TY  - JOUR
A1  - Mulansky, Mario
A1  - Ahnert, Karsten
A1  - Pikovskij, Arkadij
A1  - Shepelyansky, Dima L.
T1  - Dynamical thermalization of disordered nonlinear lattices
N2  - We study numerically how the energy spreads over a finite disordered nonlinear one-dimensional lattice, where all linear modes are exponentially localized by disorder. We establish emergence of dynamical thermalization characterized as an ergodic chaotic dynamical state with a Gibbs distribution over the modes. Our results show that the fraction of thermalizing modes is finite and grows with the nonlinearity strength.
Y1  - 2009
UR  - http://pre.aps.org/
U6  - https://doi.org/10.1103/Physreve.80.056212
SN  - 1539-3755
ER  - 
TY  - JOUR
A1  - Mulansky, Mario
A1  - Ahnert, Karsten
A1  - Pikovskij, Arkadij
A1  - Shepelyansky, Dima L.
T1  - Strong and weak chaos in weakly nonintegrable many-body hamiltonian systems
JF  - Journal of statistical physics
N2  - We study properties of chaos in generic one-dimensional nonlinear Hamiltonian lattices comprised of weakly coupled nonlinear oscillators by numerical simulations of continuous-time systems and symplectic maps. For small coupling, the measure of chaos is found to be proportional to the coupling strength and lattice length, with the typical maximal Lyapunov exponent being proportional to the square root of coupling. This strong chaos appears as a result of triplet resonances between nearby modes. In addition to strong chaos we observe a weakly chaotic component having much smaller Lyapunov exponent, the measure of which drops approximately as a square of the coupling strength down to smallest couplings we were able to reach. We argue that this weak chaos is linked to the regime of fast Arnold diffusion discussed by Chirikov and Vecheslavov. In disordered lattices of large size we find a subdiffusive spreading of initially localized wave packets over larger and larger number of modes. The relations between the exponent of this spreading and the exponent in the dependence of the fast Arnold diffusion on coupling strength are analyzed. We also trace parallels between the slow spreading of chaos and deterministic rheology.
KW  - Lyapunov exponent
KW  - Arnold diffusion
KW  - Chaos spreading
Y1  - 2011
U6  - https://doi.org/10.1007/s10955-011-0335-3
SN  - 0022-4715
VL  - 145
IS  - 5
SP  - 1256
EP  - 1274
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Mulansky, Mario
A1  - Ahnert, Karsten
A1  - Pikovskij, Arkadij
T1  - Scaling of energy spreading in strongly nonlinear disordered lattices
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - To characterize a destruction of Anderson localization by nonlinearity, we study the spreading behavior of initially localized states in disordered, strongly nonlinear lattices. Due to chaotic nonlinear interaction of localized linear or nonlinear modes, energy spreads nearly subdiffusively. Based on a phenomenological description by virtue of a nonlinear diffusion equation, we establish a one-parameter scaling relation between the velocity of spreading and the density, which is confirmed numerically. From this scaling it follows that for very low densities the spreading slows down compared to the pure power law.
Y1  - 2011
U6  - https://doi.org/10.1103/PhysRevE.83.026205
SN  - 1539-3755
VL  - 83
IS  - 2
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Ahnert, Karsten
A1  - Pikovskij, Arkadij
T1  - Compactons and chaos in strongly nonlinear lattices
N2  - We study localized traveling waves and chaotic states in strongly nonlinear one-dimensional Hamiltonian lattices. We show that the solitary waves are superexponentially localized and present an accurate numerical method allowing one to find them for an arbitrary nonlinearity index. Compactons evolve from rather general initially localized perturbations and collide nearly elastically. Nevertheless, on a long time scale for finite lattices an extensive chaotic state is generally observed. Because of the system's scaling, these dynamical properties are valid for any energy.
Y1  - 2009
UR  - http://pre.aps.org/
U6  - https://doi.org/10.1103/Physreve.79.026209
SN  - 1539-3755
ER  -