Thermal Conductivity of the Toda Lattice with Conservative Noise

We study the thermal conductivity of the one dimensional Toda lattice perturbed by a stochastic dynamics preserving energy and momentum. The strength of the stochastic noise is controlled by a parameter γ. We show that heat transport is anomalous, and that the thermal conductivity diverges with the length n of the chain according to κ(n)∼n ^α , with 0<α≤1/2. In particular, the ballistic heat conduction of the unperturbed Toda chain is destroyed. Besides, the exponent α of the divergence depends on γ.     

Influence of heat bath on the heat conductivity in disordered anharmonic chain

We study heat conduction in a one-dimensional disordered anharmonic chain with arbitrary heat bath by using extended Ford, Kac and Mazur (FKM) formulation, which satisfy the fluctuation-dissipation theorem. A simple formal expression for the heat conductivity κ is obtained, from which the asymptotic system-size (N) dependence is extracted. It shows κ∼N^α. As a special case we give the expression that κ∼N^1/2 for free boundaries, and κ∼ N^-1/2 for fixed boundaries, from which we can get the conclusion that the momentum conservation is a key factor of the anomalous heat conduction. Comparing with different ∇T, the heat conductivity shows large difference between the linear system and the nonlinear system.     

Anomalous energy diffusion and heat conduction in one-dimensional system

We propose a new concept, the centre of energy, to study energy diffusion and heat conduction in one-dimensional hard-point model. For diatom model, we find an anomalous energy diffusion as $\langle x^2 \rangle\sim t^\beta$ with $\beta=1.33$, which is independent of initial condition and mass rate. The present model can be viewed as the model composed by independent quasi-particles, the centre of energy. In this way, heat current can be calculated. Based on theory of dynamic billiard, the divergent exponent of heat conductivity is estimated to be $\alpha=0.33$, which is confirmed by a simple numerical calculation.     

Heat transport in low-dimensional systems

Recent results on theoretical studies of heat conduction in low-dimensional systems are presented. These studies are on simple, yet non-trivial, models. Most of these are classical systems, but some quantum-mechanical work is also reported. Much of the work has been on lattice models corresponding to phononic systems, and some on hard-particle and hard-disc systems. A recently developed approach, using generalized Langevin equations and phonon Green's functions, is explained and several applications to harmonic systems are given. For interacting systems, various analytic approaches based on the Green–Kubo formula are described, and their predictions are compared with the latest results from simulation. These results indicate that for momentum-conserving systems, transport is anomalous in one and two dimensions, and the thermal conductivity κ diverges with system size L as κ ～ L ^α. For one-dimensional interacting systems there is strong numerical evidence for a universal exponent α = 1/3, but there is no exact proof for this so far. A brief discussion of some of the experiments on heat conduction in nanowires and nanotubes is also given.     

Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels

We study anomalous heat conduction and anomalous diffusion in low-dimensional systems ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels. We find that in all discussed systems, the anomalous heat conductivity can be connected with the anomalous diffusion, namely, if energy diffusion is sigma(2)(t)=2Dt(alpha) (01) implies an anomalous heat conduction with a divergent thermal conductivity (beta>0), and more interestingly, a subdiffusion (alpha<1) implies an anomalous heat conduction with a convergent thermal conductivity (beta<0), consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our theoretical prediction.     

Phonon relaxation and heat conduction in one-dimensional Fermiben Pastaben Ulam β lattices by molecular dynamics simulations

The phonon relaxation and heat conduction in one-dimensional Fermi-Pasta-Ulam (FPU) β lattices are studied by using molecular dynamics simulations. The phonon relaxation rate, which dominates the length dependence of the FPU β lattice, is first calculated from the energy autocorrelation function for different modes at various temperatures through equilibrium molecular dynamics simulations. We find that the relaxation rate as a function of wave number k is proportional to k^1.688, which leads to a N^0.41 divergence of the thermal conductivity in the framework of Green-Kubo relation. This is also in good agreement with the data obtained by non-equilibrium molecular dynamics simulations which estimate the length dependence exponent of the thermal conductivity as 0.415. Our results confirm the N^2/5 divergence in one-dimensional FPU β lattices. The effects of the heat flux on the thermal conductivity are also studied by imposing different temperature differences on the two ends of the lattices. We find that the thermal conductivity is insensitive to the heat flux under our simulation conditions. It implies that the linear response theory is applicable towards the heat conduction in one-dimensional FPU β lattices.     

Coarsening process in one-dimensional surface growth models

Surface growth models may give rise to instabilities with mound formation whose typical linear size L increases with time (coarsening process). In one dimensional systems coarsening is generally driven by an attractive interaction between domain walls or kinks. This picture applies to growth models for which the largest surface slope remains constant in time (corresponding to model B of dynamics): coarsening is known to be logarithmic in the absence of noise ( L(t) ∼ ln t) and to follow a power law ( L(t) ∼t ^1/3) when noise is present. If the surface slope increases indefinitely, the deterministic equation looks like a modified Cahn-Hilliard equation: here we study the late stages of coarsening through a linear stability analysis of the stationary periodic configurations and through a direct numerical integration. Analytical and numerical results agree with regard to the conclusion that steepening of mounds makes deterministic coarsening faster : if α is the exponent describing the steepening of the maximal slope M of mounds ( M ^α∼L) we find that L(t) ∼t ⁿ: n is equal to for 1≤α≤2 and it decreases from to for α≥2, according to n = α/(5α - 2). On the other side, the numerical solution of the corresponding stochastic equation clearly shows that in the presence of shot noise steepening of mounds makes coarsening slower than in model B: L(t) ∼t ^1/4, irrespectively of α. Finally, the presence of a symmetry breaking term is shown not to modify the coarsening law of model α = 1, both in the absence and in the presence of noise. Received 28 September 2001 and Received in final form 21 November 2001     

von Neumann entropy signatures of a transition in one-dimensional electron systems with long-range correlated disorder

We study the von Neumann entropy and related quantities in one-dimensional electron systems with on-site long-range correlated potentials. The potentials are characterized by a power-law power spectrum S(k) μ\propto 1/k ^α, where α is the correlation exponent. We find that the first-order derivative of spectrum-averaged von Neumann entropy is maximal at a certain correlation exponent α _m for a finite system, and has perfect finite-size scaling behaviors around α _m . It indicates that the first-order derivative of the spectrum-averaged von Neumann entropy has singular behavior, and α _m can be used as a signature for transition points. For the infinite system, the threshold value α _c = 1.465 is obtained by extrapolating α _m .     

A simple theory of condensation

A simple assumption of the emergence in gas of small atomic clusters consisting of c particles each leads to a phase separation (first-order transition). It reveals itself by the emergence of a “forbidden” density range starting at a certain temperature. Defining this latter value as the critical temperature predicts the existence of an interval with the anomalous heat capacity behavior c _p ∝ ΔT ^−1/c . The value c = 13 suggested in the literature yields the heat capacity exponent α = 0.077.     

Thermoelectric power in quasi-two-dimensional systems with scattering of current carriers by phonons

The thermopower α in electron systems with a quasi-two-dimensional energy spectrum is investigated in the relaxation-time tensor approximation. The longitudinal and transverse components of the thermopower are calculated for scattering of the current carriers by different types of phonons. It is shown that the anisotropy of the thermopower in such systems is substantial. The dependence of a on the ratio of the Fermi level ɛ _F to the half-width ɛ ₀ of the one-dimensional conduction band is considered. For scattering by acoustical and nonpolar optical phonons, the thermopower changes sign: α becomes positive for ɛ _F<ɛ ₀. Comparison of the theory with published experimental data demonstrates good qualitative agreement. Fiz. Tverd. Tela (St. Petersburg) 39, 1857–1858 (October 1997)     

Mean-Field Behavior for Long- and Finite Range Ising Model,Percolation and Self-Avoiding Walk

We consider self-avoiding walk, percolation and the Ising model with long and finite range. By means of the lace expansion we prove mean-field behavior for these models if d>2(α ∧2) for self-avoiding walk and the Ising model, and d>3(α ∧2) for percolation, where d denotes the dimension and α the power-law decay exponent of the coupling function. We provide a simplified analysis of the lace expansion based on the trigonometric approach in Borgs et al. (Ann. Probab. 33(5):1886–1944, 2005).      

Theory of one-dimensional and quasi-one-dimensional heat conduction

It is shown that the heat conduction process in a one-dimensional flow of a fluid moving with a velocity V in a constant temperature field follows a law that is considerably more complicated than an “ordinary” exponential law. It is demonstrated that in the quasi-one-dimensional case the heat conduction process in an abstract space of dimension 1+ɛ, where ɛ varies from zero to unity, is described by a modified Fourier equation. Its solution for an infinite space is found. Zh. Tekh. Fiz. 67, 8–12 (July 1997)     

Critical behavior of the heat capacity of the manganite La<Subscript>0.87</Subscript>K<Subscript>0.13</Subscript>MnO<Subscript>3</Subscript>

The heat capacity of the manganite La_0.87K_0.13MnO₃ has been measured in the temperature range 80–350 K. The nature of the ferromagnetic phase transition and the critical properties of heat capacity near the Curie temperature have been studied. The regularities of variations in the universal critical parameters near the phase transition point have been established. The calculated critical exponent and amplitudes of the heat capacity with allowance for corrections on the scaling (α = −0.13 and A ⁺/A ⁻ = 1.178) correspond to the critical behavior of the 3D Heizenberg model.     

Transport properties of hexanoyl chitosan-based gel electrolyte

Films of hexanoyl chitosan-based polymer electrolyte were prepared by the technique of solution casting. The effect of plasticizer on the transport properties of hexanoyl chitosan:lithium trifluoromethanesulfonate (LiCF₃SO₃) electrolytes have been investigated. The plasticizer used was ethylene carbonate (EC). The highest room temperature conductivity achieved in the EC-plasticized hexanoyl chitosan-based electrolytes is 2.75×10⁻⁵ S cm⁻¹. The Rice and Roth model was used to explain the variations in the dc conductivity observed. The exponent, s, in Jonscher’s universal power law equation σ(ω)=σ _dc+Aω ^s , was analyzed as a function of temperature for the sample containing 30 wt% of EC. The analysis suggests that the conduction mechanism follows that proposed by the overlapping large polaron tunneling model.     

Universality in diffusion front growth dynamics

We have studied the scaling properties of diffusion fronts by numerical calculations based on the mean field approach in the context of a lattice gas model, performed in a triangular lattice. We find that the height-height correlation function scales with time t and length l as C(l, t) ≈l ^α f (t/l ^α/β) with α = 0.62±0.01 and β = 0.39±0.02. These exponent values are identical to those characterising the roughness of the diffusion fronts evolving through a square lattice [1,2], thus confirming their universality. Received 14 November 2001 / Received in final form 20 April 2002 Published online 31 July 2002     

Specific heat and thermal conductivity of superionic conductors in the superionic phase

The temperature dependences of the specific heat and the thermal conductivity of crystalline superionic conductors LnF₃ (Ln = La, Ce, Pr), Li₂B₄O₇ and α-LiIO₃ in the superionic phase have been investigated experimentally. The specific heat C _p and the thermal conductivity K are observed to increase monotonically over a wide range of temperatures above the Debye temperature Θ_D. This increase is attributed to the relaxational interaction of high-frequency phonons with two-level systems. Fiz. Tverd. Tela (St. Petersburg) 39, 1548–1553 (September 1997)     

Side wall effects in Rayleigh Bénard experiments

In Rayleigh Bénard experiments, the side wall conductivity is traditionally taken into account by subtracting the empty cell heat conductivity from the measured one. We present a model showing that the correction to apply could be considerably larger. We compare to experiments and find good agreement. One of the consequences is that the Nusselt behavior for Ra < 10¹⁰ could be closer to Nu∝Ra ^1/3 than currently assumed. Also, the wall effect can appear as a continuous change in the γ exponent Nu∝Ra ^γ. Received 26 April and Received in final form 1st October 2001     

Differential thermopower of a superlattice in a strong electric field

The effect of an electric field on the differential thermopower α(E) of a one-dimensional superlattice is investigated in the semiclassical approximation. A nonmonotonic temperature dependence of α(0) is established for a degenerate electron gas. It is shown that, in principle, an electric field can be used to control the thermoelectric properties of superlattices. Fiz. Tverd. Tela (St. Petersburg) 41, 1314–1316 (July 1999)     

Material parameters for thermoelectric performance

The thermoelectric performance of a thermoelement is ideally defined in terms of the so-called figure-of-meritZ = α²σ/λ, where α,σ and λ refer respectively to the Seebeck coefficient, electrical conductivity and thermal conductivity of the thermoelement material. However, there are other parameters which are fairly good indicators of a material’s thermoelectric ‘worth’. A simple yet useful performance indicator is possible with only two parameters — energy gap and lattice thermal conductivity. This indicator can outline all potentially useful thermoelectric materials. Thermal conductivity in place of lattice thermal conductivity can provide some additional information about the temperature range of operation. Yet another performance indicator may be based on the slope of α vs. ln σ plots. α plotted against ln σ shows a linear relationship in a simplified model, but shows a variation with temperature and carrier concentration. Assuming that such a relationship is true for a narrow range of temperature and carrier concentration, one can calculate the slope m of α vs. ln σ plots against temperature and carrier concentrations. A comparison between the variation ofZT and slopem suggests that such plots may be useful to identify potential thermoelectric materials.     

Heat conductivity and the Lorentz number of the Sm1−x GdxS “black” phase

Measurement of the heat conductivity and electrical resistivity of two Sm_1−x Gd_xS compositions with x=0.1 and 0.14 is reported within the 80–300 K interval. An analysis of experimental data on the electronic component of heat conductivity permits a conclusion that the d subband of “heavy” carriers in the conduction band of these materials lies above the s “light”-carrier subband. Fiz. Tverd. Tela (St. Petersburg) 41, 26–29 (January 1999)