Coined quantum walks on the line: Disorder, entanglement, and localization.

Disorder in coined quantum walks generally leads to localization. We investigate the influence of the localization on the entanglement properties of coined quantum walks. Specifically, we consider quantum walks on the line and explore the effects of quenched disorder in the coin operations. After confirming that our choice of disorder localizes the walker, we study how the localization affects the properties of the coined quantum walk. We find that the mixing properties of the walk are altered nontrivially with mixing being improved at short time scales. Special focus is given to the influence of coin disorder on the properties of the quantum state and the coin-walker entanglement. We find that disorder alters the quantum state significantly even when the walker probability distribution is still close to the nondisordered case. We observe that, generically, coin disorder decreases the coin-walker entanglement and that the localization leaves distinct traces in the entanglement entropy and the entanglement negativity of the coined quantum walk.

Critical dynamics of the antiferromagnetic O(3) nonlinear sigma model with conserved magnetization.

We study the near-equilibrium critical dynamics of the O(3) nonlinear sigma model describing isotropic antiferromagnets with a nonconserved order parameter reversibly coupled to the conserved total magnetization. To calculate response and correlation functions, we set up a description in terms of Langevin stochastic equations of motion, and their corresponding Janssen-De Dominicis response functional. We find that in equilibrium, the dynamics is well-separated from the statics, at least to one-loop order in a perturbative treatment with respect to the static and dynamical nonlinearities. Since the static nonlinear sigma model must be analyzed in a dimensional d=2+ɛ expansion about its lower critical dimension d_{lc}=2, whereas the dynamical mode-coupling terms are governed by the upper critical dimension d_{c}=4, a simultaneous perturbative dimensional expansion is not feasible, and the reversible critical dynamics for this model cannot be accessed at the static critical renormalization group fixed point. However, in the coexistence limit addressing the long-wavelength properties of the low-temperature ordered phase, we can perform an ε=4-d expansion near d_{c}. This yields anomalous scaling features induced by the massless Goldstone modes, namely subdiffusive relaxation for the conserved magnetization density with asymptotic scaling exponent z_{Γ}=d-2, which may be observable in neutron scattering experiments. Intriguingly, if initialized near the critical point, the renormalization group flow for the effective dynamical exponents recovers their universal critical values z_{c}=d/2 in an intermediate crossover region.

Social distancing and epidemic resurgence in agent-based susceptible-infectious-recovered models.

Once an epidemic outbreak has been effectively contained through non-pharmaceutical interventions, a safe protocol is required for the subsequent release of social distancing restrictions to prevent a disastrous resurgence of the infection. We report individual-based numerical simulations of stochastic susceptible-infectious-recovered model variants on four distinct spatially organized lattice and network architectures wherein contact and mobility constraints are implemented. We robustly find that the intensity and spatial spread of the epidemic recurrence wave can be limited to a manageable extent provided release of these restrictions is delayed sufficiently (for a duration of at least thrice the time until the peak of the unmitigated outbreak) and long-distance connections are maintained on a low level (limited to less than five percent of the overall connectivity).