Universal post-quench coarsening and quantum aging at a quantum critical point
The non-equilibrium dynamics of a system that is located in the vicinity of a quantum critical point is affected by the critical slowing down of order-parameter correlations with the potential for novel out-of-equilibrium universality. After a quantum quench, i.e. a sudden change of a parameter in the Hamiltonian such a system is expected to almost instantly fall out of equilibrium and undergo aging dynamics, i.e. dynamics that depends on the time passed since the quench. Investigating the quantum dynamics of a $N$-component $φ^{4}$-model coupled to an external bath, we determine this universal aging and demonstrate that the system undergoes a coarsening, governed by a critical exponent that is unrelated to the equilibrium exponents of the system. We analyze this behavior in the large-$N$ limit, which is complementary to our earlier renormalization group analysis, allowing in particular the direct investigation of the order-parameter dynamics in the symmetry broken phase and at the upper critical dimension. By connecting the long time limit of fluctuations and response, we introduce a distribution function that shows that the system remains non-thermal and exhibits quantum coherence even on long timescales.