Observation of thermal transport close to diffusive in a weak long-ranged Fermi-Pasta-Ulam-Tsingou-type model

We explore thermal transport in a one-dimensional Fermi-Pasta-Ulam-Tsingou-type (FPUT-type) system with long-range (LR) interactions. In such a system, the harmonic part of the potential is nearest-neighbor coupled, while the strength of the quartic part of the potential between two lattice sites decays as a power <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>σ</a:mi></a:math> of the inverse of their distance, demonstrating the LR feature of the system. The relevant strong LR model <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mo>(</b:mo><b:mn>0</b:mn><b:mo>≤</b:mo><b:mi>σ</b:mi><b:mo>≤</b:mo><b:mn>1</b:mn><b:mo>)</b:mo></b:mrow></b:math> has been considered in detail in our recent study [Xiong and Wang, ], and here, we focus on the weak LR regime <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mo>(</c:mo><c:mn>1</c:mn><c:mo>≤</c:mo><c:mi>σ</c:mi><c:mo>≤</c:mo><c:mn>3</c:mn><c:mo>)</c:mo></c:mrow></c:math>. We show that the thermal transport behaviors in this regime are quite unexpected. We discovered a subregime <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mo>(</d:mo><d:mn>1</d:mn><d:mo>≤</d:mo><d:mi>σ</d:mi><d:mo>≤</d:mo><d:mn>1.5</d:mn><d:mo>)</d:mo></d:mrow></d:math> wherein the thermal transport behaviors are very close to diffusive. This suggests that even a momentum-conserving system with appropriate LR interactions can still exhibit normal heat conduction. By meticulously analyzing the space-time scaling properties of equilibrium heat correlations, we also determine the center of this diffusive thermal transport at approximately <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>σ</e:mi><e:mo>≃</e:mo><e:mn>1.25</e:mn></e:mrow></e:math>. These discoveries, together with our prior results, provide a comprehensive understanding of thermal transport of this kind of LR-FPUT-type model.