We discovered an error in our code that affected the dynamical behavior of the energy current. In determining the current we numerically calculate several integrals using the trapezoidal rule. The integrals in Eq. (7), however, were numerically calculated incorrectly because of an error (a misplaced division by 2) in the code. This resulted in the current to erroneously decay faster than the correct behavior. The figures for the numerical results in our manuscript should therefore be replaced by Figs. 1-3 shown in this erratum.Comparing the previously published figures and the corrected figures, we find that for long times the current in both cases do approach the steady-state values calculated independently from the Landauer formula. Furthermore, the initial negative spike in the transient current do also occur in both cases. The difference lies in how fast the current decays to the long-time steady-state value. From the corrected figures, the characteristic decay time is about 30 × 10 −14 s. All of our other conclusions remain the same. 0 20 40 60 80 100 time [10 -14 s] -160 -120 -80 -40 0 40 80 I L [nW] 0 20 40 60 80 100 time [10 -14 s] -160 -120 -80 -40 0 40 80 I R [nW] first-order all orders first-order all orders (a) (b) FIG. 1. (Color online) Corrected figure replacing the previously published Fig. 3. Shown are plots of the current flowing out of the (a) left and (b) right leads. The (red) lines are the results when only the first-order term in the perturbation is used in the calculation. The left lead has temperature T L = 330 K while the right lead has temperature T R = 270 K. The interparticle spring constant is k = 0.625 eV/(Å 2 u) and the on-site spring constant is k 0 = 0.0625 eV/(Å 2 u).0 1 0 2 0 3 0 4 0 time [10 -14 s] -600 -400 -200 0 200 I S [nW] 0 200 400 600 800 1000 temperature [K] -600 -400 -200 0 I S [nW] (a) (b) FIG. 2. (Color online) Corrected figures replacing the previously published Fig. 4. (a) The sum of the currents, I S = I L + I R , when the average temperature between the leads are T = 10 K (red triangles), T = 300 K (green squares), and T = 1000 K (blue circles). The temperature offsets of the leads are ±10%. (b) Plots of I S as functions of the average temperature T at time t = 12.7[t] (red triangles), t = 24.6[t] (green squares), and t = 38.2[t] (blue circles), where [t] = 10 −14 s.0 1 0 2 0 3 0 4 0 50 60 time [10 -14 s] -140 -120 -100 -80 -60 -40 -20 0 20 40 current [nW] FIG. 3. (Color online) Corrected figures replacing the previously published Fig. 5. Shown are plots of the current when the left and right leads have the same temperature T , where T = 10 K for the (red) squares and T = 300 K for the (blue) circles. 019902-1

We study the transport of energy in a finite linear harmonic chain by solving the Heisenberg equation of motion, as well as by using nonequilibrium Green's functions to verify our results. The initial state of the system consists of two separate and finite linear chains that are in their respective equilibriums at different temperatures. The chains are then abruptly attached to form a composite chain. The time evolution of the current from just after switch-on to the transient regime and then to later times is determined numerically. We expect the current to approach a steady-state value at later times. Surprisingly, this is possible only if a nonzero quadratic on-site pinning potential is applied to each particle in the chain. If there is no on-site potential a recurrent phenomenon appears when the time scale is longer than the traveling time of sound to make a round trip from the midpoint to a chain edge and then back. Analytic expressions for the transient and steady-state currents are derived to further elucidate the role of the on-site potential.

We follow the nonequilibrium Green's function formalism to study time-dependent thermal transport in a linear chain system consisting of two semi-infinite leads connected together by a coupling that is harmonically modulated in time. The modulation is driven by an external agent that can absorb and emit energy. We determine the energy current flowing out of the leads exactly by solving numerically the Dyson equation for the contour-ordered Green's function. The amplitude of the modulated coupling is of the same order as the interparticle coupling within each lead. When the leads have the same temperature, our numerical results show that modulating the coupling between the leads may direct energy to either flow into the leads simultaneously or flow out of the leads simultaneously, depending on the values of the driving frequency and temperature. A special combination of values of the driving frequency and temperature exists wherein no net energy flows into or out of the leads, even for long times. When one of the leads is warmer than the other, net energy flows out of the warmer lead. For the cooler lead, however, the direction of the energy current flow depends on the values of the driving frequency and temperature. In addition, we find transient effects to become more pronounced for higher values of the driving frequency.

Multilevel Monte Carlo simulations of the vortex matter in the highly anisotropic high-temperature superconductor Bi2Sr2CaCu2O8 were performed. We introduced low concentration of columnar defects satisfying Bphi < or = B. Both the electromagnetic and Josephson interactions among pancake vortices were included. The nanocrystalline, nanoliquid, and homogeneous liquid phases were identified in agreement with experiments. We observed the two-step melting process and also noted an enhancement of the structure factor just prior to the melting transition. A proposed theoretical model is in agreement with our findings.

We study the time-dependent transport of heat in a nanoscale thermal switch. The switch consists of left and right leads that are initially uncoupled. During switch-on the coupling between the leads is abruptly turned on. We use the nonequilibrium Green's function formalism and numerically solve the constructed Dyson equation to determine the nonperturbative heat current. At the transient regime we find that the current initially flows simultaneously into both of the leads and then afterwards oscillates between flowing into and out of the leads. At later times the oscillations decay away and the current settles into flowing from the hotter to the colder lead. We find the transient behavior to be influenced by the extra energy added during switch-on. Such a transient behavior also exists even when there is no temperature difference between the leads. The current at the long-time limit approaches the steady-state value independently calculated from the Landauer formula.Comment: version accepted for publication in PR