Dissipation in solids: thermal oscillations of atoms

Dissipation in solids describes conversion of kinetic energy to thermal energy. Heat capacity of a solid relates to the kinetic energy of the oscillations of its atoms with the assumption that they are in thermal equilibrium. Previous studies investigated criteria related to thermal relaxation, the process by which thermal equilibrium is established. They examined conditions for irreversible distribution of energy among the modes of a nonlinear periodic structure that represents atoms in a solid. These studies all point to the chaotic behavior of a freely vibrating nonlinear lattice as the kernel of the problem in addressing thermal relaxation. This paper extends the results of previous studies on thermalization to modeling of dissipation as energy absorption that takes place during forced vibration of particles in a nonlinear lattice. Results show that dissipation and chaotic behavior of the particles develop simultaneously. Such behavior develops when the forcing frequency falls within a resonance band. The results also support the argument that for a real solid, both in terms of size and complexity, resonance bands overlap significantly broadening the frequency range within which dissipation takes place.     

Discrete breathers and delocalization in nonlinear disordered systems

We find exact localized time-periodic solutions with frequencies inside the linearized spectrum [intraband discrete breathers (IDBs)] in random nonlinear models using a new self-consistent method. The IDB frequencies belong to intervals between forbidden gaps generated by resonances with the linear modes, becoming fat Cantor sets in infinite systems. When localized IDBs are continued versus frequency, they delocalize and become multisite IDBs (not predicted by existing theorems), which can propagate energy. Some implications for energy relaxation in glasses are discussed.     

Computer simulation of the Fröhlich coherent vibrations

In a nonlinear vibration system with energy supply the lowest frequency mode may be coherently excited as was predicted by Fröhlich. Computer simulation of nonlinear vibration systems reveals that even the higher frequency modes may be excited. The conditions for higher frequency modes excitation are specified. Coherent states may be excited in the time period less than about one hour after switching on the energy supply.     

A thermodynamic theory of mechanical relaxation due to energy transfer between strain-sensitive and strain-insensitive modes in polymers

A thermodynamic theory has been developed on the relaxation strength of mechanical relaxation due to energy-transfer between strain-sensitive (intermolecular) modes and strain-insensitive (intramolecular) modes. Assuming that the strain-insensitive modes exhibit an overwhelmingly large heat capacity and function as a heat reservoir of constant temperature during the relaxation process, the relaxation strength ΔG, the difference between instantaneous and equilibrium moduli, is given as ΔG = TG² _Tα² ₁/C_z1, where T is the absolute temperature, G_T is the isothermal elastic modulus, and ₁ and C_z1 are the thermal expansion coefficient and the specific heat at constant strain of the strainsensitive modes, respectively. This assumption is reasonable for a polymeric solid in which backbone chains have a lot of vibrational degrees of freedom whose energy is rather insensitive to intermolecular distance and, on the contrary, the potential for localized motion such as motion of side chains is highly sensitive to intermolecular distance.

In a special case where the strain-sensitive modes are a set of vibrators with an angular frequency ω, ΔG = γ²C_z1T, where γ is the Grüneisen constant, defined by the strain-derivative of ω, = ?? In ω?z. The case where the strainsensitive modes are a set of rotators in an n-fold symmetrical potential can be treated as an extension of the above case. In the case where the strain-sensitive modes involve the transition between two states, ΔG in the present theory is reduced to that of the well-known two-state transition theory. Agreement is obtained between theory and experiment for a-methyl relaxation of poly(methy1 methacrylate).     

Multistability of states of a molecular gas with the V-T relaxation time dependent on the vibrational energy

The possibility of realizing multistability of states under the action of IR radiation on a molecule under conditions of nonlinear absorption of light energy and dependence of the V-T relaxation time on its vibrational energy is shown. A two-wave optically bistable arrangement potentially having a highly contrasting range of states is proposed. The nonlinear dependence of the V-T relaxation time on the vibrational energy is shown to allow the realization of optical bistability based on the absorption of light energy at the frequency of the fundamental vibrational transition.     

Nonlinear dielectric response and thermodynamic heterogeneity in liquids

If large amplitude time-dependent fields (e.g., dielectric, magnetic, mechanical) are applied to a sample that displays relaxational modes, some energy of the external field is absorbed by the slow degrees of freedom. The weak coupling of these modes to the phonon bath leads to long persistence times of the resulting higher fictive temperature. Assuming heterogeneities regarding dielectric and thermal relaxation times, extremely strong nonlinear dielectric effects are predicted and experimentally verified. For glycerol at T = 213 K, the dielectric loss measured at 280 kV/cm increases by more than 6% over its low-field value. This nonlinearity shows a characteristic frequency dependence and implies that dielectric and thermal time constants are locally correlated in viscous liquids.     

Magnetic excitations in solids

This article presents a review of low to moderate frequency magnetic excitations, termed magnons or spin waves, in magnetically ordered materials. The emphasis is on intuitive behavior rather than analytical theory. Topics include spin waves, magnetostatic modes, dipole-exchange modes, surface anisotropy, dispersion properties, nonlinear effects, and relaxation. These phenomena are illustrated with experimental examples based on magnon light scattering results as well as conventional microwave techniques.     

硝基甲烷振动能量弛豫的集体模型

用分子动力学方法结合Dlott等人提出的"门槛模"理论研究集体相互作用下硝基甲烷振动能量弛豫过程.其中振动冷却过程与实验符合的很好.在振动激发过程的分子动力学模拟中观测到与实验一致的基频频移现象.用分子动力学方法从微观上详细地描述出分子"门槛模"振动激发过程.研究表明,在高温高压作用下,集体作用效应对多原子振动激发具有不可忽视的作用,能量传递过程中除了基频的作用外,强烈的非线性相互作用引起的振动模泛频也携带有大量的振动能,这些泛频也对分子振动能量传递产生重要影响.     

Energy transmission in the forbidden band gap of a nonlinear chain

A nonlinear chain driven by one end may propagate energy in the forbidden band gap by means of nonlinear modes. For harmonic driving at a given frequency, the process occurs at a threshold amplitude by sudden large energy flow that we call nonlinear supratransmission. The bifurcation of energy transmission is demonstrated numerically and experimentally on the chain of coupled pendula (sine-Gordon and nonlinear Klein-Gordon equations) and sustained by an extremely simple theory.     

[Russian Text Ignored]

The plasmon turbulence parametrically excited by two strong external waves with a frequency difference close to twice the electron plasma frequency is investigated in underdense plasmas. The nonlinear stabilization of the growing plasmons due to scattering by ions is described by a nonlinear integro-differential equation for the spectral plasmon energy density. The dependence of the turbulent relaxation of the plasmon energy and its stationary level on the parameters of the plasma and the pump waves is given by analytical and numerical solutions of this equation.     

捕光复合物中起源于电子-振动耦合的长时间相干

We theoretically investigate the evolutions of two-dimensional, third-order, nonlinear pho-ton echo rephasing spectra with population time by using an exact numerical path integral method. It is shown that for the same system, the coherence time and relaxation time of excitonic states are short, however, if the couplings of electronic and intra-pigment vibra-tional modes are considered, the coherence time and relaxation time of this vibronic states are greatly extended. It means that the couplings between electronic and vibrational modes play important roles in keeping long-lived coherence in light-harvesting complexes. Particularly, by using the method we can fix the transition path of the energy transfer in bio-molecular systems.     

Microscopic theory of the long-wavelength modes of two-component plasmas and ionic liquids: II. The longitudinal modes

The modification of the damping rate of the sound modes by Coulomb phenomena is demonstrated from first principles. The heat modes of one- and two-component systems of charged particles are shown to differ by a factor c_p/c_v. Microscopic expressions for the interspecies energy and longitudinal momentum relaxation frequencies are provided. The charge relaxation modes are shown to reduce in the limit of weak-coupling to a pair of plasma oscillations occurring slightly below the plasma frequency while being slightly damped even at infinite wavelength. In the opposite limit of strong-coupling the same pair of charge relaxation modes is shown to split into an interspecies momentum relaxation mode and an approximate hydrodynamic diffusion mode. An Einstein relation between the diffusion constant and the electric conductivity is also demonstrated. All expressions are obtained for arbitrary density and coupling.     

High-resolution nonlinear laser spectroscopy of exciton relaxation in GaAs quantum wells

This paper describes measurements of exciton relaxation in GaAs/AlGaAs quantum well structures based on high resolution nonlinear laser spectroscopy. The nonlinear optical measurements show that low energy excitons can be localized by monolayer disorder of the quantum well interface. We show that these excitons migrate between localization sites by phonon assisted migration, leading to spectral diffusion of the excitons. The frequency domain measurements give a direct measure of the quasi-equilibrium exciton spectral redistribution due to exciton energy relaxation, and the temperature dependence of the measured migration rates confirms recent theoretical predictions. The observed line shapes are interpreted based on solutions we obtain to modified Bloch equations which include the effects of spectral diffusion.     

Self-induced high-speed modulation in microchip solid-state lasers with asymmetric end pumping

We applied laser-diode sheetlike end pumping to a multimode Nd:YVO(4) laser and observed high-speed (>400-MHz) modulation of the intensity of chaotic pulsation near 1 MHz. The frequencies of modulation were the beat frequencies for pairs of closely spaced lasing modes. Asymmetric optical confinement and the resultant modal interference are shown to lead to oval-hollow-mode operation in which modal beat notes induce high-speed modulation, the frequency range of which is 2 orders of magnitude higher than the intrinsic relaxation oscillation frequency. Good numerical reproduction of the observed chaotic pulsations and their high-speed modulation was obtained with model equations in which such effects as nonlinear gain coupling among modes and field interference between pairs of modes were included. High-speed pulsations in nonchaotic lasers were also demonstrated.     

Spectral transformation of the energy in Fröhlich systems

Spectral energy transformation is one of the general properties of nonlinear systems. We examined the Fröhlich vibration system as a model nonlinear system. Energy is transferred down towards low frequency vibration modes with considerable damping.     

Behaviors of thermalization for the Fermi–Pasta–Ulam–Tsingou system with small number of particles

We study the behaviors of thermalization in Fermi–Pasta–Ulam–Tsingou(FPUT) system with small number of particles using periodic boundary conditions. The total energy has initially equidistributed among some of the lowest frequency modes. The thermalization time t_(eq) depending on system's energy density ε scales as t_(eq) ∝ε~(-4) only within a certain range of nonlinearity. In this range of nonlinearity, energies can interchange between the initial excited modes and other modes continuously with time until reaching the thermalized state. With a further decreasing nonlinearity, a steeper growth than ε~(-4) will appear. In the very weakly nonlinear regime, energies on low frequency modes are found to be frozen on large time scales. Redistribution of mode energies happens through the resonances of high frequency modes.     

Study of intrinsic localized vibrational modes in micromechanical oscillator arrays

Intrinsic localized modes (ILMs) have been observed in micromechanical cantilever arrays, and their creation, locking, interaction, and relaxation dynamics in the presence of a driver have been studied. The micromechanical array is fabricated in a 300 nm thick silicon-nitride film on a silicon substrate, and consists of up to 248 cantilevers of two alternating lengths. To observe the ILMs in this experimental system a line-shaped laser beam is focused on the 1D cantilever array, and the reflected beam is captured with a fast charge coupled device camera. The array is driven near its highest frequency mode with a piezoelectric transducer. Numerical simulations of the nonlinear Klein-Gordon lattice have been carried out to assist with the detailed interpretation of the experimental results. These include pinning and locking of the ILMs when the driver is on, collisions between ILMs, low frequency excitation modes of the locked ILMs and their relaxation behavior after the driver is turned off.     

Modulational instability in isolated and driven Fermi–Pasta–Ulam lattices

We present a detailed analysis of the modulational instability of the zone-boundary mode for one and higher-dimensional Fermi–Pasta–Ulam (FPU) lattices. The growth of the instability is followed by a process of relaxation to equipartition, which we have called the Anti-FPU problem because the energy is initially fed into the highest frequency part of the spectrum, while in the original FPU problem low frequency excitations of the lattice were considered. This relaxation process leads to the formation of chaotic breathers in both one and two space dimensions. The system then relaxes to energy equipartition, on time scales that increase as the energy density is decreased. We supplement this study by considering the nonconservative case, where the FPU lattice is homogeneously driven at high frequencies. Standing and travelling nonlinear waves and solitonic patterns are detected in this case. Finally we investigate the dynamics of the FPU chain when one end is driven at a frequency located above the zone boundary. We show that this excitation stimulates nonlinear bandgap transmission effects.     

Quantum Solitons and Localized Modes in a One-Dimensional Lattice Chain with Nonlinear Substrate Potential

In the classical lattice theory, solitons and localized modes can exist in many one-dimensional nonlinear lattice chains, however, in the quantum lattice theory, whether quantum solitons and localized modes can exist or not in the one-dimensional lattice chains is an interesting problem. By using the number state method and the Hartree approximation combined with the method of multiple scales, we investigate quantum solitons and localized modes in a one-dimensional lattice chain with the nonlinear substrate potential. It is shown that quantum solitons do exist in this nonlinear lattice chain, and at the boundary of the phonon Brillouin zone, quantum solitons become quantum localized modes, phonons are pinned to the lattice of the vicinity at the central position j=j₀.     

石墨烯的声子热学性质研究

声子是石墨烯导热过程中的主要载体,而声子的弛豫时间又是其中最基本、最重要的物理量.本文采用简正模式分解法研究了石墨烯声子的弛豫时间,并且借此分析了不同声子在导热过程中的贡献.该方法通过平衡分子动力学模拟实现,首先通过模拟得到单个声子的能量自相关函数衰减曲线,并进一步采用拟合和积分两种方法得到单个声子的弛豫时间.然后,研究了弛豫时间与波矢、频率和温度的关系.结果发现,弛豫时间随波矢的变化与对应的色散关系相近,弛豫时间与频率和温度的关系符合理论模型:1/τ=νnTm,其中声学支的n为1.56,而光学支结果较为发散,指数m对于不同声子支结果略有不同.最后,还研究了不同频率声子对导热的贡献,发现低频声子在态密度上占有绝对优势,并且其弛豫时间整体高于高频声子,所以低频声子对导热的贡献占据主导地位.