Related papers: Generalized phase transitions in finite coupled ma…
We present a construction method for mappings between generalized connections, comprising, e.g., the action of gauge transformations, diffeomorphisms and Weyl transformations. Moreover, criteria for continuity and measure preservation are…
We review connections between phase transitions in high-dimensional combinatorial geometry and phase transitions occurring in modern high-dimensional data analysis and signal processing. In data analysis, such transitions arise as abrupt…
We re-examine attempts to study the many-body localization transition using measures that are physically natural on the ergodic/quantum chaotic regime of the phase diagram. Using simple scaling arguments and an analysis of various models…
Synchronization among globally coupled, chaotic map lattices can be related to stable periodic windows in isolated chaotic maps. This relation provides a simple predictive tool for the understanding of complicated behavior in coupled…
Two replicas of spatially extended chaotic systems synchronize to a common spatio-temporal chaotic state when coupled above a critical strength. As a prototype of each single spatio-temporal chaotic system a lattice of maps interacting via…
We develop a simple and general variational method to estimate the solutions of the Gross-Pitaevskii equations and obtain the corresponding density profiles for all spin states of a trapped spin-1 Bose-Einstein condensate. We further employ…
Synchronisation between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the strength of coupling often leads to qualitative changes in the complex dynamics of the mutually coupled…
We review our recent work on the synchronization of a network of delay-coupled maps, focusing on the interplay of the network topology and the delay times that take into account the finite velocity of propagation of interactions. We assume…
In this paper we report for the first time on the necessity of the refinement of the concept of generalized chaotic synchronization. We show that the state vectors of the interacting chaotic systems being in the generalized synchronization…
We establish the connection between a multichannel disordered model --the 1D Dirac equation with $N\times N$ matricial random mass-- and a random matrix model corresponding to a deformation of the Laguerre ensemble. This allows us to derive…
We consider a class of generalised single mode Dicke Hamiltonians with arbitrary boson coupling in the pseudo-spin $x$-$z$ plane. We find exact solutions in the thermodynamic, large-spin limit as a function of the coupling angle, which…
We study circle maps with a flat interval where the critical exponents at the two boundary points of the flat spot might be different. The space of such systems is partitioned in two connected parts whose common boundary only depends on the…
We investigate the spatio-temporal dynamics of coupled chaotic systems with nonlocal interactions, where each element is coupled to its nearest neighbors within a finite range. Depending upon the coupling strength and coupling radius, we…
The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent attractors, has not been realized yet even though it has been well studied in chaotic dynamical systems without delay. We report the…
We present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of "chaoticity". The systems to be quantized are piecewise affine maps on the two-torus, viewed as phase space, and include the…
Though the notion of phase synchronization has been well studied in chaotic dynamical systems without delay, it has not been realized yet in chaotic time-delay systems exhibiting non-phase coherent hyperchaotic attractors. In this article…
The universal mechanism resulting in the generalized synchronization regime arising in the chaotic oscillators with the dissipative coupling has been described. The reasons of the generalized synchronization occurrence may be clarified by…
We investigate the effects of phase-breaking events on electronic transport through ballistic chaotic cavities. We simulate phase-breaking by a fictitious lead connecting the cavity to a phase-randomizing reservoir and introduce a…
We provide sufficient conditions for the uniqueness of an invariant measure of a Markov process as well as for the weak convergence of transition probabilities to the invariant measure. Our conditions are formulated in terms of generalized…
We analyze the size limits of coupled map lattices with diffusive coupling at the crossover of low-dimensional to high-dimensional chaos. We investigate the existence of standing-wave-type periodic patterns, within the low-dimensional…