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How do isolated quantum systems approach an equilibrium state? We experimentally and theoretically address this question for a prototypical spin system formed by ultracold atoms prepared in two Rydberg states with different orbital angular momenta. By coupling these states with a resonant microwave driving, we realize a dipolar XY spin-1/2 model in an external field. Starting from a spin-polarized state, we suddenly switch on the external field and monitor the subsequent many-body dynamics. Our key observation is density dependent relaxation of the total magnetization much faster than typical decoherence rates. To determine the processes governing this relaxation, we employ different theoretical approaches that treat quantum effects on initial conditions and dynamical laws separately. This allows us to identify an intrinsically quantum component to the relaxation attributed to primordial quantum fluctuations.

We outline a kinetic theory of non-thermal fixed points for the example of a dilute Bose gas, partially reviewing results obtained earlier, thereby extending, complementing, generalizing and straightening them out. We study universal dynamics after a cooling quench, focusing on situations where the time evolution represents a pure rescaling of spatial correlations, with time defining the scale parameter. The non-equilibrium initial condition set by the quench induces a redistribution of particles in momentum space. Depending on conservation laws, this can take the form of a wave-turbulent flux or of a more general self-similar evolution, signaling the critically slowed approach to a non-thermal fixed point. We identify such fixed points using a non-perturbative kinetic theory of collective scattering between highly occupied long-wavelength modes. In contrast, a wave-turbulent flux, possible in the perturbative Boltzmann regime, builds up in a critically accelerated self-similar manner. A key result is the simple analytical universal scaling form of the non-perturbative many-body scattering matrix, for which we lay out the concrete conditions under which it applies. We derive the scaling exponents for the time evolution as well as for the power-law tail of the momentum distribution function, for a general dynamical critical exponent z and an anomalous scaling dimension η. The approach of the non-thermal fixed point is, in particular, found to involve a rescaling of momenta in time t by t β , with β = 1/z, within our kinetic approach independent of η. We confirm our analytical predictions by numerically evaluating the kinetic scattering integral as well as the non-perturbative many-body coupling function. As a side result we obtain a possible finite-size interpretation of wave-turbulent scaling recently measured by Navon et al.

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