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We apply a notion of quantum complexity, called "Krylov complexity", to study the evolution of systems from integrability to chaos. For this purpose we investigate the integrable XXZ spin chain, enriched with an integrability breaking…
This paper focuses on a fundamental inquiry in a coupled oscillator model framework. It specifically addresses the direction of net information flow in mutually coupled non-identical chaotic oscillators. Adopting a specific form of…
Until now, most memristor-based chaotic circuits proposed in the literature are based on mathematical models which assume ideal characteristics such as piece-wise linear or cubic non-linearities. The idea, illustrated here and originating…
The mixed initial-boundary value problem for infinite one-dimensional chain of harmonic oscillators on the half-line is considered. We study the large time behavior of solutions and derive the dispersive bounds.
A general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled, heterogeneous, continuous-time dynamical systems. The formalism allows for the…
The harmonic oscillator is an essential tool, widely used in all branches of Physics in order to understand more realistic systems, from classical to quantum and relativistic regimes. We know that the harmonic oscillator is integrable in…
Chaotic features of systems of coupled Josephson junctions are studied. Manifestation of chaos in the temporal dependence of the electric charge, related to a parametric resonance, is demonstrated through the calculation of the maximal…
Loschmidt echo (LE) is a measure of reversibility and sensitivity to perturbations of quantum evolutions. For weak perturbations its decay rate is given by the width of the local density of states (LDOS). When the perturbation is strong…
Pulses applied to an inhomogeneously broadened set of harmonic oscillators, previously prepared in squeezed states, can lead to a recovery of coherence, manifesting itself as echoes, similar to those exhibited by an ensemble of spins when…
This paper proposes an innovative chaotic circuit based on Chua's oscillator. It combines traditional realization of a non-linear resistor in Chua's chaotic oscillator with a promising memristive circuitry. This mixed implementation…
Classical chaotic dynamics is characterized by the exponential sensitivity to initial conditions. Quantum mechanics, however, does not show this feature. We consider instead the sensitivity of quantum evolution to perturbations in the…
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…
The evolution of any factorized time-reversible symplectic integrators, when applied to the harmonic oscillator, can be exactly solved in a closed form. The resulting modified Hamiltonians demonstrate the convergence of the Lie series…
We study an ensemble of identical noisy phase oscillators with a blinking mean-field coupling, where one-cluster and two-cluster synchronous states alternate. In the thermodynamic limit the population is described by a nonlinear…
We study and compare the information loss of a large class of Gaussian bipartite systems. It includes the usual Caldeira-Leggett type model as well as Anosov models (parametric oscillators, the inverted oscillator environment, etc), which…
The existence of a quantum butterfly effect in the form of exponential sensitivity to small perturbations has been under debate for a long time. Lately, this question gained increased interest due to the proposal to probe chaotic dynamics…
We investigate circuit complexity to characterize chaos in multiparticle quantum systems. In the process, we take a stride to analyze open quantum systems by using complexity. We propose a new diagnostic of quantum chaos from complexity…
The combined influence of oscillatory excitations and multiplicative stochastic perturbations of white noise type on isochronous systems in the plane is investigated. It is assumed that the intensity of perturbations decays with time and…
We study the dynamics of two symmetrically coupled populations of identical leaky integrate-and-fire neurons characterized by an excitatory coupling. Upon varying the coupling strength, we find symmetry-breaking transitions that lead to the…
Out-of-time order correlators (OTOCs) are crucial tools for studying quantum chaos as they show distinct scrambling behavior for chaotic Hamiltonians. We calculate OTOC and analyze the quantum information scrambling in atom-field and…