Thermal conductivity of molecular chains with asymmetric potentials of pair interactions

Transient diffusion and thermal processes in a finite one-dimensional harmonic crystal

In this paper, an instant homogeneous thermal perturbation in the periodic one-dimensional harmonic crystal is studied. The exact solution for thermal and diffusive characteristics is obtained, namely, particle velocity dispersion (kinetic temperature) and particle displacement dispersion. It is found that thermal and diffusion processes demonstrate a quasi-periodic recurrence. The recurrence interval is equal to the time it takes the sound wave to travel the half-length of the crystal. The 'thermal echo' (sharp peaks in kinetic temperature) occurs in the system with the specified periodicity. Diffusion characteristics reveal large-scale time changes with a nearly complete return to the initial state at each quasi-period. It is also shown that the spatial mean squared displacements of particles are significantly different from the ensemble mean squared displacements.

Effect of the Base-Pair Sequence on B-DNA Thermal Conductivity

The thermal conductivity of double-stranded (ds) B-DNA was systematically investigated using classical molecular dynamics (MD) simulations. The effect of changing the base pair (bp) on the thermal conductivity of dsDNA needed investigation at a molecular level. Hence, four sequences, viz., poly(A), poly(G), poly(CG), and poly(AT), were initially analyzed in this work. First, the length of these sequences was varied from 4 to 40 bp at 300 K, and the respective thermal conductivity (κ) was computed. Second, the temperature-dependent thermal conductivities between 100 and 400 K were obtained in 50 K steps at 28 bp length. The Müller-Plathe reverse nonequilibrium molecular dynamics (RNEMD) was employed to set a thermal gradient and obtain all thermal conductivities in this work. Moreover, mixed sequences using AT and CG sequences, namely, A(CG)_nT (n = 3-7), ACGC(AT)_mGCGT (m = 0-5), and ACGC(AT)_nAGCGT (n = 1-4), were investigated based on the hypothesis that these sequences could be better thermoelectrics. One-dimensional lattices are said to have diverging thermal conductivities at longer lengths, which violate the Fourier law. These follow the power law, where κ ∝ L^β. At longer lengths, the exponent β needs to satisfy the condition β > 1/3 for divergent thermal conductivity. We find no such significant Fourier law violation through divergence of thermal conductivities at 80 bp lengths or 40 bp lengths. Also, in the case of the second study, the presence of short (m ≤ 2) encapsulated AT sequences within CG sequences shows an increasing trend. These results are important for engineering DNA-based thermal devices.

Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion

Energy transport in one-dimensional chains of particles with three conservation laws is generically anomalous and belongs to the Kardar-Parisi-Zhang dynamical universality class. Surprisingly, some examples where an apparent normal heat diffusion is found over a large range of length scales were reported. We propose a novel physical explanation of these intriguing observations. We develop a scaling analysis that explains how this may happen in the vicinity of an integrable limit, such as, but not only, the famous Toda model. In this limit, heat transport is mostly supplied by quasiparticles with a very large mean free path ℓ. Upon increasing the system size L, three different regimes can be observed: a ballistic one, an intermediate diffusive range, and, eventually, the crossover to the anomalous (hydrodynamic) regime. Our theoretical considerations are supported by numerical simulations of a gas of diatomic hard-point particles for almost equal masses and of a weakly perturbed Toda chain. Finally, we discuss the case of the perturbed harmonic chain, which exhibits a yet different scenario.

Energy and spin diffusion in the one-dimensional classical Heisenberg spin chain at finite and infinite temperatures

The energy and spin diffusion behaviors in the one-dimensional classical Heisenberg spin chain have been systematically investigated using the equilibrium diffusion method. The spatiotemporal autocorrelation functions for energy and spin are calculated at finite and infinite temperatures. As conserved quantities, the spreading of excess energy and spin can be used to determine their actual diffusion behaviors. At low temperatures, the energy diffusion shows almost ballistic behavior, and spin shows superdiffusion behavior for finite chain size. For energy diffusion, normal diffusion behavior can be obtained when the temperature is higher than 0.75. For spin diffusion, normal diffusion behavior is observed at infinite temperature.

Energy and momentum diffusion in one-dimensional periodic and asymmetric nonlinear lattices with momentum conservation

The energy diffusion in one-dimensional (1D) momentum conserving nonlinear lattices usually exhibits anomalous superdiffusion, except the coupled rotator lattice with symmetric and periodic interacting potential which has normal energy diffusion corresponding to normal heat conduction. For nonperiodic 1D lattices with momentum conservation, it has been argued that the asymmetric potential can induce normal heat conduction. Later results indicate the observed normal behavior might be the finite size effect and the anomalous behavior will appear in the thermodynamical limit. Here we propose asymmetric and periodic 1D nonlinear lattices with momentum conservation. The energy and momentum diffusion behaviors will be investigated in detail and the same normal diffusion behaviors for both energy and momentum can be observed. These results confirm that the periodicity is the key for normal transport behavior in 1D momentum conserving lattices, whether the potential is symmetric or asymmetric.

Change of entropy for the one-dimensional ballistic heat equation: Sinusoidal initial perturbation

This work presents a thermodynamic analysis of the ballistic heat equation from two viewpoints: classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT). A formula for calculating the entropy within the framework of EIT for the ballistic heat equation is derived. The entropy is calculated for a sinusoidal initial temperature perturbation by using both approaches. The results obtained from CIT show that the entropy is a non-monotonic function and that the entropy production can be negative. The results obtained for EIT show that the entropy is a monotonic function and that the entropy production is nonnegative. A comparison between the entropy behaviors predicted for the ballistic, for the ordinary Fourier-based, and for the hyperbolic heat equation is made. A crucial difference of the asymptotic behavior of the entropy for the ballistic heat equation is shown. It is argued that mathematical time reversibility of the partial differential ballistic heat equation is not consistent with its physical irreversibility. The processes described by the ballistic heat equation are irreversible because of the entropy increase.

Temperature-dependent divergence of thermal conductivity in momentum-conserving one-dimensional lattices with asymmetric potential

In this study we used a nonequilibrium simulation method to investigate the temperature dependent divergence of thermal conductivity in a one-dimensional momentum conserving system with an asymmetric double well nearest-neighbor interaction potential. We show that across all temperatures thermal conductivity exhibits power-law divergence with the chain length and the value of the divergence exponent (α) depends on the temperature of the system. At low and high temperatures α reaches close to ∼0.5 and ∼0.33, respectively. Whereas in the intermediate temperature the divergence of thermal conductivity with the chain length saturates with α∼0.07. Subsequent analysis showed that the estimated value of α in the intermediate temperature may not have reached its thermodynamic limit. Further calculations of local α revealed that its approach towards the thermodynamic limit is crucially dependent on the temperature of the system. At low and high temperatures local α reaches its thermodynamic limits in shorter chain lengths. On the contrary, in the case of intermediate temperature its progress towards the asymptotic limit is nonmonotonic.

Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices

Currently, effective phonons (renormalized or interacting phonons) rather than solitary waves (for short, solitons) are regarded as the energy carriers in nonlinear lattices. In this work, by using the approximate soliton solutions of the corresponding equations of motion and adopting the Boltzmann distribution for these solitons, the average velocities of solitons are obtained and are compared with the sound velocities of energy transfer. Excellent agreements with the numerical results and the predictions of other existing theories are shown in both the symmetric Fermi-Pasta-Ulam-β lattices and the asymmetric Fermi-Pasta-Ulam-αβ lattices. These clearly indicate that solitons are suitable candidates for energy carriers in Fermi-Pasta-Ulam lattices. In addition, the root-mean-square velocity of solitons can be obtained from the effective phonons theory.

Discrete breathers assist energy transfer to ac-driven nonlinear chains

A one-dimensional chain of pointwise particles harmonically coupled with nearest neighbors and placed in sixth-order polynomial on-site potentials is considered. The power of the energy source in the form of single ac driven particle is calculated numerically for different amplitudes A and frequencies ω within the linear phonon band. The results for the on-site potentials with hard and soft anharmonicity types are compared. For the hard-type anharmonicity, it is shown that when the driving frequency is close to (far from) the upper edge of the phonon band, the power of the energy source normalized to A^{2} increases (decreases) with increasing A. In contrast, for the soft-type anharmonicity, the normalized power of the energy source increases (decreases) with increasing A when the driving frequency is close to (far from) the lower edge of the phonon band. Our further demonstrations indicate that in the case of hard (soft) anharmonicity, the chain can support movable discrete breathers (DBs) with frequencies above (below) the phonon band. It is the energy source quasiperiodically emitting moving DBs in the regime with driving frequency close to the DB frequency that induces the increase of the power. Therefore, our results here support the mechanism that the moving DBs can assist energy transfer from the ac driven particle to the chain.

Fourier heat conduction as a strong kinetic effect in one-dimensional hard-core gases

For a one-dimensional (1D) momentum conserving system, intensive studies have shown that generally its heat current autocorrelation function (HCAF) tends to decay in a power-law manner and results in the breakdown of the Fourier heat conduction law in the thermodynamic limit. This has been recognized to be a dominant hydrodynamic effect. Here we show that, instead, the kinetic effect can be dominant in some cases and leads to the Fourier law for finite-size systems. Usually the HCAF undergoes a fast decaying kinetic stage followed by a long slowly decaying hydrodynamic tail. In a finite range of the system size, we find that whether the system follows the Fourier law depends on whether the kinetic stage dominates. Our Rapid Communication is illustrated by the 1D hard-core gas models with which the HCAF is derived analytically and verified numerically by molecular dynamics simulations.

Crossover from ballistic to normal heat transport in the ϕ^{4} lattice: If nonconservation of momentum is the reason, what is the mechanism?

Anomalous (non-Fourier) heat transport is no longer just a theoretical issue since it has been observed experimentally in a number of low-dimensional nanomaterials, such as SiGe nanowires, carbon nanotubes, and others. To understand these anomalous behaviors, exploring the microscopic origin of normal (Fourier) heat transport is a fascinating theoretical topic. However, this issue has not yet been fully understood even for one-dimensional (1D) model chains, in spite of a great amount of thorough studies done to date. From those studies, it has been widely accepted that the conservation of momentum is a key ingredient to induce anomalous heat transport, while momentum-nonconserving systems usually support normal heat transport where Fourier's law is valid. But if the nonconservation of momentum is the reason, what is the underlying microscopic mechanism for the observed normal heat transport? Here we carefully revisit a typical 1D momentum-nonconserving ϕ^{4} model, and we present evidence that the mobile discrete breathers, or, in other words, the moving intrinsic localized modes with frequency components above the linear phonon band, can be responsible for that.

Scattering of lattice solitons and decay of heat-current correlation in the Fermi-Pasta-Ulam-α-β model

As is well known, solitons can be excited in nonlinear lattice systems; however, whether, and if so, how, this kind of nonlinear excitation can affect the energy transport behavior is not yet fully understood. Here we study both the scattering dynamics of solitons and heat transport properties in the Fermi-Pasta-Ulam-α-β model with an asymmetric interparticle interaction. By varying the asymmetry degree of the interaction (characterized by α), we find that (i) for each α there exists a momentum threshold for exciting solitons from which one may infer an α-dependent feature of probability of presentation of solitons at a finite-temperature equilibrium state and (ii) the scattering rate of solitons is sensitively dependent on α. Based on these findings, we conjecture that the scattering between solitons will cause the nonmonotonic α-dependent feature of heat conduction. Fortunately, such a conjecture is indeed verified by our detailed examination of the time decay behavior of the heat current correlation function, but it is only valid for an early time stage. Thus, this result may suggest that solitons can have only a relatively short survival time when exposed in a thermal environment, eventually affecting the heat transport in a short time.

Resonance phonon approach to phonon relaxation time and mean free path in one-dimensional nonlinear lattices

We extend a previously proposed resonance phonon approach that is based on the linear response theory. By studying the complex response function in depth, we work out the phonon relaxation time besides the oscillating frequency of the phonons in a few one-dimensional nonlinear lattices. The results in the large wave-number-k regime agree with the expectations of the effective phonon theory. However, in the small-k limit they follow different scaling laws. The phonon mean free path can also be calculated indirectly. It coincides well with that derived from the anharmonic phonon approach. A power-law divergent heat conduction, i.e., the heat conductivity κ depends on lattice length N by κ∼N^{β} with β>0, then is supported for the momentum-conserving lattices. Furthermore, this approach can be applied to diatomic lattices. So obtained relaxation time quantitatively agrees with that from the effective phonon theory. As for the mean free path, the resonance phonon approach can detect both the acoustic and the optical branches, whereas the anharmonic phonon approach can only detect a combined branch, i.e., the acoustic branch for small k and the optical branch for large k.

Anomalous temperature-dependent heat transport in one-dimensional momentum-conserving systems with soft-type interparticle interaction

We numerically investigate the heat transport problem in a one-dimensional momentum-conserving lattice with a soft-type (ST) anharmonic interparticle interaction. It is found that with the increase of the system's temperature, while the introduction of ST anharmonicity softens phonons and decreases their velocities, this type of nonlinearity like its hard type (HT) counterpart, can still not be able to fully damp the longest wavelength phonons. Therefore, a usual anomalous temperature dependence of heat transport with certain scaling properties similarly to those shown in the Fermi-Pasta-Ulam-β-like systems with HT interactions can be seen. Our detailed examination from simulations verifies this temperature-dependent behavior well.

Heat conduction in a chain of colliding particles with a stiff repulsive potential

One-dimensional billiards, i.e., a chain of colliding particles with equal masses, is a well-known example of a completely integrable system. Billiards with different particle masses is generically not integrable, but it still exhibits divergence of a heat conduction coefficient (HCC) in the thermodynamic limit. Traditional billiards models imply instantaneous (zero-time) collisions between the particles. We relax this condition of instantaneous impact and consider heat transport in a chain of stiff colliding particles with the power-law potential of the nearest-neighbor interaction. The instantaneous collisions correspond to the limit of infinite power in the interaction potential; for finite powers, the interactions take nonzero time. This modification of the model leads to a profound physical consequence-the probability of multiple (in particular triple) -particle collisions becomes nonzero. Contrary to the integrable billiards of equal particles, the modified model exhibits saturation of the heat conduction coefficient for a large system size. Moreover, the identification of scattering events with triple-particle collisions leads to a simple definition of the characteristic mean free path and a kinetic description of heat transport. This approach allows us to predict both the temperature and density dependencies for the HCC limit values. The latter dependence is quite counterintuitive-the HCC is inversely proportional to the particle density in the chain. Both predictions are confirmed by direct numerical simulations.

Role of the range of the interactions in thermal conduction

We investigate thermal transport along a one-dimensional lattice of classical inertial rotators, with attractive couplings that decrease with distance as r^{-α} (α≥0), subject at its ends to Brownian heat reservoirs at different temperatures with average value T. By means of numerical integration of the equations of motion, we show the effects of the range of the interactions in the temperature profile and energy transport and determine the domain of validity of Fourier's law in this context. We find that Fourier's law, as signaled by a finite κ in the thermodynamic limit, holds only for sufficiently short-range interactions, with α>α_{c}(T). For α<α_{c}(T), a kind of insulator behavior emerges at any T.

Pressure-induced recovery of Fourier's law in one-dimensional momentum-conserving systems

We report the two typical models of normal heat conduction in one-dimensional momentum-conserving systems. They show the Arrhenius and the non-Arrhenius temperature dependence. We construct the two corresponding phenomenologies, transition-state theory of thermally activated dissociation and the pressure-induced crossover between two fixed points in fluctuating hydrodynamics. Compressibility yields the ballistic fixed point, whose scaling is observed in Fermi-Pasta-Ulam (FPU) β lattices.

Heat conduction and energy diffusion in momentum-conserving one-dimensional full-lattice ding-a-ling model

The ding-a-ling model is a kind of half lattice and half hard-point-gas (HPG) model. The original ding-a-ling model proposed by Casati et al. does not conserve total momentum and has been found to exhibit normal heat conduction behavior. Recently, a modified ding-a-ling model which conserves total momentum has been studied and normal heat conduction has also been claimed. In this work, we propose a full-lattice ding-a-ling model without hard point collisions where total momentum is also conserved. We investigate the heat conduction and energy diffusion of this full-lattice ding-a-ling model with three different nonlinear inter-particle potential forms. For symmetrical potential lattices, the thermal conductivities diverges with lattice length and their energy diffusions are superdiffusive signaturing anomalous heat conduction. For asymmetrical potential lattices, although the thermal conductivity seems to converge as the length increases, the energy diffusion is definitely deviating from normal diffusion behavior indicating anomalous heat conduction as well. No normal heat conduction behavior can be found for the full-lattice ding-a-ling model.

Ballistic Thermal Transport in Carbyne and Cumulene with Micron-Scale Spectral Acoustic Phonon Mean Free Path

The elastic modulus of carbyne, a one-dimensional carbon chain, was recently predicted to be much higher than graphene. Inspired by this discovery and the fundamental correlation between elastic modulus and thermal conductivity, we investigate the intrinsic thermal transport in two carbon allotropes: carbyne and cumulene. Using molecular dynamics simulations, we discover that thermal conductivities of carbyne and cumulene at the quantum-corrected room temperature can exceed 54 and 148 kW/m/K, respectively, much higher than that for graphene. Such conductivity is attributed to high phonon energies and group velocities, as well as reduced scattering from non-overlapped acoustic and optical phonon modes. The prolonged spectral acoustic phonon lifetime of 30–110 ps and mean free path of 0.5–2.5 μm exceed those for graphene, and allow ballistic phonon transport along micron-length carbon chains. Tensile extensions can enhance the thermal conductivity of carbyne due to the increased phonon density of states in the acoustic modes and the increased phonon lifetime from phonon bandgap opening. These findings provide fundamental insights into phonon transport and band structure engineering through tensile deformation in low-dimensional materials, and will inspire studies on carbyne, cumulene, and boron nitride chains for their practical deployments in nano-devices.

Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

We study the anomalous dynamical scaling of equilibrium correlations in one-dimensional systems. Two different models are compared: the Fermi-Pasta-Ulam chain with cubic and quartic nonlinearity and a gas of point particles interacting stochastically through multiparticle collision dynamics. For both models-that admit three conservation laws-by means of detailed numerical simulations we verify the predictions of nonlinear fluctuating hydrodynamics for the structure factors of density and energy fluctuations at equilibrium. Despite this, violations of the expected scaling in the currents correlation are found in some regimes, hindering the observation of the asymptotic scaling predicted by the theory. In the case of the gas model this crossover is clearly demonstrated upon changing the coupling constant.

Deviation from the Maxwell-Cattaneo law: Role of asymmetric interparticle interactions

Nonstationary heat conduction in a few one-dimensional nonlinear lattices is studied numerically based on the Maxwell-Cattaneo (MC) law. We simulate the relaxation process and calculate the magnitudes of the temperature oscillation A(T)(t) and the local heat current oscillation A(j)(t). A phase difference between A(T)(t) and A(j)(t) is observed, which not only verifies the existence of the time lag τ in the MC law but also provides a better way of determining the critical wavelength L(*) that separates between oscillatory and diffusive relaxation modes. However, clear deviations from the MC law are observed. Not only do the decay exponents differ from the theoretical expectations, but, more importantly, suboscillation in the diffusive regime, which is not expected by the MC law, is found in the lattices with asymmetric interactions as well. These findings imply that higher-order effects must be considered in order to well describe the nonstationary heat conduction process in these systems.

Effects of interaction symmetry on delocalization and energy transport in one-dimensional disordered lattices

We study effects of interaction symmetry in one-dimensional, momentum-conserving disordered lattices. It is found that asymmetric and symmetric interparticle interactions may result in significant difference: localized modes can be delocalized by very weak asymmetric interactions but survive much stronger symmetric interactions. Moreover, in the delocalization regime, asymmetric and symmetric interactions also have qualitatively different effects on transport: the former (the latter) may lead to a fast decaying (slow power-law decaying) heat current correlation function and in turn a convergent (divergent) heat conductivity. A method for detecting delocalization in systems at a nonzero temperature is proposed as well.

Thermoelectricity of interacting particles: a numerical approach

A method for computing the thermopower in interacting systems is proposed. This approach, which relies on Monte Carlo simulations, is illustrated first for a diatomic chain of hard-point elastically colliding particles and then in the case of a one-dimensional gas with (screened) Coulomb interparticle interaction. Numerical simulations up to N>10^{4} particles confirm the general theoretical arguments for momentum-conserving systems and show that the thermoelectric figure of merit increases linearly with the system size.

Super heat diffusion in one-dimensional momentum-conserving nonlinear lattices

Heat diffusion processes in various one-dimensional total-momentum-conserving nonlinear lattices with symmetric interaction and asymmetric interaction are systematically studied. It is revealed that the asymmetry of interaction largely enhances the heat diffusion; while according to our existing studies for heat conduction in the same lattices, it slows the divergence of heat conductivity in a wide regime of system size. These findings violate the proposed relations that connect anomalous heat conduction and super heat diffusion. The generality of those expectations is thus questioned.

Thermal transport in phononic Cayley-tree networks

We analytically investigate the heat current I and its thermal fluctuations Δ in a branching network without loops (Cayley tree). The network consists of two types of harmonic masses: vertex masses M placed at the branching points where phononic scattering occurs and masses m at the bonds between branching points where phonon propagation takes place. The network is coupled to thermal reservoirs consisting of one-dimensional harmonic chains of coupled masses m. Due to impedance mismatch phenomena, both I and Δ are non-monotonic functions of the mass ratio μ=M/m. Furthermore, we find that in the low-temperature limit the thermal conductance approaches zero faster than linearly due to the small transmittance of the long-wavelength modes.

Renormalized phonons in nonlinear lattices: A variational approach

We propose a variational approach to study renormalized phonons in momentum-conserving nonlinear lattices with either symmetric or asymmetric potentials. To investigate the influence of pressure for phonon properties, we derive an inequality which provides both the lower and upper bound of the Gibbs free energy as the associated variational principle. This inequality is a direct extension to the Gibbs-Bogoliubov inequality. Taking the symmetry effect into account, the reference system for the variational approach is chosen to be harmonic with an asymmetric quadratic potential which contains variational parameters. We demonstrate the power of this approach by applying it to one-dimensional nonlinear lattices with a symmetric or asymmetric Fermi-Pasta-Ulam-type potential. For a system with a symmetric potential and zero pressure, we recover existing results. For other systems which are beyond the scope of existing theories, including those having symmetric potential and pressure and those having the asymmetric potential with or without pressure, we also obtain accurate sound velocity.

Heat conduction in a chain of dissociating particles: Effect of dimensionality

The paper considers heat conduction in a model chain of composite particles with hard core and elastic external shell. Such model mimics three main features of realistic interatomic potentials--hard repulsive core, quasilinear behavior in a ground state, and possibility of dissociation. It has become clear recently that this latter feature has crucial effect on convergence of the heat conduction coefficient in thermodynamic limit. We demonstrate that in one-dimensional chain of elastic particles with hard core the heat conduction coefficient also converges, as one could expect. Then we explore effect of dimensionality on the heat transport in this model. For this sake, longitudinal and transversal motions of the particles are allowed in a long narrow channel. With varying width of the channel, we observe sharp transition from "one-dimensional" to "two-dimensional" behavior. Namely, the heat conduction coefficient drops by about order of magnitude for relatively small widening of the channel. This transition is not unique for the considered system. Similar phenomenon of transition to quasi-1D behavior with growth of aspect ratio of the channel is observed also in a gas of densely packed hard (billiard) particles, both for two- and three-dimensional cases. It is the case despite the fact that the character of transition in these two systems is not similar, due to different convergence properties of the heat conductivity. In the billiard model, the divergence pattern of the heat conduction coefficient smoothly changes from logarithmic to power-like law with increase of the length.

Ultradiscrete kinks with supersonic speed in a layered crystal with realistic potentials

In this paper we develop a dynamical model of the propagating nonlinear localized excitations, supersonic kinks, in the cation layer in a silicate mica crystal. We start from purely electrostatic Coulomb interaction and add the Ziegler-Biersack-Littmark short-range repulsive potential and the periodic potential produced by other atoms of the lattice. The proposed approach allows the construction of supersonic kinks which can propagate in the lattice within a large range of energies and velocities. Due to the presence of the short-range repulsive component in the potential, the interparticle distances in the lattice kinks with high energy are limited by physically reasonable values. The introduction of the periodic lattice potential results in the important feature that the kinks propagate with the single velocity and single energy, which are independent on the excitation conditions. The unique average velocity of the supersonic kinks on the periodic substrate potential we relate with the kink amplitude of the relative particle displacements, which is determined by the interatomic distance corresponding to the minimum of the total, interparticle plus substrate, lattice potential. The found kinks are ultradiscrete and can be described with the "magic wave number" q=2π/3a, which was previously revealed in the nonlinear sinusoidal waves and supersonic kinks in the Fermi-Pasta-Ulam lattice. The extreme discreteness of the observed supersonic kinks, with basically two particles moving at the same time, allows the detailed interpretation of their double-kink structure, which is not possible for the multikinks without an account for the lattice discreteness. Analytical calculations of the displacement patterns and energies of the supersonic kinks are confirmed by numerical simulations. The computed energy of the found supersonic kinks in the considered realistic lattice potential is in a good agreement with the experimental evidence for the transport of localized energetic excitations in silicate mica crystals between the points of ^{40}K recoil and subsequent sputtering.

Heat-current correlation loss induced by finite-size effects in a one-dimensional nonlinear lattice

The Green-Kubo formula provides a mathematical expression for heat conductivity in terms of integrals of the heat-current correlation function, which should be calculated in the thermodynamic limit. In finite systems this function generally decreases, i.e., it decays faster than it does in infinite systems. We compared the values of the correlation function in a one-dimensional purely quartic lattice with various lengths, and found that this loss is much smaller than is conventionally estimated. By studying the heat diffusion process in this lattice, we found that, in contrast to the conventional belief, the collisions between sound modes do not noticeably affect the current correlation function. Therefore, its loss being surprisingly small can be well understood. This finding allows one to calculate the heat conductivity in a very large system with desirable accuracy by performing simulations in a system with much smaller size, and thus greatly broadens the application of the Green-Kubo method.

Nonintegrability and the Fourier heat conduction law

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.

Temperature dependence of heat conduction in the Fermi-Pasta-Ulam-β lattice with next-nearest-neighbor coupling

We show numerically that introducing the next-nearest-neighbor interactions (of appropriate strength) into the one-dimensional (1D) Fermi-Pasta-Ulam-β (FPU-β) lattice can result in an unusual, nonmonotonic temperature dependent divergence behavior in a wide temperature range, which is in clear contrast to the universal divergence manner independent of temperature as suggested previously in the conventional 1D FPU-β models with nearest-neighbor (NN) coupling only. We also discuss the underlying mechanism of this finding by analyzing the temperature variations of the properties of discrete breathers, especially that with frequencies having the intraband components. The results may provide useful information for establishing the connection between the macroscopic heat transport properties and the underlying dynamics in general 1D systems with interactions beyond NN couplings.

Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain

Recent work has developed a nonlinear hydrodynamic fluctuation theory for a chain of coupled anharmonic oscillators governing the conserved fields, namely, stretch, momentum, and energy. The linear theory yields two propagating sound modes and one diffusing heat mode, all three with diffusive broadening. In contrast, the nonlinear theory predicts that, at long times, the sound mode correlations satisfy Kardar-Parisi-Zhang scaling, while the heat mode correlations have Lévy-walk scaling. In the present contribution we report on molecular dynamics simulations of Fermi-Pasta-Ulam chains to compute various spatiotemporal correlation functions and compare them with the predictions of the theory. We obtain very good agreement in many cases, but also some deviations.

Cross-correlations between phonon modes in anharmonic oscillator chains: role in heat transport

We have computed current-current correlation functions in chains of anharmonic oscillators described by various models (FPU-β, FPU-αβ, ϕ4), considering both the total current and the currents associated with individual phonon modes, which are important in view of the Green-Kubo relation for heat conductivity. Our simulations show that, contrary to the common hypothesis, there are, under some circumstances, significant correlations between neighboring modes. These cross-mode correlations are the dominant contribution to the conductivity in the low anharmonicity regime. The inverse of the timescale over which they are significant, 1/τc, is related to the anharmonicity level in a way similar to the largest Lyapunov exponent, suggesting that the two quantities are related. Cross-mode correlations exist in both anomalous and regular heat-conducting systems although we are unable to observe a transition to the independent-mode regime in the latter case.