement with our theoretical predictions both for the evolution of the wave packet with and without dephasing (for $sigma geq 2$ in the latter case). We discuss evidence of the existence of a regime of strong chaos, and observe destruction of Anderson localization in the packet tails for small values of $sigma$.
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We consider the spatiotemporal evolution of a wave packet in disordered nonlinear Schrodinger and anharmonic oscillator chains. In the absence of nonlinearity all eigenstates are spatially localized with an upper bound on the localization length (Anderson localization). Nonlinear terms in the equations of motion destroy Anderson localization due to nonintegrability and deterministic chaos. At least a finite part of an initially localized wave packet will subdiffusively spread without limits. We analyze the details of this spreading process. We compare the evolution of single site, single mode and general finite size excitations, and study the statistics of detrapping times. We investigate the properties of mode-mode resonances, which are responsible for the incoherent delocalization process.
We reveal the generic characteristics of wave packet delocalization in two-dimensional nonlinear disordered lattices by performing extensive numerical simulations in two basic disordered models: the Klein-Gordon system and the discrete nonlinear Schr{o}dinger equation. We find that in both models (a) the wave packets second moment asymptotically evolves as $t^{a_m}$ with $a_m approx 1/5$ ($1/3$) for the weak (strong) chaos dynamical regime, in agreement with previous theoretical predictions [S.~Flach, Chem.~Phys.~{bf 375}, 548 (2010)], (b) chaos persists, but its strength decreases in time $t$ since the finite time maximum Lyapunov exponent $Lambda$ decays as $Lambda propto t^{alpha_{Lambda}}$, with $alpha_{Lambda} approx -0.37$ ($-0.46$) for the weak (strong) chaos case, and (c) the deviation vector distributions show the wandering of localized chaotic seeds in the lattices excited part, which induces the wave packets thermalization. We also propose a dimension-independent scaling between the wave packets spreading and chaoticity, which allows the prediction of the obtained $alpha_{Lambda}$ values.
We study the problem of wave transport in a one-dimensional disordered system, where the scatterers of the chain are $n$ barriers and wells with statistically independent intensities and with a spatial extension $l_c$ which may contain an arbitrary number $delta/2pi$ of wavelengths, where $delta = k l_c$. We analyze the average Landauer resistance and transmission coefficient of the chain as a function of $n$ and the phase parameter $delta$. For weak scatterers, we find: i) a regime, to be called I, associated with an exponential behavior of the resistance with $n$, ii) a regime, to be called II, for $delta$ in the vicinity of $pi$, where the system is almost transparent and less localized, and iii) right in the middle of regime II, for $delta$ very close to $pi$, the formation of a band gap, which becomes ever more conspicuous as $n$ increases. In regime II, both the average Landauer resistance and the transmission coefficient show an oscillatory behavior with $n$ and $delta$. These characteristics of the system are found analytically, some of them exactly and some others approximately. The agreement between theory and simulations is excellent, which suggests a strong motivation for the experimental study of these systems. We also present a qualitative discussion of the results.
Formation of bright envelope solitons from wave packets with a repulsive nonlinearity was observed for the first time. The experiments used surface spin-wave packets in magnetic yttrium iron garnet (YIG) thin film strips. When the wave packets are narrow and have low power, they undergo self-broadening during the propagation. When the wave packets are relatively wide or their power is relatively high, they can experience self-narrowing or even evolve into bright solitons. The experimental results were reproduced by numerical simulations based on a modified nonlinear Schrodinger equation model.
Using Gaussian integral transform techniques borrowed from functional-integral field theory and the replica trick we derive a version of the coherent-potential approximation (CPA) suited for describing ($i$) the diffusive (hopping) motion of classical particles in a random environment and ($ii$) the vibrational properties of materials with spatially fluctuating elastic coefficients in topologically disordered materials. The effective medium in the present version of the CPA is not a lattice but a homogeneous and isotropic medium, representing an amorphous material on a mesoscopic scale. The transition from a frequency-independent to a frequency-dependent diffusivity (conductivity) is shown to correspond to the boson peak in the vibrational model. The anomalous regimes above the crossover are governed by a complex, frequency-dependent self energy. The boson peak is shown to be stronger for non-Gaussian disorder than for Gaussian disorder. We demonstrate that the low-frequency non-analyticity of the off-lattice version of the CPA leads to the correct long-time tails of the velocity autocorrelation function in the hopping problem and to low-frequency Rayleigh scattering in the wave problem. Furthermore we show that the present version of the CPA is capable to treat the percolative aspects of hopping transport adequately.
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