Roles of GARCH and ARCH effects on the stability in stock market crash

We theoretically stochastic simulate and empirically analyze the escape process of stock market price nonequilibrium dynamics under the influence of GARCH and ARCH effects, and explore the impact of ARCH and GARCH effects on stock market stability. Based on the nonlinear GARCH model of econophysics, and combined with GARCH and ARCH effects of volatility, we propose a delay stochastic monostable potential model. We use the mean escape time, or mean hitting time, as an indicator for measuring price stability, as first introduced in Ref. [1]. Based on the comparative analysis of actual Chinese A-share data, the theoretical and empirical findings of this paper are as follows} (1) The theoretical simulation results and actual data are consistent. (2) There exist optimal GARCH and ARCH effects maximally enhancing stock market stability.

Topological holographic quench dynamics in a synthetic frequency dimension

The notion of topological phases extended to dynamical systems stimulates extensive studies, of which the characterization of nonequilibrium topological invariants is a central issue and usually necessitates the information of quantum dynamics in both the time and momentum dimensions. Here, we propose the topological holographic quench dynamics in synthetic dimension, and also show it provides a highly efficient scheme to characterize photonic topological phases. A pseudospin model is constructed with ring resonators in a synthetic lattice formed by frequencies of light, and the quench dynamics is induced by initializing a trivial state, which evolves under a topological Hamiltonian. Our key prediction is that the complete topological information of the Hamiltonian is encoded in quench dynamics solely in the time dimension, and is further mapped to lower-dimensional space, manifesting the holographic features of the dynamics. In particular, two fundamental time scales emerge in the dynamical evolution, with one mimicking the topological band on the momentum dimension and the other characterizing the residue time evolution of the state after the quench. For this, a universal duality between the quench dynamics and the equilibrium topological phase of the spin model is obtained in the time dimension by extracting information from the field evolution dynamics in modulated ring systems in simulations. This work also shows that the photonic synthetic frequency dimension provides an efficient and powerful way to explore the topological nonequilibrium dynamics.

X-ray scattering from light-driven spin fluctuations in a doped Mott insulator

Manipulating spin fluctuations with ultrafast laser pulses is a promising route to dynamically control collective phenomena in strongly correlated materials. However, understanding how photoexcited spin degrees of freedom evolve at a microscopic level requires a momentum- and energy-resolved characterization of their nonequilibrium dynamics. Here, we study the photoinduced dynamics of finite-momentum spin excitations in two-dimensional Mott insulators on a square lattice. By calculating the time-resolved resonant inelastic x-ray scattering cross-section, we show that an ultrafast pump above the Mott gap induces a prompt softening of the spin excitation energy, compatible with a transient renormalization of the exchange interaction. While spin fluctuations in a hole-doped system (paramagnons) are well described by Floquet theory, magnons at half filling are found to deviate from this picture. Furthermore, we show that the paramagnon softening is accompanied by an ultrafast suppression of d-wave pairing correlations, indicating a link between the transient spin excitation dynamics and superconducting pairing far from equilibrium.