We consider heat transport via systems with broken time-reversal symmetry. We apply magnetic fields to the one-dimensional charged particle systems with transverse motions. The standard momentum conservation is not satisfied. To focus on this effect clearly, we introduce a solvable model. We exactly demonstrate that the anomalous transport with a new exponent can appear. We numerically show the violation of the standard relation between the power-law decay in the equilibrium correlation and the diverging exponent of the thermal conductivity in the open system. Introduction.-It is generally believed that heat conduction in low-dimensional nonlinear systems is anomalous from many theoretical and experimental studies [24][25][26]. In a one-dimensional system of N particles connected at the ends to heat baths with a small temperature difference ∆T , the thermal conductivity is defined as κ = JN/∆T , where J is the steady state current per site. The anomalous heat transport is given by the divergence of κ with increasing system size:
We consider heat transfer in one-dimensional systems with long-range interactions. It is known that short-range interacting systems generally shows anomalous behavior in heat transport when total momentum is conserved, whereas momentum-nonconserving systems do not exhibit anomaly. In this study, we focus on the effect of long-range interaction. We propose an exactly solvable model that reduces to the so-called momentum-exchange model in the short-range interaction limit. We exactly calculate the asymptotic time-decay in the energy current correlation function, which is related to the thermal conductivity via the Green-Kubo formula. From the time-decay of the current correlation, we show two qualitatively crucial results. First, the anomalous exponent in the time-decay continuously changes as a function of the index of the long-range interaction. Second, even momentum-nonconserving systems can show the anomalous exponent indicating anomalous heat transport.
We investigate heat transport via a charged flexible chain in the presence of magnetic fields. We focus on the Nernst-like effect, where the average positions of particles deviate in the perpendicular direction to the heat flow. This phenomenon is induced by the nonlinear dynamics as well as nonequilibrium state. We develop a linear response formalism to derive a thermodynamic force which induces the Nernst-like effect, and show that the phenomenon is quantitatively explained. We also discuss the inverse effect, where an external ac-driving force induces finite net heat current in the homogeneous system attached to heat baths with the same temperature. arXiv:1802.10234v3 [cond-mat.stat-mech]
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