Role of pinning potentials in heat transport through disordered harmonic chain

The role of quadratic onsite pinning potentials on determining the size (N) dependence of the disorder averaged steady state heat current , in a isotopically disordered harmonic chain connected to stochastic heat baths, is investigated. For two models of heat baths, namely white noise baths and Rubin's model of baths, we find that the N dependence of is the same and depends on the number of pinning centers present in the chain. In the absence of pinning, ~ 1/N^{1/2} while in presence of one or two pins ~ 1/N^{3/2}. For a finite (n) number of pinning centers with 2 <= n << N, we provide heuristic arguments and numerical evidence to show that ~ 1/N^{n-1/2}. We discuss the relevance of our results in the context of recent experiments.Comment: 5 pages, 2 figures, quantum case is added in modified versio

Heat transport in harmonic lattices

We work out the non-equilibrium steady state properties of a harmonic lattice which is connected to heat reservoirs at different temperatures. The heat reservoirs are themselves modeled as harmonic systems. Our approach is to write quantum Langevin equations for the system and solve these to obtain steady state properties such as currents and other second moments involving the position and momentum operators. The resulting expressions will be seen to be similar in form to results obtained for electronic transport using the non-equilibrium Green's function formalism. As an application of the formalism we discuss heat conduction in a harmonic chain connected to self-consistent reservoirs. We obtain a temperature dependent thermal conductivity which, in the high-temperature classical limit, reproduces the exact result on this model obtained recently by Bonetto, Lebowitz and Lukkarinen.Comment: One misprint and one error have been corrected; 22 pages, 2 figure

Strong Bounds on Sum of Neutrino Masses in a 12 Parameter Extended Scenario with Non-Phantom Dynamical Dark Energy (w(z)≥−1w(z)\geq -1)

We obtained constraints on a 12 parameter extended cosmological scenario including non-phantom dynamical dark energy (NPDDE) with CPL parametrization. We also include the six $\Lambda$CDM parameters, number of relativistic neutrino species ($N_{\textrm{eff}}$) and sum over active neutrino masses ($\sum m_{\nu}$), tensor-to-scalar ratio ($r_{0.05}$), and running of the spectral index ($n_{run}$). We use CMB Data from Planck 2015; BAO Measurements from SDSS BOSS DR12, MGS, and 6dFS; SNe Ia Luminosity Distance measurements from the Pantheon Sample; CMB B-mode polarization data from BICEP2/Keck collaboration (BK14); Planck lensing data; and a prior on Hubble constant ($73.24\pm1.74$ km/sec/Mpc) from local measurements (HST). We have found strong bounds on the sum of the active neutrino masses. For instance, a strong bound of $\sum m_{\nu} <$ 0.123 eV (95\% C.L.) comes from Planck+BK14+BAO. Although we are in such an extended parameter space, this bound is stronger than a bound of $\sum m_{\nu} <$ 0.158 eV (95\% C.L.) obtained in $\Lambda \textrm{CDM}+\sum m_{\nu}$ with Planck+BAO. Varying $A_{\textrm{lens}}$ instead of $r_{0.05}$ however leads to weaker bounds on $\sum m_{\nu}$. Inclusion of the HST leads to the standard value of $N_{\textrm{eff}} = 3.045$ being discarded at more than 68\% C.L., which increases to 95\% C.L. when we vary $A_{\textrm{lens}}$ instead of $r_{0.05}$, implying a small preference for dark radiation, driven by the $H_0$ tension.Comment: 23 pages, 10 figures, matches the published versio

Heat conduction and phonon localization in disordered harmonic crystals

We investigate the steady state heat current in two and three dimensional isotopically disordered harmonic lattices. Using localization theory as well as kinetic theory we estimate the system size dependence of the current. These estimates are compared with numerical results obtained using an exact formula for the current given in terms of a phonon transmission function, as well as by direct nonequilibrium simulations. We find that heat conduction by high-frequency modes is suppressed by localization while low-frequency modes are strongly affected by boundary conditions. Our {\color{black}heuristic} arguments show that Fourier's law is valid in a three dimensional disordered solid except for special boundary conditions. We also study the pinned case relevant to localization in quantum systems and often used as a model system to study the validity of Fourier's law. Here we provide the first numerical verification of Fourier's law in three dimensions. In the two dimensional pinned case we find that localization of phonon modes leads to a heat insulator.Comment: 5 pages, 3 figure