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.     

Thermal conductivity of high-porosity biocarbon preforms of beech wood

This paper reports on measurements performed in the temperature range 5–300 K for the thermal conductivity κ and electrical resistivity ρ of high-porosity (cellular pores) biocarbon preforms prepared by pyrolysis (carbonization) of beech wood in an argon flow at carbonization temperatures of 1000 and 2400°C. X-ray structure analysis of the samples has been performed at 300 K. The samples have revealed the presence of nanocrystallites making up the carbon matrices of these biocarbon preforms. Their size has been determined. For samples prepared at T _carb = 1000 and 2400°C, the nanocrystallite sizes are found to be in the ranges 12–25 and 28–60 κ(T) are determined for the samples cut along and across the tree growth direction. The thermal conductivity κ increases with increasing carbonization temperature and nanocrystallite size in the carbon matrix of the sample. Thermal conductivity measurements conducted on samples of both types have revealed an unusual temperature dependence of the phonon thermal conductivity for amorphous materials. As the temperature increases from 5 to 300 K, it first increases in proportion to T, to transfer subsequently to ∼T ^1.5 scaling. The results obtained are analyzed.     

Low-temperature thermal conductivity of highly enriched and natural germanium

Experimental data on the thermal conductivity K(T) of crystals of natural and highly enriched germanium (99.99%) ⁷⁰Ge with lapped and polished surfaces are analyzed in the temperature range ∼1.5–8 K. In all the samples in the temperature range ∼1.5–4 K the standard boundary mechanism of scattering dominates. As the temperature is raised, an isotopic scattering mechanism is observed in the natural samples. In the highly enriched samples the theoretical values of K(T) turn out to be much smaller than the experimental ones. It is conjectured that a Poiseuille viscous flow regime of the phonon gas emerges in this case. Zh. éksp. Teor. Fiz. 114, 1757–1764 (November 1998)     

Fluctuation-induced pseudogap in high-temperature superconductors

We study the effect of fluctuations on the ac conductivity of a layered superconductor for c-axis electromagnetic wave polarization. The fluctuation contributions of different physical nature and sign (paraconductivity, Maki-Thompson anomalous contribution, one-electron density-of-states renormalization) are found to be suppressed by the external field at different characteristic frequencies (ω _AL∼T-T _c , ω _MT∼max{T-T _c ,τ _ϕ ⁻¹ }, ω _DOS∼min{T, τ ⁻¹}). As a result, the appearance of a nonmonotonic frequency dependence (pseudogap) in the infrared optical conductivity of high-temperature superconductor is predicted. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 6, 397–401 (25 September 1996) Department of Theoretical Physics Moscow Institute of Steel and Alloys. Published in English in the original Russian journal. Edited by Steve Torstveit.     

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001     

Logarithmic temperature dependence of the conductivity of the two-dimensional metal

We report on the first observation and studies of a weak delocalizing logarithmic temperature dependence of the conductivity, which causes the conductivity of the 2D metal to increase as T decreases down to 16 mK. The prefactor of the logarithmic dependence is found to decrease gradually with density, to vanish at a critical density n _c , 2∼2×10¹² cm⁻², and then to have the opposite sign at n>n _c ,2. The second critical density sets the upper limit on the existence region of the 2D metal, whereas the conductivity at the critical point, G _c ,2∼120e ²/h, sets an upper (low-temperature) limit on its conductivity. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 497–501 (25 September 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Thermopower in quasi-two-dimensional (BEDT-TTF) m X n organic conductors

Thermopower of (BEDT-TTF) _m X _n organic conductors has been studied using a dedicated measurement technique in the temperature range of 4.2 to 300 K. It turned out that some features of the thermopower in quasi-two-dimensional metals, namely the presence of a peak in the thermopower of α-(BEDT-TTF)₂MHg(SCN)₄ and a plateau in κ-(BEDT-TTF)₂Cu(NCS)₂ in the temperature interval between 10 and 50 K, are probably due to the phonon drag effect. Similar temperature dependences of the Seebeck coefficient can be satisfactorily interpreted in terms of a simple model taking into account the real experimental curve of the phonon heat capacity versus temperature, C ∝ T ², which is not described by the Debye formula. One feature distinguishing organic superconductors from magnetically ordered metals is a stronger temperature dependence of the characteristic electron-phonon scattering time τ _e-ph(T). Phonon drag effects also determine the behavior of the thermopower in the (BEDT-TTF)₃Cl₂·2H₂O organic conductor, which is characterized by a metal-insulator transition at T∼150 K. An analysis of measurements of the conductivity and thermopower vs. temperature taken together indicates that the transition in this compound has a complex nature: first (at T∼150 K) a metal-insulator transition occurs, which produces an energy gap in the band spectrum, then at a lower temperature (T∼20 K) a transition to a charge-density wave state takes place. Zh. éksp. Teor. Fiz. 113, 323–338 (January 1998)     

Temperature dependence of electric resistance and magnetoresistance of pressed nanocomposites of multilayer nanotubes with the structure of nested cones

Bulk samples of carbon multilayer nanotubes with the structure of nested cones (fishbone structure) suitable for transport measurements, were prepared by compressing under high pressure (∼25 kbar) a nanotube precursor synthesized through thermal decomposition of polyethylene catalyzed by nickel. The structure of the initial nanotube material was studied using high-resolution transmission electron microscopy. In the low-temperature range (4.2–100 K) the electric resistance of the samples changes according to the law ln R ∝ (T ₀/T)^1/3, where T ₀∼7 K. The measured magnetoresistance is quadratic in the magnetic field and linear in the reciprocal temperature. The measurements have been interpreted in terms of two-dimensional variable-range hopping conductivity. It is suggested that the space between the inside and outside walls of nanotubes acts as a two-dimensional conducting medium. Estimates suggest a high value of the density of electron states at the Fermi level of about 5×10²¹ eV⁻¹ cm⁻³. Zh. éksp. Teor. Fiz. 113, 2221–2228 (June 1998)     

The effect of temperature on the pulsed conductivity of a KCl crystal excited by picosecond electron pulses

This paper discusses the temperature dependence of the pulsed conductivity of a KCl crystal in the interval 12–300K when it is excited by an electron beam (0.2 MeV, 50 ps, 300A/cm²) with a time resolution of 150 ps. It is shown that the electron lifetime is τ<100 ps in the entire interval under consideration, while the conductivity increases with temperature. The experimental results make it possible to obtain the temperature dependences of the effective electron-hole recombination cross section S∼T ^3.5 and the separation probability of genetic pairs. Fiz. Tverd. Tela (St. Petersburg) 41, 429–430 (March 1999)     

Thermally activated conductivity and current-voltage characteristic of dielectric phase in granular metals

Models of thermally activated linear and high-field nonlinear conductivity of a dielectric phase in granular metals (nanocomposites), i.e., aggregates of small metallic grains in a dielectric matrix, have been suggested. Given a sufficiently large spread of grain sizes, the temperature dependence of the nanocomposite conductivity should be described by a universal “power-1/2” law: G∝exp[−(T ₀/T)^1/2]. An analytical expression for T ₀ has been obtained. It is found that there are two regimes of nonlinear conductivity in a high electric field, namely, a low-field regime, when both the number and mobility of carriers change with the field strength, and a high-field regime, when only the mobility of carriers is variable. Analytical expressions for the nonlinear conductance in both regimes have been obtained. Zh. éksp. Teor. Fiz. 115, 1484–1496 (April 1999)     

On the effective Debye temperatures of the C60 fullerite

The effective Debye temperatures Θ_eff determined for solids by different physical methods have been analyzed and compared. Attention has been focused on the original parameter of the Debye theory of heat capacity, i.e., the translational calorimetric Debye temperature Θ _c ^t (0), and the X-ray Debye temperature Θ _x in the framework of the Debye-Waller theory for the C₆₀ fullerite. It has been established that the true Debye law T ³ is satisfied for the C₆₀ fullerite over a very narrow range of temperatures: 0.4 K ≤ T ≤ 1.8 K. For this reason, the experimental Debye temperatures Θ _c ^t (0) obtained for the C₆₀ fullerite by different authors in the range T > 4.2 K are characterized by a large scatter (by a factor of ∼5). It has been revealed that the value Θ _c ^t (0) = 77.12 K calculated in this paper with the use of the six-term Betts formula from the harmonic elastic constants $ \tilde C_{ijkl} $ \tilde C_{ijkl} of the C₆₀ single crystal in the limit T = 0 K is closest to the true Debye temperature. It has been demonstrated using the method of equivalent moments that the real spectral frequency distribution of translational lattice vibrations g(ω) for the C₆₀ fullerite deviates from a parabolic distribution. The effective Debye temperatures Θ_eff involved in applied problems of thermodynamics of crystals and elastic scattering of different radiations from lattice vibrations have been determined. The quantitative measure of anharmonicity of translational and librational lattice vibrations of the C₆₀ fullerite has been determined. This has made it possible to empirically evaluate the lattice thermal conductivity κ of the C₆₀ fullerite at T ≈ 300 K: κ(300) = 0.80 W (m/K), which is in good agreement with the experimental thermal conductivity κ_exp = 0.78 W (m/K) at T ≈ 250 K.     

Differential approximation for Kelvin wave turbulence

I present a nonlinear differential equation model (DAM) for the spectrum of Kelvin waves on a thin vortex filament. This model preserves the original scaling of the six-wave kinetic equation, its direct and inverse cascade solutions, as well as the thermodynamic equilibrium spectra. Further, I extend DAM to include the effect of sound radiation by Kelvin waves. I show that, because of the phonon radiation, the turbulence spectrum ends at a maximum frequency of ω* ∼ (ε³ c _s ²⁰ /κ¹⁶)^1/13, where ε is the total energy injection rate, c _s is the speed of sound, and κ is the quantum of circulation. The text was submitted by the author in English.     

Relation between vortex excitation and thermal conductivity in superconductors

Thermal conductivity κ _xx(T) under a field is investigated in d _{x2 - y2}-wave superconductors and isotropic s-wave superconductors by the linear response theory, using a microscopic wave function of the vortex lattice states. To study the origin of the different field dependence of κ_xx(T) between higher and lower temperature regions, we analyze the spatially-resolved thermal conductivity around a vortex at each temperature, which is related to the spectrum of the local density of states. We also discuss the electric conductivity in the same formulation for a comparison. Received 8 December 2001 and Received in final form 20 March 2002 Published online 6 June 2002     

Thermal conductivity of crystalline fullerite C60 in the simple cubic phase

The behavior of the thermal conductivity k(T) of bulk faceted fullerite C₆₀ crystals is investigated at temperatures T=8–220 K. The samples are prepared by the gas-transport method from pure C₆₀, containing less than 0.01% impurities. It is found that as the temperature decreases, the thermal conductivity of the crystal increases, reaches a maximum at T=15–20 K, and drops by a factor of ∼2, proportional to the change in the specific heat, on cooling to 8 K. The effective phonon mean free path λ _p, estimated from the thermal conductivity and known from the published values of the specific heat of fullerite, is comparable to the lattice constant of the crystal λ _p∼d=1.4 nm at temperatures T>200 K and reaches values λ_p∼50d at T<15 K, i.e., the maximum phonon ranges are limited by scattering on defects in the volume of the sample in the simple cubic phase. In the range T=25−75 K the observed temperature dependence k(T) can be described by the expression k(T)∼exp(Θ/bT), characteristic for the behavior of the thermal conductivity of perfect nonconducting crystals at temperatures below the Debye temperature Θ (Θ=80 K in fullerite), where umklapp phonon-phonon scattering processes predominate in the volume of the sample. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 651–656 (25 April 1997)     

Characteristic features of the low-temperature thermal conductivity of highly-enriched and natural germanium

Experimental data on the thermal conductivity K(T) of natural and highly enriched (99.99%) Ge⁷⁰ crystals with ground and polished surfaces are analyzed in the temperature interval ∼2–8 K. In all samples, the boundary scattering mechanism predominates in the interval from 2 to 4.0 K. As temperature increases, in highly enriched samples N processes start to contribute to phonon transport and the behavior of K(T) corresponds to viscous Poiseuille flow of a phonon gas. The isotopic scattering mechanism plays a large role in isotopically nonideal samples. Fiz. Tverd. Tela (St. Petersburg) 40, 1604–1607 (September 1998)     

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.     

Dynamic fluctuation phenomena in double membrane films

Dynamics of double membrane films is investigated in the long-wavelength limit qh≪1 (q is the wave vector, and h is the thickness of the film) including the overdamped squeezing mode. We demonstrate that thermal fluctuations essentially modify the character of the mode due to its nonlinear coupling to the transverse shear hydrodynamic mode. The renormalization can be analyzed if the condition g≪1 is satisfied (where g∼T/κ, T is the temperature, and κ is the bending modulus). The corresponding Green’s function acquires as a function of the frequency ω a cut along the imaginary semiaxis. At the effective length of the cut is ∼Tq ³/η (where η is the shear viscosity of the liquid). At the fluctuations lead to an increase in the attenuation of the squeezing mode: it is larger than the ‘bare’ value by a factor . We also present the analysis of the elastic modes. Zh. éksp. Teor. Fiz. 113, 2096–2108 (June 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Heat conductivity of a nonlinear β-FPU lattice

In this work, we propose a new approach to the computation of heat conductivity in nonlinear systems. The total heat conductivity process is decomposed into two parts: one part is an equilibrium process at the same temperature T of either end of the lattice, which does not transfer energy and the other is a nonequilibrium process at temperature ΔT of one end and a zero temperature of the opposite end of the lattice. This approach makes it possible to somewhat reduce the time of computation of heat conductivity at ΔT → 0. The threshold temperature T _thr is found to behave as T _thr ∼ N ⁻³, where N is the lattice length. The threshold temperature conventionally separates two mechanisms of heat conductivity: at T < T _thr, phonon heat conductivity is dominant; at T > T _thr, the contribution of soliton heat conductivity increases with increasing temperature. The problem of the computation of heat conductivity in the limit ΔT → 0 reduces to the heat conductivity of a harmonic lattice with time-dependent bond rigidities determined by an equilibrium process at temperature T. An exact expression for the temperature dependence of sound velocity in a lattice with a β-FPU potential at T < 10 is derived. A numerical experiment confirmed the existence of solitons and breathers that correspond to a modified Korteweg-de Vries (KdV) equation. The problem of the quantitative contribution of solitons and breathers to heat conductivity requires further study.     

Weak Coupling and Continuous Limits for Repeated Quantum Interactions

We consider a quantum system in contact with a heat bath consisting in an infinite chain of identical sub-systems at thermal equilibrium at inverse temperature β. The time evolution is discrete and such that over each time step of duration τ, the reference system is coupled to one new element of the chain only, by means of an interaction of strength λ. We consider three asymptotic regimes of the parameters λ and τ for which the effective evolution of observables on the small system becomes continuous over suitable macroscopic time scales T and whose generator can be computed: the weak coupling limit regime λ → 0, τ = 1, the regime τ → 0, λ²τ → 0 and the critical case λ²τ = 1, τ → 0. The first two regimes are perturbative in nature and the effective generators they determine is such that a non-trivial invariant sub-algebra of observables naturally emerges. The third asymptotic regime goes beyond the perturbative regime and provides an effective dynamics governed by a general Lindblad generator naturally constructed from the interaction Hamiltonian. Conversely, this result shows that one can attach to any Lindblad generator a repeated quantum interactions model whose asymptotic effective evolution is generated by this Lindblad operator.     

On the lower critical field and phase diagram of a thin cylindrical type-II superconductor

The lower critical field H _c1 ^cyl (T) of a superconducting cylinder with radius r ₀∼ξ(T)≪λ(T) is found on the basis of the Ginzburg-Landau theory with various boundary conditions. These results together with the well-known results for the upper critical field are used to construct phase diagrams in terms of the field versus the reduced radius r ₀∼ξ(T) variables. The jump in the average magnetization at H _c1 ^cyl (T) is calculated as a function of the reduced radius. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 8, 537–542 (25 April 1999)