arXiv subjects

Nianbei Li

Publications and source records attributed to Nianbei Li.

At least 19 recordsLinked to original sources

arXiv2019

Anomalous energy diffusion in two-dimensional nonlinear lattices

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 momentum-conserving lattices is anomalous and can be well described by the Lévy-stable distribution. We also find that the disappear of side peaks of heat mode may suggest a weak coupling between heat mode and sound mode in the 2D nonlinear system. It is also observed that the harmonic interactions in the 2D nonlinear lattices can accelerate the energy diffusion. Contrary to the hypothesis of 1D system, we clarify that anomalous heat transport in the 2D momentum-conserving system cannot be corroborated by the momentum superdiffusion any more. Moreover, as is expected, lattices with a nonlinear on-site potential exhibit normal energy diffusion, independent of the dimension. Our findings offer some valuable insights into the mechanism of thermal transport in 2D system.

cond-mat.stat-mech↗

arXiv2019

Energy Super-Diffusion in One-Dimensional Momentum Non-Conserving Nonlinear Lattices

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 energy super-diffusion instead of normal diffusion can be found for this model, which indicates that neither momentum non-conservation is a sufficient condition for energy normal diffusion nor momentum conservation is a necessary condition for energy super-diffusion. Zero frequency phonon mode at Brillouin zone boundary induces a new conserved momentum parity, which is the key for the energy super-diffusion and anomalous heat conduction. Removing the zero frequency mode, such as by on-site potential, is a sufficient condition for normal heat conduction in 1D nonlinear lattices.

cond-mat.stat-mech↗

arXiv2018

Novel Two-Dimensional Silicon Dioxide with in-plane Negative Poisson's Ratio

Silicon dioxide or silica, normally existing in various bulk crystalline and amorphous forms, is recently found to possess a two-dimensional structure. In this work, we use ab initio calculation and evolutionary algorithm to unveil three new 2D silica structures whose themal, dynamical and mechanical stabilities are compared with many typical bulk silica. In particular, we find that all these three 2D silica have large in-plane negative Poisson's ratios with the largest one being double of penta-graphene and three times of borophenes. The negative Poisson's ratio originates from the interplay of lattice symmetry and Si-O tetrahedron symmetry. Slab silica is also an insulating 2D material, with the highest electronic band gap (> 7 eV) among reported 2D structures. These exotic 2D silica with in-plane negative Poisson's ratios and widest band gaps are expected to have great potential applications in nanomechanics and nanoelectronics.

cond-mat.mtrl-sci↗

arXiv2017

Thermal conductance of the coupled-rotator chain: Influence of temperature and size

Thermal conductance of a homogeneous 1D nonlinear lattice system with neareast neighbor interactions has recently been computationally studied in detail by Li et al [Eur. Phys. J. B {\bf 88}, 182 (2015)], where its power-law dependence on temperature $T$ for high temperatures is shown. Here, we address its entire temperature dependence, in addition to its dependence on the size $N$ of the system. We obtain a neat data collapse for arbitrary temperatures and system sizes, and numerically show that the thermal conductance curve is quite satisfactorily described by a fat-tailed $q$-Gaussian dependence on $TN^{1/3}$ with $q \simeq 1.55$. Consequently, its $T \to\infty$ asymptotic behavior is given by $T^{-α}$ with $α=2/(q-1) \simeq 3.64$.

cond-mat.stat-mech↗

arXiv2016

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.

cond-mat.stat-mech↗

arXiv2015

Temperature and Frequency Dependent Mean Free Paths of Renormalized Phonons in Nonlinear Lattices

In the regime of strong nonlinearity, the validity of conventional perturbation based phonon transport theories is questionable. In particular, the renormalized phonons instead of phonons are responsible for heat transport in nonlinear lattices. In this work, we directly study the temperature and frequency dependent Mean Free Path (MFP) of renormalized phonons with the newly developed numerical tuning fork method. The typical 1D nonlinear lattices such as Fermi-Pasta-Ulam $β$ (FPU-$β$) lattice and $ϕ^4$ lattice are investigated in details. It is found that the MFPs are inversely proportional to the frequencies of renormalized phonons rather than the square of phonon frequencies predicted by existing phonon scattering theory.

cond-mat.stat-mech↗

arXiv2015

Heat conduction and energy diffusion in momentum-conserving 1D 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 {\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 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.

cond-mat.stat-mech↗

arXiv2015

Stretch diffusion and heat conduction in 1D nonlinear lattices

In the study of 1D nonlinear Hamiltonian lattices, the conserved quantities play an important role in determining the actual behavior of heat conduction. Besides the total energy, total momentum and total stretch could also be conserved quantities. In microcanonical Hamiltonian dynamics, the total energy is always conserved. It was recently argued by Das and Dhar that whenever stretch (momentum) is not conserved in a 1D model, the momentum (stretch) and energy fields exhibit normal diffusion. In this work, we will systematically investigate the stretch diffusions for typical 1D nonlinear lattices. No clear connection between the conserved quantities and heat conduction can be established. The actual situation is more complicated than what Das and Dhar claimed.

cond-mat.stat-mech↗

arXiv2015

1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport

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 correlation of the total momentum flux. This result in turn relates, via the integrated momentum flux correlation, to an effective viscosity, or equivalently, to the underlying momentum diffusivity. We put forward the intriguing hypothesis that a fluid-like momentum dynamics with a {\it finite viscosity} causes {\it normal} heat transport; its corollary being that superdiffusive momentum diffusion with an intrinsic {\it diverging viscosity} in turn yields {\it anomalous} heat transport. This very hypothesis is corroborated over wide extended time scales by use of precise molecular dynamics simulations. The numerical validation of the hypothesis involves three distinct archetype classes of nonlinear pair-interaction potentials: (i) a globally bounded pair interaction (the noted rotator model), (ii) unbounded interactions acting at large distances (the Fermi-Pasta-Ulam $β$ model, or the rotator model amended with harmonic pair interactions) and (iii), a pair interaction potential being unbounded at short distances while displaying an asymptotic free part (Lennard-Jones model).

cond-mat.stat-mech↗

arXiv2015

Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map

In contrary to other 1D momentum-conserving lattices such as the Fermi-Pasta-Ulam $β$ (FPU-$β$) lattice, the 1D coupled rotator lattice is a notable exception which conserves total momentum while exhibits normal heat conduction behavior. The temperature behavior of the thermal conductivities of 1D coupled rotator lattice had been studied in previous works trying to reveal the underlying physical mechanism for normal heat conduction. However, two different temperature behaviors of thermal conductivities have been claimed for the same coupled rotator lattice. These different temperature behaviors also intrigue the debate whether there is a phase transition of thermal conductivities as the function of temperature. In this work, we will revisit the temperature dependent thermal conductivities for the 1D coupled rotator lattice. We find that the temperature dependence follows a power law behavior which is different with the previously found temperature behaviors. Our results also support the claim that there is no phase transition for 1D coupled rotator lattice. We also give some discussion about the similarity of diffusion behaviors between the 1D coupled rotator lattice and the single kicked rotator also called the Chirikov standard map.

cond-mat.stat-mech↗

arXiv2015

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 to 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 beyond the scope of existing theories, including those having the symmetric potential and pressure, and those having the asymmetric potential with or without pressure, we also obtain accurate sound velocity.

cond-mat.stat-mech↗

arXiv2014

Temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential

The temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential (soft-KG) have been investigated systematically. Similar to the previously studied hard-KG lattices, the existence of renormalized phonons has also been confirmed in soft-KG lattices. In particular, the temperature-dependence of renormalized phonon frequency predicted by a classical field theory has been verified by detailed numerical simulations. However, the thermal conductivities of soft-KG lattices exhibit opposite trend in the temperature dependence in comparison with the hard-KG lattices. The interesting thing is that both the temperature-dependent thermal conductivities of soft- and hard-KG lattices can be interpreted in the same framework of effective phonon theory. According to the effective phonon theory, the exponents of the power-law dependence of the thermal conductivities as the function of temperature are only determined by the exponents of the soft or hard on-site potentials. These theoretical predictions have been consistently verified very well by extensive numerical simulations.

cond-mat.stat-mech↗

arXiv2014

An Electrohydrodynamics Model for Non-equilibrium Electron and Phonon Transport in Metal Films after Ultra-short Pulse Laser Heating

The electrons and phonons in metal films after ultra-short pulse laser heating are in highly non-equilibrium states not only between the electron sub-system and the phonon sub-system but also within the electron sub-system. An electrohydrodynamics model consisting of the balance equations of electron density, energy density of electrons, and energy density of phonons is derived from the coupled non-equilibrium electron and phonon Boltzmann transport equations to study the nonlinear transport phenomena, such as the electron density fluctuation and the transient electrical current in metal films, after ultra-short pulse laser heating. The time-dependent temperature distributions is calculated by the coupled electron and phonon Boltzmann transport equations, the electrohydrodynamics model derived in this work, and the two-temperature model for different laser pulse durations, film thicknesses, and laser fluences. We find that the two-temperature model overestimates the electron temperature at the frontsurface of the film and underestimates the damage threshold when the nonlinear thermal transport of electrons is important. The electrohydrodynamics model proposedin this work could be a more accurate prediction tool to study the non-equilibrium electron phonon transport process than the two-temperature model and it is much easier to be solved than the coupled electron and phonon Boltzmann transport equations.

cond-mat.mtrl-sci↗

arXiv2014

Inhomogeneous Thermal Conductivity Enhances Thermoelectric Cooling

We theoretically investigate the enhancement of thermoelectric cooling performance in thermoelectric devices made of materials with inhomogeneous thermal conductivity, beyond the usual practice of enhancing thermoelectric figure of merit ZT. The dissipation of Joule heat in such thermoelectric devices is asymmetric which can give rise to better thermoelectric cooling performance. Although the thermoelectric figure of merit and the coefficient-of-performance are only slightly enhanced, both the maximum cooling power and the maximum cooling temperature difference can be enhanced significantly. This finding can be used to increase the heat absorption at the cold end. The asymmetric dissipation of Joule heat also leads to thermal rectification.

cond-mat.mes-hall↗

arXiv2014

Non-Reciprocal Geometric Wave Diode by Engineering Asymmetric Shapes of Nonlinear Materials

Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear materials to realize the function of non-reciprocal wave propagations. We first show analytical results revealing that both nonlinearity and asymmetry are necessary to induce such non-reciprocal (asymmetric) wave propagations. Detailed numerical simulations are further performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect is demonstrated. Finally, we discuss the scalability of geometric wave diodes. The results open a flexible way for designing wave diodes efficiently simply through shape engineering of nonlinear materials, which may find broad implications in controlling energy, mass and information transports.

cond-mat.mes-hall↗

arXiv2014

Anomalous Heat Diffusion

Consider anomalous energy spread in solid phases, i.e., $MSD= \int (x -{\langle x \rangle}_E)^2 ρ_E(x,t)dx \propto t^β$, as induced by a small initial excess energy perturbation distribution $ρ_{E}(x,t=0)$ away from equilibrium. The associated total thermal equilibrium heat flux autocorrelation function $C_{JJ}(t)$ is shown to obey rigorously the intriguing relation, $d^2 MSD/dt^2 = 2C_{JJ}(t)/(k_BT^2c)$, where $c$ is the specific volumetric heat capacity. Its integral assumes a time-local Helfand-moment relation; i.e. $ dMSD/dt|_{t=t_s} = 2/(k_BT^2c)\int_0^{t_s} C_{JJ}(s)ds$, where the chosen cut-off time $t_s$ is determined by the maximal signal velocity for heat transfer. Given the premise that the averaged nonequilibrium heat flux is governed by an anomalous heat conductivity, energy diffusion scaling determines a corresponding anomalous thermal conductivity scaling behaviour.

cond-mat.stat-mech↗

arXiv2013

Appearance of Mobility Edge in Self-Dual Quasiperiodic Lattices

Within the framework of the Aubry-Andre model, one kind of self-dual quasiperiodic lattice, it is known that a sharp transition occurs from \emph{all} eigenstates being extended to \emph{all} being localized. The common perception for this type of quasiperiodic lattice is that the self-duality excludes the appearance of the mobility edge separating localized from extended states. In this work, we propose a multi-chromatic quasiperiodic lattice model retaining the self-duality identical to the Aubry-Andre model, and demonstrate numerically the occurrence of the localization-delocalization transition with definite mobility edges. This contrasts with the Aubry-Andre model. As a result, the diffusion of wave packet exhibits a transition from ballistic to diffusive motion, and back to ballistic motion. We point out that experimental realizations of the predicted transition can be accessed with light waves in photonic lattices and matter waves in optical lattices.

cond-mat.dis-nn↗

arXiv2012

Thermal conductivities of one-dimensional anharmonic/nonlinear lattices: renormalized phonons and effective phonon theory

Heat transport in low-dimensional systems has attracted enormous attention from both theoretical and experimental aspects due to its significance to the perception of fundamental energy transport theory and its potential applications in the emerging filed of phononics: manipulating heat flow with electronic anologs. We consider the heat conduction of one-dimensional nonlinear lattice models. The energy carriers responsible for the heat transport have been identified as the renormalized phonons. Within the framework of renormalized phonons, a phenomenological theory, effective phonon theory, has been developed to explain the heat transport in general one-dimensional nonlinear lattices. With the help of numerical simulations, it has been verified that this effective phonon theory is able to predict the scaling exponents of temperature-dependent thermal conductivities quantitatively and consistently.

nlin.CD↗