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We study a system of $N\gg 1$ degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing to an equilibrium…
A wide variety of physical systems ranging from the firing of neurons to eutrophication of lakes to the presence of Arctic summer sea ice exhibit a phenomenon known as tipping. In mathematical models, tipping can be caused by bifurcations,…
Three abilities - the ability to recognize sounds, the ability to visually recognize movement and the ability to keep an upright standing position - can function only with using precise measurements of the short time intervals. Other…
Bistable autonomous systems can be found inmany areas of science. When the intrinsic noise intensity is large, these systems exhibits stochastic transitions from onemetastable steady state to another. In electronic bistable memories, these…
The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…
Algorithms are developed for the quickest detection of a change in statistically periodic processes. These are processes in which the statistical properties are nonstationary but repeat after a fixed time interval. It is assumed that the…
When matter undergoes a phase transition from one state to another, usually a change in symmetry is observed, as some of the symmetries exhibited are said to be spontaneously broken. The superconducting phase transition in the underdoped…
This article provides a characterization of stability for switched nonlinear systems under average dwell-time constraints, in terms of necessary and sufficient conditions involving multiple Lyapunov functions. Earlier converse results focus…
Across natural and human-made systems, transition points mark sudden changes of order and are thus key to understanding overarching system features. Motivated by recent experimental observations, we here uncover an intriguing class of…
We analyst in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems (see Phys. Rev. Lett . vol. 113, 264102 (2014)) by application to the Tangled Nature Model of evolutionary…
Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…
Self-gravitating systems are expected to reach a statistical equilibrium state either through collisional relaxation or violent collisionless relaxation. However, a maximum entropy state does not always exist and the system may undergo a…
We demonstrate that turbulent zonal jets, analogous to Jovian ones, which are quasi-stationary, are actually metastable. After extremely long times, they randomly switch to new configurations with a different number of jets. The genericity…
Existence of Anderson localization is considered a manifestation of coherence of classical and quantum waves in disordered systems. Signatures of localization have been observed in condensed matter and cold atomic systems where the coupling…
We consider phase transitions, in the form of spontaneous symmetry breaking (SSB) bifurcations of solitons, in dual-core couplers with fractional diffraction and cubic self-focusing acting in each core, characterized by Levy index $\alpha$.…
Statistical behavior of a classical $\phi ^{4}$ Hamiltonian lattice is investigated from microscopic dynamics. The largest Lyapunov exponent and entropies are considered for manifesting chaos and equipartition behaviors of the system. It is…
In this work, the interplay between non-Hermiticity, quasi-disorder, and repulsive interaction is studied for hard-core bosons confined in a one-dimensional optical lattice, where non-Hermiticity is induced by the non-reciprocal hoppings…
We suggest a technique for the observation of a predicted supersolid phase in extended Bose-Hubbard models which are potentially realizable in cold atom optical lattice systems. In particular, we discuss important subtleties arising from…
The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The…
Phase transitions are fundamental features of statistical physics. While the well-studied continuous phase transitions are known to be controlled by external \textit{macroscopic} changes in the order parameter, the origin of abrupt…