Bambi Hu

Asymmetric heat conduction in nonlinear lattices.

In this Letter, we show numerically that the rectifying effect of heat flux in a one-dimensional two-segment Frenkel-Kontorova chain demonstrated in recent literature is merely available under the limit of the weak coupling between the two constituent segments. Surprisingly, the rectifying effect will be reversed when the properties of the interface and the system size change. The two types of asymmetric heat conduction are dominated by different mechanisms, which are all induced by the nonlinearity. We further discuss the possibility of the experimental realization of thermal diode or rectifier devices.

Heat conduction in one-dimensional chains

We study numerically the thermal conductivity in several different one-dimensional chains. We show that the phonon-lattice interaction is the main ingredient of the Fourier heat law. Our argument provides a rather satisfactory explanation to all existing numerical results concerning this problem.

Suppression of thermal conductivity in graphene nanoribbons with rough edges

We analyze numerically thermal conductivity of graphene nanoribbons with perfect and rough edges. We demonstrate that edge roughness can suppress thermal conductivity by two orders of magnitude. This effect is associated with the edge-induced energy localization and suppression of the phonon transport, and it becomes more pronounced for longer nanoribbons and low temperatures.

Subwavelength plasmonic lattice solitons in arrays of metallic nanowires.

We predict theoretically that stable subwavelength plasmonic lattice solitons (PLSs) are formed in arrays of metallic nanowires embedded in a nonlinear medium. The tight confinement of the guiding modes of the metallic nanowires, combined with the strong nonlinearity induced by the enhanced field at the metal surface, provide the main physical mechanisms for balancing the wave diffraction and the formation of PLSs. As the conditions required for the formation of PLSs are satisfied in a variety of plasmonic systems, we expect these nonlinear modes to have important applications to subwavelength nanophotonics. In particular, we show that the subwavelength PLSs can be used to optically manipulate with nanometer accuracy the power flow in ultracompact photonic systems.

Introduction to real-space renormalization-group methods in critical and chaotic phenomena

Abstract The methods of the real-space renormalization group, and their application to critical and chaotic phenomena are reviewed. The article consists of two parts: the first part deals with phase transitions and critical phenomena; the second part, bifurcations and transitions to chaos. We begin with an introduction to the phenomenology of phase transitions and critical phenomena. Seminal concepts such as scaling and universality, and their characterization by critical exponents are discussed. The basic ideas of the renormalization group are then explained. A survey of real-space renormalization-group methods: decimation, Migdal-Kadanoff approximation, cumulant and cluster expansions, is given. The Hamiltonian formulation of classical statistical systems into quantum mechanical systems by the method of the transfer matrix is introduced. Quantum renormalization-group methods of truncation and projection, and their application to the transcribed quantum mechanical Ising model in a transverse field are illustrated. Finally, the quantum cumulant-expansion method as applied to the one-dimensional quantum mechanical XY model is discussed. The second part of the article is devoted to the subject of bifurcations and transitions to chaos. The three most commonly discussed kinds of bifurcations: the pitchfork, tangent and Hopf bifurcations, and the associated routes to chaos: period doubling, intermittency and quasiperiodicity are discussed. Period doubling based on the logistic map is explained in detail. Universality and its expression in terms of functional renormalization-group equations is discussed. The Liapunov characteristic exponent and its analogy to the order parameter are introduced. The effect of external noise and its universal scaling feature are shown. The simplest characterizations of the Henon strange attractor are intuitively illustrated. The purpose of this article is primarily pedagogical. The similarity between critical and chaotic phenomena is a recurrent theme that underlines the importance and usefulness of such concepts as scaling, renormalization and universality.

Finite Thermal Conductivity in 1D Models Having Zero Lyapunov Exponents

Heat conduction in three types of 1D channels is studied. The channels consist of two parallel walls, right triangles as scattering obstacles, and noninteracting particles. The triangles are placed along the walls in three different ways: (i) periodic, (ii) disordered in height, and (iii) disordered in position. The Lyapunov exponents in all three models are zero because of the flatness of triangle sides. It is found numerically that the temperature gradient can be formed in all three channels, but the Fourier heat law is observed only in two disordered ones. The results show that there might be no direct connection between chaos (in the sense of positive Lyapunov exponent) and normal thermal conduction.

Entanglement as a Signature of Quantum Chaos

We explore the dynamics of entanglement in classically chaotic systems by considering a multiqubit system that behaves collectively as a spin system obeying the dynamics of the quantum kicked top. In the classical limit, the kicked top exhibits both regular and chaotic dynamics depending on the strength of the chaoticity parameter kappa in the Hamiltonian. We show that the entanglement of the multiqubit system, considered for both the bipartite and the pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite entanglement is enhanced in the chaotic region, pairwise entanglement is suppressed. Furthermore, we define a time-averaged entangling power and show that this entangling power changes markedly as kappa moves the system from being predominantly regular to being predominantly chaotic, thus sharply identifying the edge of chaos. When this entangling power is averaged over all states, it yields a signature of global chaos. The qualitative behavior of this global entangling power is similar to that of the classical Lyapunov exponent.

Heat conduction in the Frenkel–Kontorova model

Heat conduction is an old yet important problem. Since Fourier introduced the law bearing his name almost 200 years ago, a first-principle derivation of this simple law from statistical mechanics is still lacking. Worse still, the validity of this law in low dimensions, and the necessary and sufficient conditions for its validity are far from clear. In this paper we will review recent works on heat conduction in a simple nonintegrable model called the Frenkel-Kontorova model. The thermal conductivity of this model has been found to be finite. We will study the dependence of the thermal conductivity on the temperature and other parameters of the model such as the strength and the periodicity of the external potential. We will also discuss other related problems such as phase transitions and finite-size effects. The study of heat conduction is not only of theoretical interest but also of practical interest. We will show various recent designs of thermal rectifiers and thermal diodes by coupling nonlinear chains together. The study of heat conduction in low dimensions is also important to the understanding of the thermal properties of carbon nanotubes.

Can Disorder Induce a Finite Thermal Conductivity in 1D Lattices

We study heat conduction in one-dimensional mass-disordered harmonic and anharmonic lattices. It is found that the thermal conductivity kappa of the disordered anharmonic lattice is finite at low temperature, whereas it diverges as kappa approximately N0.43 at high temperature. Moreover, we demonstrate that a unique nonequilibrium stationary state in the disordered harmonic lattice does not exist at all.

Analytical results for the steady state of traffic flow models with stochastic delay

Exact mean field equations are derived analytically to give the fundamental diagrams, i.e., the average speed-car density relations, for the Fukui-Ishibashi one-dimensional traffic flow cellular automaton model of high speed vehicles (v max5M.1) with stochastic delay. Starting with the basic equation describing the time evolution of the number of empty sites in front of each car, the concepts of intercar spacings longer and shorter than M are introduced. The probabilities of having long and short spacings on the road are calculated. For high car densities ( r>1/M), it is shown that intercar spacings longer than M will be shortened as the traffic flow evolves in time, and any initial configurations approach a steady state in which all the intercar spacings are of the short type. Similarly for low car densities ( r<1/M), it can be shown that traffic flow approaches an asymptotic steady state in which all the intercar spacings are longer than M22. The average traffic speed is then obtained analytically as a function of car density in the asymptotic steady state. The fundamental diagram so obtained is in excellent agreement with simulation data. @S1063-651X~98!04709-6#