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Register a new userRelaxation dynamics and interrupted coarsening in irrationally frustrated superconducting arrays
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Equilibrium and non-equilibrium relaxation behaviors of two-dimensional superconducting arrays are investigated via numerical simulations at low temperatures in the presence of incommensurate transverse magnetic fields, with frustration parameter f= (3-sqrt{5})/2. We find that the non-equilibrium relaxation, beginning with random initial states quenched to low temperatures, exhibits a three-stage relaxation of chirality autocorrelations. At the early stage, the relaxation is found to be described by the von Schweidler form. Then it exhibits power-law behavior in the intermediate time scale and faster decay in the long-time limit, which together can be fitted to the Ogielski form; for longer waiting times, this crosses over to a stretched exponential form. We argue that the power-law behavior in the intermediate time scale may be understood as a consequence of the coarsening behavior, leading to the local vortex order corresponding to f=2/5 ground-state configurations. High mobility of the vortices in the domain boundaries, generating slow wandering motion of the domain walls, may provide mechanism of dynamic heterogeneity and account for the long-time stretched exponential relaxation behavior. It is expected that such meandering fluctuations of the low-temperature structure give rise to finite resistivity at those low temperatures; this appears consistent with the zero-temperature resistive transition in the limit of irrational frustration.
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We investigate the nonequilibrium coarsening dynamics in two-dimensional overdamped superconducting arrays under zero external current, where ohmic dissipation occurs on junctions between superconducting islands through uniform resistance. The nonequilibrium relaxation of the unfrustrated array and also of the fully frustrated array, quenched to low temperature ordered states or quasi-ordered ones, is dominated by characteristic features of coarsening processes via decay of point and line defects, respectively. In the case of unfrustrated arrays, it is argued that due to finiteness of the friction constant for a vortex (in the limit of large spatial extent of the vortex), the typical length scale grows as $ell_s sim t^{1/2}$ accompanied by the number of point vortices decaying as $N_v sim 1/t $. This is in contrast with the case that dominant dissipation occurs between each island and the substrate, where the friction constant diverges logarithmically and the length scale exhibits diffusive growth with a logarithmic correction term. We perform extensive numerical simulations, to obtain results in reasonable agreement. In the case of fully frustrated arrays, the domain growth of Ising-like chiral order exhibits the low-temperature behavior $ell_q sim t^{1/z_q}$, with the growth exponent $1/z_q$ apparently showing a strong temperature dependence in the low-temperature limit.
We report large-scale simulations of the resistively-shunted Josephson junction array in strip geometry. As the strip width increases, the voltage first decreases following the dynamic scaling ansatz proposed by Minnhagen {it et al.} [Phys. Rev. Lett. {bf 74}, 3672 (1995)], and then rises towards the asymptotic value predicted by Ambegaokar {it et al.} [Phys. Rev. Lett. {bf 40}, 783 (1978)]. The nonmonotonic size-dependence is attributed to shortened life time of free vortices in narrow strips, and points to the danger of single-scale analysis applied to a charge-neutral superfluid state.
We establish a one-to-one mapping between a model for hexagonal polyelectrolyte bundles and a model for two-dimensional, frustrated Josephson-junction arrays. We find that the T=0 insulator-to-superconductor transition of the {it quantum} system corresponds to a continuous liquid-to-solid transition of the condensed charge in the finite temperature {it classical} system. We find that the role of the vector potential in the quantum system is played by elastic strain in the classical system. Exploiting this correspondence we show that the transition is accompanied by a spontaneous breaking of chiral symmetry and that at the transition the polyelectrolyte bundle adopts a universal response to shear.
We investigate the coarsening dynamics in the two-dimensional Hamiltonian XY model on a square lattice, beginning with a random state with a specified potential energy and zero kinetic energy. Coarsening of the system proceeds via an increase in the kinetic energy and a decrease in the potential energy, with the total energy being conserved. We find that the coarsening dynamics exhibits a consistently superdiffusive growth of a characteristic length scale with 1/z > 1/2 (ranging from 0.54 to 0.57). Also, the number of point defects (vortices and antivortices) decreases with exponents ranging between 1.0 and 1.1. On the other hand, the excess potential energy decays with a typical exponent of 0.88, which shows deviations from the energy-scaling relation. The spin autocorrelation function exhibits a peculiar time dependence with non-power law behavior that can be fitted well by an exponential of logarithmic power in time. We argue that the conservation of the total Josephson (angular) momentum plays a crucial role for these novel features of coarsening in the Hamiltonian XY model.
We consider coupled quantum two-state systems (qubits) exposed to a global relaxation process. The global relaxation refers to the assumption that qubits are coupled to the same quantum bath with approximately equal strengths, appropriate for long-wavelength environmental fluctuations. We show that interactions do not spoil the picture of Dickes subradiant and superradiant states where quantum interference effects lead to striking deviations from the independent relaxation picture. Remarkably, the system possess a stable entangled state and a state decaying faster than single qubit excitations. We propose a scheme how these effects can be experimentally accessed in superconducting flux qubits and, possibly, used in constructing long-lived entangled states.
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