Effect of phonon-phonon interactions on localization

We study the heat current J in a classical one-dimensional disordered chain with on-site pinning and with ends connected to stochastic thermal reservoirs at different temperatures. In the absence of anharmonicity all modes are localized and there is a gap in the spectrum. Consequently J decays exponentially with system size N. Using simulations we find that even a small amount of anharmonicity leads to a J~1/N dependence, implying diffusive transport of energy.Comment: 4 pages, 2 figures, Published versio

Heat transport and phonon localization in mass-disordered harmonic crystals

We investigate the steady state heat current in two and three dimensional disordered harmonic crystals in a slab geometry, connected at the boundaries to stochastic white noise heat baths at different temperatures.The disorder causes short wavelength phonon modes to be localized so the heat current in this system is carried by the extended phonon modes which can be either diffusive or ballistic. Using ideas both from localization theory and from kinetic theory we estimate the contribution of various modes to the heat current and from this we obtain the asymptotic system size dependence of the current. These estimates are compared with results obtained from a numerical evaluation of an exact formula for the current, given in terms of a frequency transmission function, as well as from direct nonequilibrium simulations. These yield a strong dependence of the heat flux on boundary conditions. Our analytical arguments show that for realistic boundary conditions the conductivity is finite in three dimensions but we are not able to verify this numerically, except in the case where the system is subjected to an external pinning potential. This case is closely related to the problem of localization of electrons in a random potential and here we numerically verify that the pinned three dimensional system satisfies Fourier's law while the two dimensional system is a heat insulator. We also investigate the inverse participation ratio of different normal modes.Comment: 30 pages, 28 figures (Revised and improved version

Heat conduction in disordered harmonic lattices with energy conserving noise

We study heat conduction in a harmonic crystal whose bulk dynamics is supplemented by random reversals (flips) of the velocity of each particle at a rate $\lambda$. The system is maintained in a nonequilibrium stationary state(NESS) by contacts with Langevin reservoirs at different temperatures. We show that the one-body and pair correlations in this system are the same (after an appropriate mapping of parameters) as those obtained for a model with self-consistent reservoirs. This is true both for the case of equal and random(quenched) masses. While the heat conductivity in the NESS of the ordered system is known explicitly, much less is known about the random mass case. Here we investigate the random system, with velocity flips. We improve the bounds on the Green-Kubo conductivity obtained by C.Bernardin. The conductivity of the 1D system is then studied both numerically and analytically. This sheds some light on the effect of noise on the transport properties of systems with localized states caused by quenched disorder.Comment: 19 pages, 8 figure

Thermoelectric properties of β{\beta}-FeSi2_{\text2}

We investigate the thermoelectric properties of ${\beta}$-FeSi$_{\text2}$ using first principles electronic structure and Boltzmann transport calculations. We report a high thermopower for both \textit{p}- and \textit{n}-type ${\beta}$-FeSi$_{\text2}$ over a wide range of carrier concentration and in addition find the performance for \textit{n}-type to be higher than for the \textit{p}-type. Our results indicate that, depending upon temperature, a doping level of 3$\times10{^{20}}$ - 2$\times10{^{21}}$ cm${^{-3}}$ may optimize the thermoelectric performance

Normal discrimination of spatial frequency and contrast across visual hemifields in left-onset Parkinson’s disease: evidence against perceptual hemifield biases

Individuals with Parkinson's disease (PD) with symptom onset on the left side of the body (LPD) show a mild type of left-sided visuospatial neglect, whereas those with right-onset (RPD) generally do not. The functional mechanisms underlying these observations are unknown. Two hypotheses are that the representation of left-space in LPD is either compressed or reduced in salience. We tested these hypotheses psychophysically. Participants were 31 non-demented adults with PD (15 LPD, 16 RPD) and 17 normal control adults (NC). The spatial compression hypothesis was tested by showing two sinusoidal gratings, side by side. One grating's spatial frequency (SF) was varied across trials, following a staircase procedure, whereas the comparison grating was held at a constant SF. While fixating on a central target, participants estimated the point at which they perceived the two gratings to be equal in SF. The reduced salience hypothesis was tested in a similar way, but by manipulating the contrast of the test grating rather than its SF. There were no significant differences between groups in the degree of bias across hemifields for SF discrimination or for contrast discrimination. Results did not support either the spatial compression hypothesis or the reduced salience hypothesis. Instead, they suggest that at this perceptual level, LPD do not have a systematically biased way of representing space in the left hemifield that differs from healthy individuals, nor do they perceive stimuli on the left as less salient than stimuli on the right. Neglect-like syndrome in LPD instead presumably arises from dysfunction of higher-order attention.Published versio

Comment on ``Can Disorder Induce a Finite Thermal Conductivity in 1D Lattices?''

In a recent paper [Phys. Rev. Lett. 86, 63 (2001)], Li et al have reported that the nonequilibrium heat conducting steady state of a disordered harmonic chain is not unique. In this comment we point out that for a large class of stochastic heat baths the uniqueness of the steady state can be proved, and therefore the findings of Li et al could be either due to their use of deterministic heat baths or insufficient equilibration times in the simulations. We give a simple example where the uniquness of the steady state can be explicitly demonstrated.Comment: 1 page, 1 figure, accepted for publication in Phys. Rev. Let

Application of importance sampling to the computation of large deviations in non-equilibrium processes

We present an algorithm for finding the probabilities of rare events in nonequilibrium processes. The algorithm consists of evolving the system with a modified dynamics for which the required event occurs more frequently. By keeping track of the relative weight of phase-space trajectories generated by the modified and the original dynamics one can obtain the required probabilities. The algorithm is tested on two model systems of steady-state particle and heat transport where we find a huge improvement from direct simulation methods.Comment: 5 pages, 4 figures; some modification

Work distribution functions for hysteresis loops in a single-spin system

We compute the distribution of the work done in driving a single Ising spin with a time-dependent magnetic field. Using Glauber dynamics we perform Monte-Carlo simulations to find the work distributions at different driving rates. We find that in general the work-distributions are broad with a significant probability for processes with negative dissipated work. The special cases of slow and fast driving rates are studied analytically. We verify that various work fluctuation theorems corresponding to equilibrium initial states are satisfied while a steady state version is not.Comment: 9 pages, 15 figure