The cooperative behavior of a system of atoms contained in a ring cavity is investigated under the condition that the fundamental atomic transition is a two photon transition1. Maxwell-Block equations are used to obtain the input vs. output relation by adiabatically eliminating all the atomic variables. The fundamental equation that results is a complex two dimensional map--which in the mean field limit reduces to the standard bistability equations. The characteristics of the two dimensional map are numerically investigated. Such a map is shown to lead to chaotic behavior following the Feigenbaum2 scenario. The sequence of events following first regime of chaos is a set of period halving bifurcations. The characteristics of the power spectrum in the region of chaos are presented. The effect of noise on the period doubling bifurcations in the present model, is also investigated and the connection with the theoretical predictions3 is established. The changes in the dynamical characteristics of the system when atomic inversion relaxes on the same time scale as the cavity round trip time will also be discussed in detail.
Out-of-time-ordered correlators (OTOCs) have emerged as a diagnostic of information scrambling and quantum chaos in many-body systems. We investigate the imprints of chaos in the dynamics of OTOCs in the Heisenberg spin-
1/2 chain with random fields. The system is parameterized to exhibit a crossover from integrable to chaotic dynamics. We demonstrate numerically that the approach to saturation of the OTOC can distinguish between integrable and chaotic regimes, with a power-law
(1/t) relaxation for integrable systems and a higher-degree power-law decay
(1/tα;α≥1) followed by an exponential relaxation for the chaotic regime. We further show that long-range spectral statistics, such as the number variance, are more effective in characterizing quantum chaos in the regime near saturation of OTOC. We also demonstrate that the relaxation and initial scrambling regimes exhibit distinct and universal features, with the former being sensitive and the latter being robust against different realizations of random-fields. The long-time saturation of OTOC also fluctuates with different realizations, and its exact expression is derived through the Eigenstate Thermalization Hypothesis.
This work presents the first empirical confirmation of the Static Vibrational Reality (SVR) coherence law within a fully quantum system.By reanalyzing experimental data from Rydberg-atom superradiance, we demonstrate that both the buildup and decay of coherence obey the same nonlinear scaling relation.The characteristic energy–time exponent γ≈1.9 remains invariant across the growth and relaxation phases, confirming a cyclic symmetry in quantum coherence dynamics. These results reveal that quantum amplification and decoherence are not distinct phenomena but complementary phases of a single self-regulating process.Within the SVR framework, time emerges as a phase projection of coherent energy, establishing a direct physical link between quantum reversibility and macroscopic irreversibility.The findings identify coherence as a conserved, cyclic quantity and provide a unifying bridge between quantum and classical descriptions of reality.