Thermal transport in long-range interacting Fermi-Pasta-Ulam chains

Abstract

The power-law length (L) divergence of thermal conductivity (κ) in one-dimensional (1D) systems, i.e., κ ∼ L α , has been predicted by theories and also corroborated by experiments. The theoretical predictions of the exponent α are usually ranging from 0.2 to 0.5; however sometimes, the experimental observations can be higher, e.g., α = 0.6-0.8. This dispute has not yet been settled. Here we show the first convincing evidence that an exponent of α 0.7 that falls within experimental observations, can occur in a theoretical model of 1D long-range interacting Fermi-Pasta-Ulam chain. This, for the first time, theoretically supports the possibility of a higher divergent exponent and thus sheds new light on understanding of extremely high thermal conductivity in 1D materials at macroscopic scales.

Anomalous Heat Transport in Classical Many-Body Systems: Overview and Perspectives

“…In the light of what was discussed in section 2.2, this would appear to be a possible manifestation of a chimera ballistic regime, although there is no simple argument allowing us to invoke a relation of this special case with an integrable approximation, if any. That the α = 2 case is characterized by a somewhat "weaker non-integrability" has been confirmed also for a related model [70,72]. This can be traced back to the fact that in this case the lattice supports a special type of free-tail localized excitations (traveling discrete breathers) that enhance energy transfer [72].…”

“…That the α = 2 case is characterized by a somewhat "weaker non-integrability" has been confirmed also for a related model [70,72]. This can be traced back to the fact that in this case the lattice supports a special type of free-tail localized excitations (traveling discrete breathers) that enhance energy transfer [72].…”

“…Heat transport in chains with long-range interactions has been studied only recently [68][69][70][71][72]. The main question is to what extent the anomalous properties change as the spatial range of interactions between oscillators increases.…”

Subdiffusive Energy Transport and Antipersistent Correlations Due to the Scattering of Phonons and Discrete Breathers

“…To capture the PDF of energy diffusion in such a ring at a given temperature (T = 0.5 is considered), we employ the equilibrium spatiotemporal correlation function (see Refs. [23][24][25] for details)…”

“…This is indeed indicated in the movies in zero-temperature systems (see SM [30]). However, to show DBs in finitetemperatures is more challenging and we study the spatiotemporal evolutions of local energy densities E i (t) under the equilibrium state to achieve this [25]. To do this, the ring is first thermalized to T = 0.5, then the thermal baths are removed and the results are recorded and displayed for a time scale t = 1000 by a suitable time step ∆t = 10.…”