We study heat conduction behavior of one-dimensional lattices with asymmetric, momentum conserving interparticle interactions. We find that with a certain degree of interaction asymmetry, the heat conductivity measured in nonequilibrium stationary states converges in the thermodynamical limit. Our analysis suggests that the mass gradient resulting from asymmetric interactions may provide a phonon scattering mechanism in addition to that caused by nonlinear interactions.

In order to identify the basic conditions for thermal rectification we investigate a simple model with non-uniform, graded mass distribution. The existence of thermal rectification is theoretically predicted and numerically confirmed, suggesting that thermal rectification is a typical occurrence in graded systems, which are likely to be natural candidates for the actual fabrication of thermal diodes. In view of practical implications, the dependence of rectification on the asymmetry and system's size is studied. The study of the underlying dynamical mechanisms which determine the macroscopic properties of heat conduction has opened the fascinating possibility to control the heat current. In particular a model of a thermal rectifier has been proposed [1] and since then, the phenomenon of thermal rectification has been intensively investigated [2][3][4][5][6][7][8][9] in order to analyze and improve the rectification effect, including experimental realizations [10].However, as correctly pointed out in Ref.[3], most recurrent proposals of a thermal diode, based on the sequential coupling of two or three segments with different anharmonic potentials, are difficult to be experimentally implemented and the rectification power typically decays to zero with increasing the system size. In addition, most investigations so far have been based on numerical simulations and a much better theoretical understanding is highly desirable both for fundamental reasons as well as for obtaining useful hints for the actual realization of devices with satisfactory rectification power.Along these lines, graded materials are attracting more and more interest: Papers with numerical [5][6][7], analytical [8,9] and even experimental [10] studies have appeared recently in the literature.The present paper addresses the fundamental dynamical mechanisms that lead to rectification. Our strategy is to consider a simple model that contains the minimal ingredients we theoretically judge to be necessary to rectification, and compare the numerical results with the theoretical predictions. As the features of our model are also shared by more realistic models such as anharmonic chains of oscillators, we conjecture that the obtained results may have practical implications as well. Our study allows us to understand the basic ingredients behind rectification, to describe non-trivial and important properties of the heat flow, and to show that rectification in graded materials could be a ubiquitous phenomenon.We consider a chain [11] of elastically colliding particles of two kinds referred to, in the following, as "bars" L R FIG. 1: (Color online)The schematic plot of our model. Dotted lines divide elementary unit cells. In each cell there is a bar which is subjected to elastic collisions with both cell boundaries and with neighboring bullets. The first (last) cell is coupled to a heat bath at temperature τL (τR).and "bullets", respectively. (See Fig. 1.) Each bar is confined inside a cell of unit length; that is, besides elastic collisions with its neighbor...

We study in momentum-conserving systems, how nonintegrable dynamics may affect thermal transport properties. As illustrating examples, two one-dimensional (1D) diatomic chains, representing 1D fluids and lattices, respectively, are numerically investigated. In both models, the two species of atoms are assigned two different masses and are arranged alternatively. The systems are nonintegrable unless the mass ratio is one. We find that when the mass ratio is slightly different from one, the heat conductivity may keep significantly unchanged over a certain range of the system size and as the mass ratio tends to one, this range may expand rapidly. These results establish a new connection between the macroscopic thermal transport properties and the underlying dynamics.

NNSF of China [10925525, 11275159, 10805036]; SRFDP of China [20100121110021]We study diffusion processes of local fluctuations of heat, energy, momentum, and mass in three paradigmatic one-dimensional systems. For each system, diffusion processes of four physical quantities are simulated and the cross correlations between them are investigated. We find that, in all three systems, diffusion processes of energy and mass can be perfectly expressed as a linear combination of those of heat and momentum, suggesting that diffusion processes of heat and momentum may represent the heat mode and the sound mode in the hydrodynamic theory. In addition, the dynamic structure factor, which describes the diffusion behavior of local mass density fluctuations, is in general insufficient for probing diffusion processes of other quantities because in some cases there is no correlation between them. We also find that the diffusion behavior of heat can be qualitatively different from that of energy, and, as a result, previous studies trying to relate heat conduction to energy diffusion should be revisited. DOI: 10.1103/PhysRevE.87.03215

We show that generic systems with a single relevant conserved quantity reach the Carnot efficiency in the thermodynamic limit. Such a general result is illustrated by means of a diatomic chain of hard-point elastically colliding particles where the total momentum is the only relevant conserved quantity.PACS numbers: 05.70. Ln, Conservation laws strongly affect transport properties. Conserved quantities may lead to time correlations not decaying with time, so that transport is not diffusive and is described, within the linear response theory, by diverging transport coefficients. This ideal conducting (ballistic) behavior can be firmly established as a consequence of an inequality by Mazur [1-3] which, for a system of size Λ characterized by M conserved quantities Q n , n = 1, · · · , M , bounds the time-averaged currentcurrent correlation functions aswhere · · · T denotes the thermodynamic average at temperature T . The constants of motion, Q n , are orthogonal to each other, i.e., Q n Q m T = Q 2 n T δ n,m , and relevant, that is, JQ n T = 0 for all n. A non-zero right-hand side in Eq. (1) at the thermodynamic limit implies a finite Drude weight for the current J, which in turn indicates ballistic transport [4,5]. The impact of motion constants on the electric and thermal conductivities has been widely investigated [4][5][6][7]. In particular, anomalous heat transport has been discussed for momentum conserving interacting systems in low dimensions [8,9]. However, to the best of our knowledge, conservation laws have never been discussed for coupled flows, in particular in relation to the problem of optimizing thermodynamic efficiencies.The search of a new technology capable of reducing the environmental impact of electrical power generation and refrigeration has aroused great interest in thermoelectricity, namely the possibility to build a type of solid-state heat engine capable of converting heat into electricity, or alternatively electricity into cooling [10][11][12][13][14]. The main difficulty is connected to the low efficiency of such heat engine. We recall that the maximum thermoelectric efficiency as well as the efficiency at maximum power [15][16][17][18][19] are determined, within the linear response regime and for systems with time-reversal symmetry [20], by the so called figure of merit ZT , which is a dimensionless quantity, a combination of the three main transport properties of a material: the thermal conductivity κ, the electrical conductivity σ and the thermopower (Seebeck coefficient) S, as well as of the absolute temperature T :The maximum efficiency is given bywhere η C is the Carnot efficiency, while the efficiency η(W max ) at maximum output power W max reads [15]The only restriction imposed by thermodynamics is ZT ≥ 0, so that both efficiencies are monotonous growing functions of the figure of merit and η max → η C , η(W max ) → ηC 2 when ZT → ∞. It has been suggested that the value ZT = 3 is the target to be achieved in order to make thermoelectric engines economically competitive. In spite...

We show evidence, based on extensive and carefully performed numerical experiments, that the system of two elastic hard-point masses in one-dimension is not ergodic for a generic mass ratio and consequently does not follow the principle of energy equipartition. This system is equivalent to a right triangular billiard. Remarkably, following the time-dependent probability distribution in a suitably chosen velocity direction space, we find evidence of exponential localization of invariant measure. For non-generic mass ratios which correspond to billiard angles which are rational, or weak irrational multiples of π, the system is ergodic, in consistence with existing rigorous results. Introduction.-Soon after the Sinai's proof [1] of ergodicity and mixing in the two-dimensional hard disc gas, the question has been raised if ergodicity and mixing may not also occur in an even simpler one-dimensional, unequal mass, hard point gas. In particular, as pointed out by Lebowitz long ago [2], even the simplest unequal mass case having only two moving point particles is not decided. Since those pioneering times, the analysis of simple non-trivial models has allowed a tremendous progress in our understanding of the properties of nonlinear dynamical systems. In particular, the above problem is of special interest since the local dynamical instability is only linear and therefore it is worthwhile to inquire to what extent statistical properties are present in such systems. This problem is also relevant for the understanding of the properties of the diffusion and relaxation process in quantum mechanics. Indeed, unlike the exponentially unstable classical chaotic motion, in the quantum case deviations in the initial conditions propagate only linearly in time and therefore the quantum diffusion and relaxation process takes place in the absence of exponential instability.The dynamics of the one-dimensional unequal mass, hard point gas with reflecting boundary conditions can be reduced to a simple map. Indeed let m 1 , m 2 be the masses of the two particles, x 1 , x 2 and v 1 , v 2 their positions and velocities respectively. After the collision, the new velocities v ′ 1 , v ′ 2 are given by v ′

For one-dimensional nonlinear lattices with momentum conserving interparticle interactions, intensive studies have suggested that the heat conductivity κ diverges with the system size L as κ~L(α) and the value of α is universal. But in the Fermi-Pasta-Ulam-β lattices with nearest-neighbor (NN) and next-nearest-neighbor (NNN) coupling, we find that α strongly depends on γ, the ratio of the NNN coupling to the NN coupling. The correlation between the γ-dependent heat conduction behavior and the in-band discrete breathers is also analyzed.

We study the heat conduct behavior of a lattice model with asymmetry harmonic inter-particle interactions in this paper. Normal heat conductivity independent of the system size is observed when the lattice chain is long enough. Because only the harmonic interactions are involved, the result confirms without ambiguous interpretation that the asymmetry plays the key role in resulting in the normal heat conduct of one dimensional momentum conserving lattices. Both equilibrium and non-equilibrium simulations are performed to support the conclusion.The heat transport properties of low-dimensional systems have evoked intensive studies for decades [1][2][3][4][5][6][7][8][9][10][11][12][13], aiming at to verify whether the Fourier's law of heat conduction J = −κ∇T (1)