[en] We study the statistical properties of the high-lying chaotic eigenstates (200000 and above) which are deep within the semiclassical regime. The system we are analysing is the billiard system inside the region defined by the quadratic (complex) conformal map of the unit disk as introduced by Robnik (1983). We are using Heller's method of plane-wave decomposition of the numerical eigenfunctions, and perform extensive statistical analysis with the following conclusions: (i) the local average probability density is in excellent agreement with the microcanonical assumption and all statistical properties are also in excellent agreement with the Gaussian random model; (ii) the autocorrelation function is found to be strongly direction dependent and only after averaging over all directions agrees well with Berry's (1977) prediction; (iii) although the scars of unstable classical periodic orbits (in such an ergodic regime) are expected to exist, so far we have not found any (around the 200000th state) other than a scar-like feature resembling the whispering-gallery modes. (author)

[en] Heat dissipation in micro-nano-scale devices is one of the bottlenecks which hinder the further development of the semiconductor industry. A series of procedures should be performed to dissipate the heat generated by the electronic device to the environment, which involves the thermal transport across interfaces and high performance heat conducting materials. We first review the recent progress in the field of micro-nano-scale thermal transport in solids from both the theoretical and experimental approaches. In the area of thermal transport theory and computational methodology, the Boltzmann transport equation, molecular-dynamics simulation, and Green's function are discussed. For the thermal transport experiments, we present an introduction to scanning thermal microscopy which is used to measure the spatial temperature distribution of sample surfaces, as well as the ultra-fast thermoreflectance technique which is used to measure the thermal conductivity of thin films and thermal boundary resistance. Then we tackle the problem of heat transport across an interface, including the calculation of thermal boundary resistance and how this is affected by the electron-phonon interaction. Several new heat conducting materials are also discussed, including carbon-based materials, boron-nitride whose crystal structure is similar to that of graphene, polymer chains, and thermal interface materials. (authors)

[en] Detecting coherent phonons pose different challenges compared to coherent photons due to the much stronger interaction between phonons and matter. This is especially true for high frequency heat carrying phonons, which are intrinsic lattice vibrations experiencing many decoherence events with the environment, and are thus generally assumed to be incoherent. Two photon interference techniques, especially coherent population trapping (CPT) and electromagnetically induced transparency (EIT), have led to extremely sensitive detection, spectroscopy and metrology. Here, we propose the use of two photon interference in a three-level system to sense coherent phonons. Unlike prior works which have treated phonon coupling as damping, we account for coherent phonon coupling using a full quantum–mechanical treatment. We observe strong asymmetry in absorption spectrum in CPT and negative dispersion in EIT susceptibility in the presence of coherent phonon coupling which cannot be accounted for if only pure phonon damping is considered. Our proposal has application in sensing heat carrying coherent phonons effects and understanding coherent bosonic multi-pathway interference effects in three coupled oscillator systems. (paper)

[en] Using an exact nonequilibrium Green's function formulation, the phonon Hall effect (PHE) for paramagnetic dielectrics is studied in a nanoscale four-terminal device setting. The temperature difference in the transverse direction of the heat current is calculated for two-dimensional models with the magnetic field perpendicular to the plane. We find that there is a PHE in nanoscale paramagnetic dielectrics, the magnitude of which is comparable to millimeter scale experiments. If the dynamic matrix of the system satisfies mirror reflection symmetry, the PHE disappears. The Hall temperature difference changes sign if the magnetic field is sufficiently large or if the size increases.

[en] We derive a semiclassical expression for an energy-smoothed autocorrelation function defined on a group of eigenstates of the Schroedinger equation. The system we consider is an energy-conserved Hamiltonian system possessing time-invariant symmetry. The energy-smoothed autocorrelation function is expressed as a sum of three terms. The first one is analogous to Berry's conjecture, which is a Bessel function of the zeroth order. The second and the third terms are trace formulae made from special trajectories. The second term is found to be direction dependent in the case of spacing averaging, which agrees qualitatively with previous numerical observations in high-lying eigenstates of a chaotic billiard. (author)

[en] We study thermal rectification in single-walled carbon nanohorns (SWNHs) by using a non-equilibrium molecular dynamics (MD) method. It is found that the horns with the bigger top angles show larger asymmetric heat transport due to the larger structural gradient distribution. This kind of gradient behavior can be further adjusted by applying external strain on the SWNHs. After being carefully elongated along the axial direction, thermal rectification in the elongated SWNHs can become more obvious than that in undeformed SWNHs. The maximum rectification efficiency of SWNHs is much bigger than that of carbon nanotube intramolecular junctions

[en] In this letter, we extend a previously proposed variational approach to systematically investigate general momentum-nonconserving nonlinear lattices. Two intrinsic identities characterizing optimal reference systems are firstly revealed, which enables us to derive explicit expressions for optimal variational parameters. The resulting optimal harmonic reference systems provide information for the band gap as well as the dispersion of renormalized phonons in momentum-nonconserving nonlinear lattices. As a demonstration, we consider the one-dimensional ${\mathrm{\varphi <!--\; ??\; -->}}^4$ lattice. We show that the phonon band gap endows a simple power-law temperature dependence in the weak stochasticity regime where predicted dispersion is reliable by comparing with numerical results. In addition, an exact relation between ensemble averages of the ${\mathrm{\varphi <!--\; ??\; -->}}^4$ lattice in the whole temperature range is found, regardless of the existence of the strong stochasticity threshold. (letter)

[en] We present a systematic theory of the phonon Hall effect in a ballistic crystal lattice system, and apply it on the kagome lattice which is ubiquitous in various real materials. By proposing a proper second quantization for the non-Hermitian in the polarization-vector space, we obtain a new heat current density operator with two separate contributions: the normal velocity responsible for the longitudinal phonon transport, and the anomalous velocity manifesting itself as the Hall effect of transverse phonon transport. As exemplified in kagome lattices, our theory predicts that the direction of Hall conductivity at low magnetic field can be reversed by tuning the temperatures, which we hope can be verified by experiments in the future. Three phonon-Hall-conductivity singularities induced by phonon-band-topology change are discovered as well, which correspond to the degeneracies at three different symmetric center points, Γ, K, X, in the wavevector space of the kagome lattice.

[en] An analytical model for thermal conductivity of composites with nanoparticles in a matrix is developed based on the effective medium theory by introducing the intrinsic size effect of thermal conductivity of nanoparticles and the interface thermal resistance effect between two phases. The model predicts the percolation of thermal conductivity with the volume fraction change of the second phase, and the percolation threshold depends on the size and the shape of the nanoparticles. The theoretical predictions are in agreement with the experimental results

[en] Transformation media theory, which steers waves in solids via an effective geometry induced by a refractive material (Fermat’s principle of least action), provides a means of controlling vibrations and elastic waves beyond the traditional dissipative structures regime. In particular, it could be used to create an elastic wave cloak, shielding an interior region against elastic waves while simultaneously preventing scattering in the outside domain. However, as a true elastic wave cloak would generally require materials with stiffness tensors lacking the minor symmetry (implying asymmetric stress), the utility of such an elastic wave cloak has thus far been limited by the challenge of fabricating these materials. Here we develop a means of overcoming this limitation via the development of a symmetrized elastic cloak (SEC), sacrificing some of the performance of the perfect cloak for the sake of restoring the minor symmetry. We test the performance of the SEC for shielding a tunnel against seismic waves, showing that it can be used to reduce the average displacement within the tunnel by an order of magnitude (and reduce energy by two orders of magnitude) for waves above a critical frequency of the cloak. This critical frequency, which corresponds to the generation of surface waves at the cloak-interior interface, can be used to develop a simple heuristic model of the SEC’s performance for a generic problem. (paper)