Non-equilibrium phonon dynamics in trapped ion systems

We propose a concrete experiment to probe the non-equilibrium local dynamics of the one-dimensional Bose-Hubbard model using a trapped ion system consisting of a linear chain of few Ba^+ ions prepared in a state of transverse motional mode which corresponds to a fixed number of phonons per ion. These phonons are well-known to be described by an effective Bose-Hubbard model. We propose a protocol which leads to a sudden local sign reversal of the on-site interaction strength of this Hubbard model at one of the sites and demonstrate that the subsequent non-equilibrium dynamics of the model can be experimentally probed by measuring the time-dependent phonon number in a specific motional state of the Ba+ ions. We back our experimental proposal with exact numerical calculation of the dynamics of a Bose-Hubbard model subsequent to a local quench.Comment: The submission contains 5 pages and 4 figure

Simulation of Vortex-Antivortex Pair Production in a Phase Transition with Explicit Symettry Breaking

We carry out numerical simulation of the formation of U(1) global vortices in a first order phase transition in 2+1 dimensions in the presence of small explicit symmetry breaking. Bubbles of broken symmetry phase are randomly nucleated, which grow and coalesce. Vortices form at junctions of bubbles via standard Kibble mechanism as well as due to a new mechanism, recently proposed by us, where defect-antidefect pairs are produced due to field oscillations. In a simulation involving nucleation of 63 bubbles, with bias in phase distribution inside bubbles arising from explicit symmetry breaking, we find that not a single vortex/antivortex is produced via the Kibble mechanism, while the new mechanism leads to production of 104 vortices and antivortices. Even without biasing the phase distribution inside bubbles, the vortex production is completely dominated by this new mechanism, which accounts for the production of about 80% of the vortices and antivortices, remaining 20% being produced via the Kibble mechanism. We study the dependence of the effectiveness of the new mechanism on the magnitude of explicit symmetry breaking, as well as on the nucleation rate of bubbles. We also study the effect of damping on this mechanism and show that damping suppresses this mode of vortex production.Comment: 15 pages, 13 figures(1 new figure added). A new section on the effect of bias in phases of nucleating bubbles, due to the presence of explicit symmetry breaking, has been adde

Knowing one's place: a free-energy approach to pattern regulation.

Understanding how organisms establish their form during embryogenesis and regeneration represents a major knowledge gap in biological pattern formation. It has been recently suggested that morphogenesis could be understood in terms of cellular information processing and the ability of cell groups to model shape. Here, we offer a proof of principle that self-assembly is an emergent property of cells that share a common (genetic and epigenetic) model of organismal form. This behaviour is formulated in terms of variational free-energy minimization-of the sort that has been used to explain action and perception in neuroscience. In brief, casting the minimization of thermodynamic free energy in terms of variational free energy allows one to interpret (the dynamics of) a system as inferring the causes of its inputs-and acting to resolve uncertainty about those causes. This novel perspective on the coordination of migration and differentiation of cells suggests an interpretation of genetic codes as parametrizing a generative model-predicting the signals sensed by cells in the target morphology-and epigenetic processes as the subsequent inversion of that model. This theoretical formulation may complement bottom-up strategies-that currently focus on molecular pathways-with (constructivist) top-down approaches that have proved themselves in neuroscience and cybernetics