On the anomalous thermal conductivity of one-dimensional lattices

The divergence of the thermal conductivity in the thermodynamic limit is thoroughly investigated. The divergence law is consistently determined with two different numerical approaches based on equilibrium and non-equilibrium simulations. A possible explanation in the framework of linear-response theory is also presented, which traces back the physical origin of this anomaly to the slow diffusion of the energy of long-wavelength Fourier modes. Finally, the results of dynamical simulations are compared with the predictions of mode-coupling theory.Comment: 5 pages, 3 figures, to appear in Europhysics Letter

A Symmetry Property of Momentum Distribution Functions in the Nonequilibrium Steady State of Lattice Thermal Conduction

We study a symmetry property of momentum distribution functions in the steady state of heat conduction. When the equation of motion is symmetric under change of signs for all dynamical variables, the distribution function is also symmetric. This symmetry can be broken by introduction of an asymmetric term in the interaction potential or the on-site potential, or employing the thermal walls as heat reservoirs. We numerically find differences of behavior of the models with and without the on-site potential.Comment: 13 pages. submitted to JPS

Divergent Thermal Conductivity in Three-dimensional Nonlinear lattices

Heat conduction in three-dimensional nonlinear lattices is investigated using a particle dynamics simulation. The system is a simple three-dimensional extension of the Fermi-Pasta-Ulam $\beta$ (FPU-$\beta$) nonlinear lattices, in which the interparticle potential has a biquadratic term together with a harmonic term. The system size is $L\times L\times 2L$, and the heat is made to flow in the $2L$ direction the Nose-Hoover method. Although a linear temperature profile is realized, the ratio of enerfy flux to temperature gradient shows logarithmic divergence with $L$. The autocorrelation function of energy flux $C(t)$ is observed to show power-law decay as $t^{-0.98\pm 0,25}$, which is slower than the decay in conventional momentum-cnserving three-dimensional systems ($t^{-3/2}$). Similar behavior is also observed in the four dimensional system.Comment: 4 pages, 5 figures. Accepted for publication in J. Phys. Soc. Japan Letter

Non-equilibrium Statistical Mechanics of Anharmonic Crystals with Self-consistent Stochastic Reservoirs

We consider a d-dimensional crystal with an arbitrary harmonic interaction and an anharmonic on-site potential, with stochastic Langevin heat bath at each site. We develop an integral formalism for the correlation functions that is suitable for the study of their relaxation (time decay) as well as their behavior in space. Furthermore, in a perturbative analysis, for the one-dimensional system with weak coupling between the sites and small quartic anharmonicity, we investigate the steady state and show that the Fourier's law holds. We also obtain an expression for the thermal conductivity (for arbitrary next-neighbor interactions) and give the temperature profile in the steady state

Finite thermal conductivity in 1d lattices

We discuss the thermal conductivity of a chain of coupled rotators, showing that it is the first example of a 1d nonlinear lattice exhibiting normal transport properties in the absence of an on-site potential. Numerical estimates obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those ones based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the conductivity is traced back to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis of two variants of this model.Comment: 4 pages, 3 postscript figure

A simple one-dimensional model of heat conduction which obeys Fourier's law

We present the computer simulation results of a chain of hard point particles with alternating masses interacting on its extremes with two thermal baths at different temperatures. We found that the system obeys Fourier's law at the thermodynamic limit. This result is against the actual belief that one dimensional systems with momentum conservative dynamics and nonzero pressure have infinite thermal conductivity. It seems that thermal resistivity occurs in our system due to a cooperative behavior in which light particles tend to absorb much more energy than the heavier ones.Comment: 5 pages, 4 figures, to be published in PR

Thermal conductivity of one-dimensional lattices with self-consistent heat baths: a heuristic derivation

We derive the thermal conductivities of one-dimensional harmonic and anharmonic lattices with self-consistent heat baths (BRV lattice) from the Single-Mode Relaxation Time (SMRT) approximation. For harmonic lattice, we obtain the same result as previous works. However, our approach is heuristic and reveals phonon picture explicitly within the heat transport process. The results for harmonic and anharmonic lattices are compared with numerical calculations from Green-Kubo formula. The consistency between derivation and simulation strongly supports that effective (renormalized) phonons are energy carriers in anharmonic lattices although there exist some other excitations such as solitons and breathers.Comment: 4 pages, 3 figures. accepted for publication in JPS

A Framework for Verifiable and Auditable Collaborative Anomaly Detection

Collaborative and Federated Leaning are emerging approaches to manage cooperation between a group of agents for the solution of Machine Learning tasks, with the goal of improving each agent's performance without disclosing any data. In this paper we present a novel algorithmic architecture that tackle this problem in the particular case of Anomaly Detection (or classification of rare events), a setting where typical applications often comprise data with sensible information, but where the scarcity of anomalous examples encourages collaboration. We show how Random Forests can be used as a tool for the development of accurate classifiers with an effective insight-sharing mechanism that does not break the data integrity. Moreover, we explain how the new architecture can be readily integrated in a blockchain infrastructure to ensure the verifiable and auditable execution of the algorithm. Furthermore, we discuss how this work may set the basis for a more general approach for the design of collaborative ensemble-learning methods beyond the specific task and architecture discussed in this paper