Related papers: Nonlinear Wave Chaos: Statistics of Second Harmoni…
We explore quantum chaos diagnostics of variational circuit states at random parameters and study their correlation with the circuit expressibility and the optimization of control parameters. By measuring the operator spreading coefficient…
In this paper, High-dimensional data analysis methods are proposed to deal with random matrix which is composed by the real data from power network before and after the fault. The mean spectral radius (MSR) of non-Hermitian random matrices…
The phenomenon of Stochastic Resonance (SR) is observed in a completely deterministic setting - with thermal noise being replaced by one-dimensional chaos. The piecewise linear map investigated in the paper shows a transition from…
We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when…
In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the…
The theory of mixed-feedback systems provides an effective framework for the design of robust and tunable oscillations in nonlinear systems characterized by interleaved fast positive and slow negative feedback loops. The goal of this paper…
The linear response of synchronized chaotic units with delayed couplings and feedback to small external perturbations is investigated in the context of communication with chaos synchronization. For iterated chaotic maps, the distribution of…
Random matrix spectral correlations is a defining feature of quantum chaos. Here, we study such correlations in a minimal model of chaotic many-body quantum dynamics where interactions are confined to the system's boundary, dubbed…
Despite considerable work on the energy-level and wavefunction statistics of disordered quantum systems, numerical studies of those statistics relevant for electron-electron interactions in mesoscopic systems have been lacking. We plug this…
When two resonantly interacting modes are in contact with a thermostat, their statistics is exactly Gaussian and the modes are statistically independent despite strong interaction. Considering noise-driven system, we show that when one mode…
We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by Random Matrix Theory. We demonstrate it by…
Coupled map lattices of weakly coupled Chebychev maps, so-called chaotic strings, may have a profound physical meaning in terms of dynamical models of vacuum fluctuations in stochastically quantized field theories. Here we present analytic…
The statistical model proposed in an accompanying paper is generalized to treat multiport scattering problems. Attention is first focused on two-port lossless systems and the model is shown to be consistent with Random Matrix Theory. The…
We present experimental results on eigenfunctions of a wave chaotic system in the continuous crossover regime between time-reversal symmetric and time-reversal symmetry-broken states. The statistical properties of the eigenfunctions of a…
The new phenomenon of semiquantum chaos is analyzed in a classically regular double-well oscillator model. Here it arises from a doubling of the number of effectively classical degrees of freedom, which are nonlinearly coupled in a Gaussian…
Characterizing the work statistics of driven complex quantum systems is generally challenging because of the exponential growth with the system size of the number of transitions involved between different energy levels. We consider the…
We study the parametric wave interaction in qua- dratic nonlinear media with randomized distribution of the ferroelectric domains. In particular, we discuss properties of second and cascaded third harmonic generation. We derive analytical…
Integration of electronics-based residential appliances and distributed energy resources in homes is expected to rise with grid decarbonization. These devices may introduce significant harmonics into power networks that need to be closely…
We consider a system of linear oscillators, or quantum states, described by Random Matrix Theory and analyze how its time evolution is affected by a nonlinear perturbation. Our numerical results show that above a certain chaos border a weak…
We consider the fluctuations of electromagnetic fields in chaotic microwave cavities. We calculate the transversal and longitudinal correlation function based on a random wave assumption and compare the predictions with measurements on two-…