Related papers: Weak and strong chaos in FPU models and beyond
We consider a basic model of the lossless interaction between a moving two-level atom and a standing-wave single-mode laser field. Classical treatment of the translational atomic motion provides the semiclassical Hamilton-Schrodinger…
We study the dynamics of the $(\alpha+\beta)$ Fermi-Pasta-Ulam-Tsingou lattice (FPUT lattice, for short) for an arbitrary number $N$ of interacting particles, in regimes of small enough nonlinearity so that a Birkhoff-Gustavson type of…
The purpose of this contribution is to summarize and discuss recent advances regarding the onset of turbulence in shear flows. The absence of a clear cut instability mechanism, the spatio-temporal intermittent character and extremely long…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
The Fermi--Pasta--Ulam--Tsingou (FPUT) system, describing the evolution of $N$ coupled harmonic oscillators, has been the subject of much attention since the 1950's when experiments which contradicted predictions of thermalization of the…
Autonomous randomly coupled neural networks display a transition to chaos at a critical coupling strength. We here investigate the effect of a time-varying input on the onset of chaos and the resulting consequences for information…
Recent numerical work on the fate of plasma instabilities in weakly-coupled non-Abelian gauge theory has shown the development of a cascade of energy from long to short wavelengths. This cascade has a steady-state spectrum, analogous to the…
We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth random potential, which allows us to apply the ballistic $\sigma$-model approach. We analyze conditions of…
We introduce the $\alpha$-Gauss-Logistic map, a new nonlinear dynamics constructed by composing the logistic and $\alpha$-Gauss maps. Explicitly, our model is given by $x_{t+1} = f_L(x_t)x_t^{-\alpha} - \lfloor f_L(x_t)x_t^{-\alpha} \rfloor…
It is shown that the nonlinear wave equation $\partial_t^2\phi - \partial^2_x \phi -\mu_0\partial_x(\partial_x\phi)^3 =0$, which is the continuum limit of the Fermi-Pasta-Ulam (FPU) beta model, has a positive Lyapunov exponent lambda_1,…
Simple dynamical systems -- with a small number of degrees of freedom -- can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small…
In this paper, we introduce a novel method to identify transitions from steady states to chaos in stochastic models, specifically focusing on the logistic and Ricker equations by leveraging the gamma distribution to describe the underlying…
We show the relevance of the dispersive analogue of the shock waves in the FPU dynamics. In particular we give strict numerical evidences that metastable states emerging from low frequency initial excitations, are indeed constituted by…
Stable chaos refers to the long irregular transients, with a negative largest Lyapunov exponent, which is usually observed in certain high-dimensional dynamical systems. The mechanism underlying this phenomenon has not been well studied so…
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
Small systems in a thermodynamic medium --- like colloids in a suspension or the molecular machinery in living cells --- are strongly affected by the thermal fluctuations of their environment. Physicists model such systems by means of…
We will present a survey of low energy periodic Fermi-Pasta-Ulam chains with leading idea the "breaking of symmetry". The classical periodic FPU-chain (equal masses for all particles) was analysed by Rink in 2001 with main conclusions that…
A distinct feature of Hermitian quantum chaotic dynamics is the exponential increase of certain out-of-time-order-correlation (OTOC) functions around the Ehrenfest time with a rate given by a Lyapunov exponent. Physically, the OTOCs…
Particles in pressure-driven channel flow are often inhomogeneously distributed. Two modes of low-Reynolds number instability, absent in Poiseuille flow of clean fluid, are created by inhomogeneous particle loading, and their mechanism is…
A hypothesis on the physical mechanism generating the heartbeat instability in complex (dusty) plasmas is presented. It is suggested that the instability occurs due to the periodically repeated critical transformation on the boundary…