TY - JOUR

T1 - Energy current correlation in solvable long-range interacting systems

AU - Tamaki, Shuji

AU - Saito, Keiji

N1 - Funding Information:
We are grateful to M. Sasada and H. Suda for fruitful discussions. The present work was supported by JSPS Grants-in-Aid for Scientific Research (Grants No. JP16H02211 and No. JP17K05587).
Publisher Copyright:
© 2020 American Physical Society.

PY - 2020/4

Y1 - 2020/4

N2 - We consider heat transfer in one-dimensional systems with long-range interactions. It is known that typical short-range interacting systems 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 three 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, there is a regime where the current correlation diverges with increasing the system size with fixed time, and hence, the exponent of the time decay cannot be defined. Third, even momentum-nonconserving systems can show the anomalous exponent indicating anomalous heat transport. Higher dimensions are also considered, and we found that long-range interaction can induce the anomalous exponent even in three-dimensional systems.

AB - We consider heat transfer in one-dimensional systems with long-range interactions. It is known that typical short-range interacting systems 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 three 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, there is a regime where the current correlation diverges with increasing the system size with fixed time, and hence, the exponent of the time decay cannot be defined. Third, even momentum-nonconserving systems can show the anomalous exponent indicating anomalous heat transport. Higher dimensions are also considered, and we found that long-range interaction can induce the anomalous exponent even in three-dimensional systems.

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U2 - 10.1103/PhysRevE.101.042118

DO - 10.1103/PhysRevE.101.042118

M3 - Article

C2 - 32422778

AN - SCOPUS:85084563752

VL - 101

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 4

M1 - 042118

ER -