QUROPE Quantum Information Processing and Communication in Europe

When traversing a symmetry breaking second order phase transition at a finite rate, topological defects form whose number dependence on the quench rate is given by simple power laws. We propose a general approach for the derivation of such scaling laws that is based on the analytical transformation of the associated equations of motion to a universal form rather than employing plausible physical arguments. We demonstrate the power of this approach by deriving the scaling of the number of topological defects in both homogenous and non-homogenous settings.

We investigate the equilibration dynamics of non-local order in a one-dimensional quantum system. After initializing a spin-1 chain in the Haldane phase, the time evolution of string correlations following a sudden quench is studied by means of matrix-product-state-based algorithms. Thermalization occurs only for scales up to a horizon which grows at a well defined speed, due to the finite maximal velocity at which string correlations can propagate, related to a Lieb-Robinson bound.

We analyse the sensitivity, quantied by the helicity modulus and the stiness, of the long-time stationary state of a many-body quantum system to an innitesimal twist at the boundary conditions. The standard thermalisation framework cannot be straightforwardly employed in this context, since such quantities are non-local. We apply our theory to two paradigmatic examples of hard-core bosons in a one-dimensional ring, quenched to/from super uid/insulating phases. We show that the out-of-equilibrium stiness is qualitatively dierent from the equilibrium case.

We introduce an alternative way to derive the generalized form of the master equation recently presented by J. P. Pekola et al. Phys. Rev. Lett. 105 030401 (2010) for an adiabatically steered two-level quantum system interacting with a Markovian environment. The original derivation employed the effective Hamiltonian in the adiabatic basis with the standard interaction picture approach but without the usual secular approximation. Our approach is based on utilizing a master equation for a nonsteered system in the first superadiabatic basis.