On the microscopic theory of electronic contributions to lattice dynamics of anharmonic crystals

A formalism is set up to study the electronic contribution to the phonon dynamics in an arbitrary crystal, conducting or insulating, without assuming small ionic oscillations. Therefore, in contrast to a harmonic Born-Oppenheimer approximation, such an approach allows for renormalization effects due to phonon-phonon interaction over the complete temperature range of the solid phase. The “weak coupling” approximation between nuclei and electrons is shown to be sufficient in order to obtain the dynamical matrix microscopically in terms of the complete inverse dielectric function of the electrons.     

The lattice dynamics of an anharmonic crystal

The theory of the physical properties of an anharmonic crystal is discussed by using the thermodynamic Green's functions for the phonons. A perturbation procedure is developed to obtain the Green's functions and it is shown that for some purposes a quasi-harmonic approximation is useful, in which the frequencies of the normal modes are those determined by infra-red or neutron spectrometry. The thermodynamic, elastic, dielectric and scattering properties of an anharmonic crystal are discussed in terms of the Green's functions, and detailed expressions are given for the more important contributions. Detailed numerical calculations are presented of the thermal expansion, dielectric properties and shapes of some of the inelastically scattered neutron groups, for sodium iodide and potassium bromide. The calculations, which give reasonable agreement with experiment, show that even at quite low temperatures, the lifetimes of some of the normal modes can be quite short. By using the quasi-harmonic approximation it is shown that the large temperature dependence of the normal modes in a ferroelectric crystal can be treated adequately.     

Electron heat capacity and lattice properties of Americium

The temperature dependence of the electron heat capacity of americium is calculated using the concepts on the electronic structure and magnetic properties of this element. The Debye temperature, the thermal expansion coefficient, and the bulk modulus of americium are determined on the basis of the results of calculations and experimental data on heat capacity.     

New shear-free relativistic models with heat flow

We study shear-free spherically symmetric relativistic models with heat flow. Our analysis is based on Lie’s theory of extended groups applied to the governing field equations. In particular, we generate a five-parameter family of transformations which enables us to map existing solutions to new solutions. All known solutions of Einstein equations with heat flow can therefore produce infinite families of new solutions. In addition, we provide two new classes of solutions utilising the Lie infinitesimal generators. These solutions generate an infinite class of solutions given any one of the two unknown metric functions.     

Hydrodynamics of stationary non-equilibrium states for some stochastic lattice gas models

We consider discrete lattice gas models in a finite interval with stochastic jump dynamics in the interior, which conserve the particle number, and with stochastic dynamics at the boundaries chosen to model infinite particle reservoirs at fixed chemical potentials. The unique stationary measures of these processes support a steady particle current from the reservoir of higher chemical potential into the lower and are non-reversible. We study the structure of the stationary measure in the hydrodynamic limit, as the microscopic lattice size goes to infinity. In particular, we prove as a law of large numbers that the empirical density field converges to a deterministic limit which is the solution of the stationary transport equation and the empirical current converges to the deterministic limit given by Fick's law.Dedicated to Res Jost and Arthur WightmanSupported in part by NSF Grants DMR 89-18903 and INT 8521407. H.S. also supported by the Deutsche Forschungsgemeinschaft     

Some anharmonic properties of Caesium halides

The second thermal Grüneisen parameter and isentropic Anderson-Grüneisen parameter for caesium halides are determined at different temperatures employing a pressure dependent shell model of lattice dynamics. A new thermodynamic relation is also proposed to calculate the second thermal Grüneisen parameter using experimentally measurable quantities. The agreement between experimentally estimated and theoretically calculated values is fairly good for the Anderson-Grüneisen parameter while it is very poor for the second thermal Grüneisen parameter.     

The theoretical analysis of the lattice hydrodynamic models for traffic flow theory

The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but also connected with the microscopic car following model closely. The modified Korteweg-de Vries (mKdV) equation related to the density wave in a congested traffic region has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail for the car following model. We devote ourselves to obtaining the KdV equation from the original lattice hydrodynamic models and the KdV soliton solution to describe the traffic jam. Especially, we obtain the general soliton solution of the KdV equation and the mKdV equation. We review several lattice hydrodynamic models, which were proposed recently. We compare the modified models and carry out some analysis. Numerical simulations are conducted to demonstrate the nonlinear analysis results.     

Phonon-mediated heat dissipation in a monatomic lattice: case study on Ni

The recently introduced analytical model for the heat current autocorrelation function of a crystal with a monatomic lattice [Evteev et al., Phil. Mag. 94 (2014) p. 731 and 94 (2014) p. 3992] is employed in conjunction with the Green–Kubo formalism to investigate in detail the results of an equilibrium molecular dynamics calculations of the temperature dependence of the lattice thermal conductivity and phonon dynamics in f.c.c. Ni. Only the contribution to the lattice thermal conductivity determined by the phonon–phonon scattering processes is considered, while the contribution due to phonon–electron scattering processes is intentionally ignored. Nonetheless, during comparison of our data with experiment an estimation of the second contribution is made. Furthermore, by comparing the results obtained for f.c.c. Ni model to those for other models of elemental crystals with the f.c.c. lattice, we give an estimation of the scaling relations of the lattice thermal conductivity with other lattice properties such as the coefficient of thermal expansion and the bulk modulus. Moreover, within the framework of linear response theory and the fluctuation-dissipation theorem, we extend our analysis in this paper into the frequency domain to predict the power spectra of equilibrium fluctuations associated with the phonon-mediated heat dissipation in a monatomic lattice. The practical importance of the analytical treatment lies in the fact that it has the potential to be used in the future to efficiently decode the generic information on the lattice thermal conductivity and phonon dynamics from a power spectrum of the acoustic excitations in a monatomic crystal measured by a spectroscopic technique in the frequency range of about 1–20 THz.     

Spectral properties of the period-doubling lattice: exact renormalization group study

Using an exact real space renormalization group technique, we have studied the electronic and vibrational properties of a class of one dimensional aperiodic lattice model, for which the substitution rules are A → AB and B → AA. The spectra are self-similar and exhibit hierarchical structures. Analytical and numerical analyses reveal the existence of extended eigenstates.     

Equations of state for strongly anharmonic crystals with a complex lattice

On the basis of a nonsymmetrized self-consistent-field approximation, thermal and caloric equations of state for strongly anharmonic crystals with a complex lattice are considered, allowing, in principle, anharmonism of any desired (basically, even) order to be taken into account. These equations include the moments of single-particle distribution functions, which are the solutions of some system of transcendental equations. More detailed consideration is given to the case of binary crystals with strong fourth-order anharmonism. The possibility of obtaining corrections to the approximation adopted is also discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 40–44, November, 1979.     

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.     

Analysis of heat capacity of platinum: Electron-phonon effects and anharmonic contribution

The heat capacity results for platinum from 80 to 1000 K, reported in our previous paper, have been analyzed. The contributions of bare electrons and harmonic phonons to the heat capacity have been evaluated from the available data on the band structure and the phonon spectrum of platinum. At low temperatures, the present estimates for the temperature dependence of the electron-phonon enhancement agree qualitatively with those derived from theoretical calculations found in the literature. The anharmonic heat capacity obtained is negative and linear with temperature in the vicinity of the Debye temperature (237 K), and becomes constant above 450 K. The enhancement in the heat capacity above 1000 K has been analyzed and found to be due mainly to the enlargement of the dilation term corresponding to the similar enhancement in the thermal expansion.     

The localization properties of a random steady flow on a lattice

We consider a random stationary vector field on a multidimensional lattice and investigate flow-connected subsets of the lattice invariant under the action of the associated flow. The subsets of primary interest are cycles, and vortices each of which is the set of orbits terminating in the same cycle. We prove that with probability 1 each vortex only involves a finite number of sites of the lattice. Under the assumption of independence of the vector field in different sites, we find that with probability 1 the vortices exhaust all possible maximal flowconnected invariant subsets of the lattice if and only if the probability of existence of a cycle is positive. Thus, if cycles exist, a particle under the action of the flow only moves within a bounded region, i.e., it is completely localized.     

Similarities between the lattice gas model and some other models of nuclear multifragmentation

We continue our development of the nuclear lattice gas model by exploring links and similarities with other theoretical approaches to nuclear multifragmentation: the percolation model and the statistical multifragmentation model. It is shown that there exists a limit where the lattice gas model reduces to the percolation model. The similarity between the lattice gas model and the statistical multifragmentation model is more indirect and we utilize the equations of state in the two models. By using the law of partial pressures we obtain P-ϱ diagrams for the statistical multifragmentation model and find that these are remarkably similar to those obtained in the lattice gas model via an exact evaluation of the nuclear partition function on the lattice. For completeness, we also compute the P-ϱ diagram for a system obeying pure classical molecular dynamics with a simple two-body force.