Heat transport in ordered harmonic lattices

We consider heat conduction across an ordered oscillator chain with harmonic interparticle interactions and also onsite harmonic potentials. The onsite spring constant is the same for all sites excepting the boundary sites. The chain is connected to Ohmic heat reservoirs at different temperatures. We use an approach following from a direct solution of the Langevin equations of motion. This works both in the classical and quantum regimes. In the classical case we obtain an exact formula for the heat current in the limit of system size N to infinity. In special cases this reduces to earlier results obtained by Rieder, Lebowitz and Lieb and by Nakazawa. We also obtain results for the quantum mechanical case where we study the temperature dependence of the heat current. We briefly discuss results in higher dimensions.Comment: 8 pages, 2 figures, published versio

New Samarium and Neodymium based admixed ferromagnets with near zero net magnetization and tunable exchange bias field

Rare earth based intermetallics, SmScGe and NdScGe, are shown to exhibit near zero net magnetization with substitutions of 6 to 9 atomic percent of Nd and 25 atomic percent of Gd, respectively. The notion of magnetic compensation in them is also elucidated by the crossover of zero magnetization axis at low magnetic fields (less than 103 Oe) and field-induced reversal in the orientation of the magnetic moments of the dissimilar rare earth ions at higher magnetic fields. These magnetically ordered materials with no net magnetization and appreciable conduction electron polarization display an attribute of an exchange bias field, which can be tuned. The attractively high magnetic ordering temperatures of about 270 K, underscore the importance of these materials for potential applications in spintronics.Comment: 6 page text + 5 figure

Large deviations of heat flow in harmonic chains

We consider heat transport across a harmonic chain connected at its two ends to white-noise Langevin reservoirs at different temperatures. In the steady state of this system the heat $Q$ flowing from one reservoir into the system in a finite time $\tau$ has a distribution $P(Q,\tau)$. We study the large time form of the corresponding moment generating function $\sim g(\lambda) e^{\tau\mu (\lambda)}$. Exact formal expressions, in terms of phonon Green's functions, are obtained for both $\mu(\lambda)$ and also the lowest order correction $g(\lambda)$. We point out that, in general a knowledge of both $\mu(\lambda)$ and $g(\lambda)$ is required for finding the large deviation function associated with $P(Q,\tau)$. The function $\mu(\lambda)$ is known to be the largest eigenvector of an appropriate Fokker-Planck type operator and our method also gives the corresponding eigenvector exactly.Comment: 15 pages; minor modification

The Diffusion of the Magnetization Profile in the XX-model

By the $C^*$-algebraic method, we investigate the magnetization profile in the intermediate time of diffusion. We observe a transition from monotone profile to non-monotone profile. This transition is purely thermal.Comment: Accepted for publication in Phys. Rev.

Interacting Random Walkers and Non-Equilibrium Fluctuations

We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on the particle density. A non-equilibrium stationary flux can be induced by suitable boundary conditions, and we show indeed that it is mesoscopically described by a Fourier equation with a density dependent diffusivity. A simple mean-field description predicts a critical diffusivity if the hopping amplitude vanishes for a certain walker density. Actually, we evidence that, even if the density equals this pseudo-critical value, the system does not present any criticality but only a dynamical slowing down. This property is confirmed by the fact that, in spite of interaction, the particle distribution at equilibrium is simply described in terms of a product of Poissonians. For mesoscopic systems with a stationary flux, a very effect of interaction among particles consists in the amplification of fluctuations, which is especially relevant close to the pseudo-critical density. This agrees with analogous results obtained for Ising models, clarifying that larger fluctuations are induced by the dynamical slowing down and not by a genuine criticality. The consistency of this amplification effect with altered coloured noise in time series is also proved.Comment: 8 pages, 7 figure

Quantum transport using the Ford-Kac-Mazur formalism

The Ford-Kac-Mazur formalism is used to study quantum transport in (1) electronic and (2) harmonic oscillator systems connected to general reservoirs. It is shown that for non-interacting systems the method is easy to implement and is used to obtain many exact results on electrical and thermal transport in one-dimensional disordered wires. Some of these have earlier been obtained using nonequilibrium Green function methods. We examine the role that reservoirs and contacts can have on determining the transport properties of a wire and find several interesting effects.Comment: 10 pages, 4 figure

Simulation of heat transport in low-dimensional oscillator lattices

The study of heat transport in low-dimensional oscillator lattices presents a formidable challenge. Theoretical efforts have been made trying to reveal the underlying mechanism of diversified heat transport behaviors. In lack of a unified rigorous treatment, approximate theories often may embody controversial predictions. It is therefore of ultimate importance that one can rely on numerical simulations in the investigation of heat transfer processes in low-dimensional lattices. The simulation of heat transport using the non-equilibrium heat bath method and the Green-Kubo method will be introduced. It is found that one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) momentum-conserving nonlinear lattices display power-law divergent, logarithmic divergent and constant thermal conductivities, respectively. Next, a novel diffusion method is also introduced. The heat diffusion theory connects the energy diffusion and heat conduction in a straightforward manner. This enables one to use the diffusion method to investigate the objective of heat transport. In addition, it contains fundamental information about the heat transport process which cannot readily be gathered otherwise.Comment: Article published in: Thermal transport in low dimensions: From statistical physics to nanoscale heat transfer, S. Lepri, ed. Lecture Notes in Physics, vol. 921, pp. 239 - 274, Springer-Verlag, Berlin, Heidelberg, New York (2016

From thermal rectifiers to thermoelectric devices

We discuss thermal rectification and thermoelectric energy conversion from the perspective of nonequilibrium statistical mechanics and dynamical systems theory. After preliminary considerations on the dynamical foundations of the phenomenological Fourier law in classical and quantum mechanics, we illustrate ways to control the phononic heat flow and design thermal diodes. Finally, we consider the coupled transport of heat and charge and discuss several general mechanisms for optimizing the figure of merit of thermoelectric efficiency.Comment: 42 pages, 22 figures, review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.

Simulation of dimensionality effects in thermal transport

The discovery of nanostructures and the development of growth and fabrication techniques of one- and two-dimensional materials provide the possibility to probe experimentally heat transport in low-dimensional systems. Nevertheless measuring the thermal conductivity of these systems is extremely challenging and subject to large uncertainties, thus hindering the chance for a direct comparison between experiments and statistical physics models. Atomistic simulations of realistic nanostructures provide the ideal bridge between abstract models and experiments. After briefly introducing the state of the art of heat transport measurement in nanostructures, and numerical techniques to simulate realistic systems at atomistic level, we review the contribution of lattice dynamics and molecular dynamics simulation to understanding nanoscale thermal transport in systems with reduced dimensionality. We focus on the effect of dimensionality in determining the phononic properties of carbon and semiconducting nanostructures, specifically considering the cases of carbon nanotubes, graphene and of silicon nanowires and ultra-thin membranes, underlying analogies and differences with abstract lattice models.Comment: 30 pages, 21 figures. Review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.