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Does an isolated quantum system relax?

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Interfering two isolated one-dimensional quantum gases we study how the coherence created between the two many body systems by the splitting process slowly degrades by coupling to the many internal degrees of freedom available [1]. Two distinct regimes are clearly visible: for short length scales the system is characterized by spin diffusion, for long length scales by spin decay [2]. For a sudden quench the system approaches a pre-thermalized state [3], which is characterized by thermal like correlation functions in the observed interference fringes with an effective temperature over five times lower than the kinetic temperature of the initial system. A detailed study of the time evolution of the correlation functions reveals that these thermal-like properties emerge locally in their final form and propagate through the system in a light-cone-like evolution [4]. Furthermore we demonstrate, that the pre-thermalized state is described by a generalized Gibbs ensemble [5]. This is verified through a detailed study of the full non-translation invariant phase correlation functions up to 10th order. Finally we show two distinct ways for subsequent evolution away from the pre-thermalized state. One proceeds by further de-phasing, the other by higher order phonon scattering processes. In both cases the final state is indistinguishable from a thermally relaxed state. We conjecture that our experiments points to a universal way through which relaxation in isolated many body quantum systems proceeds if the low energy dynamics is dominated by long lived excitations (quasi particles).

Supported by the Wittgenstein Prize, the Austrian Science Foundation (FWF) SFB FoQuS: F40 -P10 and the EU through the ERC -AdG QuantumRelax

[1] S. Hofferberth et al. Nature, 449, 324 (2007). [2] M. Kuhnert et al., Phys. Rev. Lett, 110, 090405 (2013). [3] M. Gring et al., Science, 337, 1318 (2012); D. Adu Smith et al. NJP , 15, 075011 (2013). [4] T. Langen et al., Nature Physics, 9, 640–643 (2013). [5] T. Langen et al., Science 348 207-211 (2015).

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