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Energy current correlation in solvable long-range interacting systems.

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Long-range interactions in physical systems can cause anomalous heat transport, even in systems that don't conserve momentum. This study reveals how interaction range affects heat transfer anomalies and their exponents.

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Area of Science:

  • Physics
  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Heat transport in one-dimensional systems with short-range interactions exhibits anomalous behavior when total momentum is conserved.
  • Momentum-nonconserving systems typically do not show such anomalies.

Purpose of the Study:

  • To investigate the effect of long-range interactions on heat transfer in one-dimensional systems.
  • To propose an exactly solvable model for studying these effects.
  • To analyze the conditions under which anomalous heat transport occurs.

Main Methods:

  • Development of an exactly solvable model for heat transfer with long-range interactions.
  • Exact calculation of the asymptotic time decay in the energy current correlation function.
  • Application of the Green-Kubo formula to relate correlation functions to thermal conductivity.
  • Analysis of heat transport in higher dimensions.

Main Results:

  • The anomalous exponent in time-decay continuously varies with the long-range interaction index.
  • A regime exists where the current correlation diverges with system size, preventing exponent definition.
  • Momentum-nonconserving systems can exhibit anomalous exponents due to long-range interactions.
  • Long-range interactions can induce anomalous exponents even in three-dimensional systems.

Conclusions:

  • Long-range interactions fundamentally alter heat transport properties, leading to anomalies even in momentum-nonconserving systems.
  • The nature and definition of anomalous exponents are sensitive to interaction range and system size.
  • Anomalous heat transport induced by long-range interactions is a phenomenon observable in various dimensions.