We here numerically investigate the heat transport behavior in a one-dimensional lattice with a soft-type (ST) anharmonic interparticle interaction. It is found that with the increase of system's temperature, while the introduction of ST anharmonicity softens phonons and decreases their velocities, this type of nonlinearity like its counterpart of hard type (HT), can still not be able to fully damp the longest wave phonons. Therefore, an anomalous temperature dependent heat transport with certain scaling properties similarly to those in the Fermi-Pasta-Ulam like systems with HT interactions can be seen. Our detailed examination from simulations well verify this temperature dependent behavior.
We have numerically studied heat conduction in a few one-dimensional momentum-conserving lattices with asymmetric interparticle interactions by the nonequilibrium heat bath method, the equilibrium Green-Kubo method, and the heat current power spectra analysis. Very strong finite-size effects are clearly observed. Such effects make the heat conduction obey a Fourier-like law in a wide range of lattice lengths. However, in yet longer lattice lengths, the heat conductivity regains its power-law divergence. Therefore the power-law divergence of the heat conductivity in the thermodynamic limit is v…
We study by means of numerical simulations the velocity reversal model, a one-dimensional mechanical model of heat transport introduced in 1985 by Ianiro and Lebowitz. Our numerical results indicate that this model, although it does not conserve momentum, exhibits an anomalous Fourier's law similar to the ones previously observed in momentum-conserving models. This is contrary to what is obtained from the solution of the Boltzmann equation (BE) for this system. The pair correlation velocity field also looks very different from the correlations usually seen in diffusive systems, and shares some…
We study the thermal conduction behaviors of one-dimensional lattice models with asymmetry harmonic interparticle interactions in this paper. Normal thermal conductivity independent of the system size is observed when the lattice chains are long enough. Because only the harmonic interactions are involved, the result confirms without ambiguous interpretation that the asymmetry plays key role in resulting in the normal thermal conduction in one-dimensional momentum conserving lattices. Both equilibrium and nonequilibrium simulations are performed to support the conclusion.
We show that the asymmetric inter-particle interactions may induce rapid decay of heat current autocorrelation in one-dimensional momentum conserving lattices. When the asymmetry degree and the temperature are appropriate, the decay is sufficient rapid for resulting a convergence conductivity practically. To understand the underlying mechanism, we further studied the relaxation behavior of the hydrodynamic modes. It is shown that for lattice with symmetric potential, the heat mode relaxs in the superdiffusive manner, while in the case of asymmetric potential, the heat mode may relax in the nor…
The heat conduction behavior of one dimensional momentum conserving lattice systems with asymmetric interparticle interactions is numerically investigated. It is found that with certain degree of interaction asymmetry, the heat conductivity measured in nonequilibrium stationary states converges in the thermodynamical limit, in clear contrast to the well accepted viewpoint that Fourier's law is generally violated in low dimensional momentum conserving systems. It suggests in nonequilibrium stationary states the mass gradient resulted from the asymmetric interactions may provide an additional ph…
Transport and diffusion of heat in one dimensional (1D) nonlinear systems which {\it conserve momentum} is typically thought to proceed anomalously. Notable exceptions, however, exist of which the rotator model is a prominent case. Therefore, the quest arises to identify the origin of manifest anomalous transport in those low dimensional systems. Here, we develop the theory for both, momentum/heat diffusion and its corresponding momentum/heat transport. We demonstrate that the second temporal derivative of the mean squared deviation of the momentum spread is proportional to the equilibrium cor…
Heat transport in one-dimensional (1D) momentum-conserving lattices is generally assumed to be anomalous, thus yielding a power-law divergence of thermal conductivity with system length. However, whether heat transport in two-dimensional (2D) system is anomalous or not is still on debate because of the difficulties involved in experimental measurements or due to the insufficiently large simulation size. Here, we simulate energy and momentum diffusion in the 2D nonlinear lattices using the method of fluctuation correlation functions. Our simulations confirm that energy diffusion in the 2D momen…
There is a well-known mapping between energy normal (super-) diffusion and normal (anomalous) heat conduction in one-dimensional (1D) nonlinear lattices. The momentum conserving nonlinear lattices exhibit energy super-diffusion behavior with the only exception of coupled rotator model. Yet, for all other 1D momentum nonconserving nonlinear lattices studied so far, the energy diffusion or heat conduction is normal. Here we propose a 1D nonlinear lattice model with negative couplings, which is momentum non-conserving due to the translational symmetry breaking. Our numerical results show that ene…
We present a theory for the coagulation reaction A+A -> A for particles moving subdiffusively in one dimension. Our theory is tested against numerical simulations of the concentration of $A$ particles as a function of time (``anomalous kinetics'') and of the interparticle distribution function as a function of interparticle distance and time. We find that the theory captures the correct behavior asymptotically and also at early times, and that it does so whether the particles are nearly diffusive or very subdiffusive. We find that, as in the normal diffusion problem, an interparticle gap respo…
A competitive (2+1)-dimensional model of deposit formation, based on the combination of random sequential absorption deposition (RSAD), ballistic deposition (BD) and random deposition (RD) models, is proposed. This model was named as RSAD$_{1-s}$(RD$_f$BD$_{1-f}$)$_s$. It allows to consider different cases of interparticle interactions from complete repulsion between near-neighbors in the RSAD model ($s=0$) to sticking interactions in the BD model ($s=1, f=0$) or absence of interactions in the RD model ($s=1$, $f=0$). The ideal checkerboard ordered structure was observed for the pure RSAD mode…
Anomalous large thermal conductivity has been observed numerically and experimentally in one and two dimensional systems. All explicitly solvable microscopic models proposed to date did not explain this phenomenon and there is an open debate about the role of conservation of momentum. We introduce a model whose thermal conductivity diverges in dimension 1 and 2 if momentum is conserved, while it remains finite in dimension $d\ge 3$. We consider a system of harmonic oscillators perturbed by a non-linear stochastic dynamics conserving momentum and energy. We compute explicitly the time correlati…
We introduce a class of one dimensional deterministic models of energy-volume conserving interfaces. Numerical simulations show that these dynamics are genuinely super-diffusive. We then modify the dynamics by adding a conservative stochastic noise so that it becomes ergodic. System of conservation laws are derived as hydrodynamic limits of the modified dynamics. Numerical evidence shows these models are still super-diffusive. This is proven rigorously for harmonic potentials.
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 {\it 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 mod…
We provide molecular dynamics simulation of heat transport in one-dimensional molecular chains with different interparticle pair potentials. We show that the thermal conductivity is finite in the thermodynamic limit in the chains with the potential, which allows for bond dissociation. The Lennard-Jones, Morse and Coulomb potentials belong to such type of potentials. The convergence of the thermal conductivity is provided by phonon scattering on the locally stretched loose interatomic bonds at low temperature and by the many-particle scattering at high temperature. On the other hand, the chains…
Momentum-conserving one-dimensional models are known to exhibit anomalous Fourier's law, with a thermal conductivity varying as a power law of the system size. Here we measure, by numerical simulations, several cumulants of the heat flux of a one-dimensional hard particle gas. We find that the cumulants, like the conductivity, vary as power laws of the system size. Our results also indicate that cumulants higher than the second follow different power laws when one compares the ring geometry at equilibrium and the linear case in contact with two heat baths (at equal or unequal temperatures). ke…
Anomalous transport in one dimensional translation invariant Hamiltonian systems with short range interactions, is shown to belong in general to the KPZ universality class. Exact asymptotic forms for density-density and current-current time correlation functions and their Fourier transforms are given in terms of the Prähofer-Spohn scaling functions, obtained from their exact solution for the Polynuclear growth model. The exponents of corrections to scaling are found as well, but not so the coefficients. Mode coupling theories developed previously are found to be adequate for weakly nonlinear c…
Dynamic renormalization group (RG) of fluctuating viscoelastic equations is investigated to clarify the cause for numerically reported disappearance of anomalous heat conduction (recovery of Fourier's law) in low-dimensional momentum-conserving systems. RG flow is obtained explicitly for simplified two model cases: a one-dimensional continuous medium under low pressure and incompressible viscoelastic medium of arbitrary dimensions. Analyses of these clarify that the inviscid fixed point of contributing the anomalous heat conduction becomes unstable under the RG flow of nonzero elastic-wave spe…
We study the heat current autocorrelation function (HCAF) in one-dimensional, momentum-conserving lattices. In particular, we explore if there is any relation between the decaying characteristics of the HCAF and asymmetric interparticle interactions. The Lennard-Jones model is intensively investigated in view of its significance to applications. It is found that in wide ranges of parameters, the HCAF decays faster than power-law manners, and in some cases it decays even exponentially. Following the Green-Kubo formula, the fast decay of HCAF implies the convergence of heat conductivity, which i…
Atypical eigenstates in the form of quantum scars and fragmentation of Hilbert space due to conservation laws provide obstructions to thermalization in the absence of disorder. In certain models with dipole and $U(1)$ conservation, the fragmentation results in subdiffusive transport. In this paper we study the interplay between scarring and weak fragmentation giving rise to anomalous hydrodynamics in a class of one-dimensional spin-$1$ frustration-free projector Hamiltonians, known as deformed Motzkin chain. The ground states and low-lying excitations of these chains exhibit large entanglement…
A system with Bose-Einstein condensate is considered in the frame of the self-consistent mean-field approximation, which is conserving, gapless, and applicable for arbitrary interaction strengths and temperatures. The main attention is paid to the thorough analysis of the condensate and superfluid fractions in a wide region of interaction strengths and for all temperatures between zero and the critical point T_c. The normal and anomalous averages are shown to be of the same order for almost all interactions and temperatures, except the close vicinity of T_c. But even in the vicinity of the cri…
Since the discovery of long-time tails, it has been clear that Fourier's law in low dimensions is typically anomalous, with a size-dependent heat conductivity, though the nature of the anomaly remains puzzling. The conventional wisdom, supported by renormalization-group arguments and mode-coupling approximations within fluctuating hydrodynamics, is that the anomaly is universal in 1d momentum-conserving systems and belongs in the Levy/Kardar-Parisi-Zhang universality class. Here we challenge this picture by using a novel scaling method to show unambiguously that universality breaks down in the…
We present analytical model and molecular dynamics simulations of phonon heat transport in nanowires and nanoribbons with anharmonic lattices and dynamically rough surfaces and edges. In agreement with recent experiments on heat transport in single-crystalline silicon nanowires with rough surfaces, our model and simulations predict finite and length-independent phonon thermal conductivity in such quasi-one-dimensional systems, in contrast to anomalous phonon thermal conductivity of corresponding momentum-conserving systems with atomically smooth surfaces, divergent with the system length. With…
Anomalous diffusion and singular transport from hydrodynamic recoupling
Laboratoire de Physique de l’École Normale Supérieure, CNRS, ENS & Université PSL（巴黎高等师范学院物理实验室，法国国家科学研究中心，巴黎高等师范学院及巴黎文理研究大学）；Department of Electrical and Computer Engineering, Princeton University（普林斯顿大学电气与计算机工程系）；Department of Theoretical Physics, University of Geneva（日内瓦大学理论物理系）；Geneva Quantum Center, University of Geneva（日内瓦大学日内瓦量子中心）
We study the static and dynamic behavior of the one dimensional pair contact process with diffusion. Several critical exponents are found to vary with the diffusion rate, while the order-parameter moment ratio m=\bar{rho^2} /\bar{rho}^2 grows logarithmically with the system size. The anomalous behavior of m is traced to a violation of scaling in the order parameter probability density, which in turn reflects the presence of two distinct sectors, one purely diffusive, the other reactive, within the active phase. Studies restricted to the reactive sector yield precise estimates for exponents bet…
