Abstract
Whether it be physical, biological or social processes, complex systems exhibit dynamics that are exceedingly difficult to understand or predict from underlying principles. Here we report a striking correspondence between the excitation dynamics of a laser driven gas of Rydberg atoms and the spreading of diseases, which in turn opens up a controllable platform for studying non-equilibrium dynamics on complex networks. The competition between facilitated excitation and spontaneous decay results in sub-exponential growth of the excitation number, which is empirically observed in real epidemics. Based on this we develop a quantitative microscopic susceptible-infected-susceptible model which links the growth and final excitation density to the dynamics of an emergent heterogeneous network and rare active region effects associated to an extended Griffiths phase. This provides physical insights into the nature of non-equilibrium criticality in driven many-body systems and the mechanisms leading to non-universal power-laws in the dynamics of complex systems.
Highlights
Whether it be physical, biological or social processes, complex systems exhibit dynamics that are exceedingly difficult to understand or predict from underlying principles
The observed dynamics follow a power-law time dependence that parallels that which is empirically observed in real-world epidemics, providing a powerful demonstration of universality reaching beyond physics
The microscopic processes governing the dynamics of ultracold atoms driven to Rydberg states by an off-resonant laser field, shown in Fig. 1a, b, bear close similarities to those in epidemics[12]
Summary
The two-body facilitation rate κ is proportional to the laser intensity which can be tuned over a wide range This can be understood as an effective rate averaged over the different excitation channels corresponding to many Rydberg pair-state interaction potentials. (instantaneous number of excitations divided by their lifetime τ = (2πΓ)−1) against its time integral C, shown by the darkest green data points This clearly shows that the incidence rate follows the GGM over several decades (evidenced by a straight line on a double logarithmic scale) with a deceleration of growth parameter p = 0.59(1) that is comparable to empirical observations of real epidemics[1]. The probability for a given node i to become infected is described by the following stochastic master equation[2]
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