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The ballistic to diffusive crossover, that occurs when quasiparticles transport heat or charge, is important in small systems. Propagation of energy from an initial localized pulse provides a useful picture of the process. This paper looks at the simplest example, vibrational pulses on a one-dimensional harmonic chain of atoms. Pure ballistic propagation occurs in ordered chains, and a crossover toward diffusive propagation can be seen in disordered chains. A full analysis is inhibited by non-perturbative effects, especially Anderson localization. A partial analysis using Boltzmann theory is given.
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We study hydrodynamic phonon heat transport in two-dimensional (2D) materials. Starting from the Peierls-Boltzmann equation within the Callaway model, we derive a 2D Guyer-Krumhansl-like equation describing non-local hydrodynamic phonon transport, taking into account the quadratic dispersion of flexural phonons. In additional to Poiseuille flow, second sound propagation, the equation predicts heat current vortices and negative nonlocal thermal conductance in 2D materials, common in classical fluid but scarcely considered in phonon transport. Our results also illustrate the universal transport behavior of hydrodynamics, independent on the type of quasi-particles and their microscopic interactions.
Using quantum gas microscopy we study the late-time effective hydrodynamics of an isolated cold-atom Fermi-Hubbard system subject to an external linear potential (a tilt). The tilt is along one of the principal directions of the two-dimensional (2D) square lattice and couples mass transport to local heating through energy conservation. We study transport and thermalization in our system by observing the decay of prepared initial density waves as a function of wavelength $lambda$ and tilt strength and find that the associated decay time $tau$ crosses over as the tilt strength is increased from characteristically diffusive to subdiffusive with $tauproptolambda^4$. In order to explain the underlying physics we develop a hydrodynamic model that exhibits this crossover. For strong tilts, the subdiffusive transport rate is set by a thermal diffusivity, which we are thus able to measure as a function of tilt in this regime. We further support our understanding by probing the local inverse temperature of the system at strong tilts, finding good agreement with our theoretical predictions. Finally, we discuss the relation of the strongly tilted limit of our system to recently studied 1D models which may exhibit nonergodic dynamics.
Thermal transport through nanosystems is central to numerous processes in chemistry, material sciences, electrical and mechanical engineering, with classical molecular dynamics as the key simulation tool. Here we focus on thermal junctions with a molecule bridging two solids that are maintained at different temperatures. The classical steady state heat current in this system can be simulated in different ways, either at the interfaces with the solids, which are represented by thermostats, or between atoms within the conducting molecule. We show that while the latter, intramolecular definition feasibly converges to the correct limit, the molecule-thermostat interface definition is more challenging to converge to the correct result. The problem with the interface definition is demonstrated by simulating heat transport in harmonic and anharmonic one-dimensional chains illustrating unphysical effects such as thermal rectification in harmonic junctions.
Fundamental conservation laws predict ballistic, i.e., dissipationless transport behaviour in one-dimensional quantum magnets. Experimental evidence, however, for such anomalous transport has been lacking ever since. Here we provide experimental evidence for ballistic heat transport in a S=1/2 Heisenberg chain. In particular, we investigate high purity samples of the chain cuprate SrCuO2 and observe a huge magnetic heat conductivity $kappa_{mag}$. An extremely large spinon mean free path of more than a micrometer demonstrates that $kappa_{mag}$ is only limited by extrinsic scattering processes which is a clear signature of ballistic transport in the underlying spin model.
The dynamic structure function $S(k,omega)$ informs about the dispersion and damping of excitations. We have recently (Phys. Rev. B {bf 97}, 184520 (2018)) compared experimental results for $S(k,omega)$ from high-precision neutron scattering experiment and theoretical results using the ``dynamic many-body theory (DMBT), showing excellent agreement over the whole experimentally accessible pressure regime. This paper focuses on the specific aspect of the propagation of low-energy phonons. We report calculations of the phonon mean-free path and phonon life time in liquid he4 as a function of wave length and pressure. Historically, the question was of interest for experiments of quantum evaporation. More recently, there is interest in the potential use of $^4$He as a detector for low-energy dark matter (K. Schulz and Kathryn M. Zurek, Phys. Rev. Lett. {bf 117}, 121302 (2016)). While the mean free path of long wave length phonons is large, phonons of intermediate energy can have a short mean free path of the order of $mu$m. Comparison of different levels of theory indicate that reliable predictions of the phonon mean free path can be made only by using the most advanced many--body method available, namely, DMBT.
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