Unusual slow energy relaxation induced by mobile discrete breathers in one-dimensional lattices with next-nearest-neighbor coupling

We study the energy relaxation process in one-dimensional (1D) lattices with next-nearest-neighbor (NNN) couplings. This relaxation is produced by adding damping (absorbing conditions) to the boundary (free-end) of the lattice. Compared to the 1D lattices with on-site potentials, the properties of discrete breathers (DBs) that are spatially localized intrinsic modes are quite unusual with the NNN couplings included, i.e. these DBs are mobile, and thus they can interact with both the phonons and the boundaries of the lattice. For the interparticle interactions of harmonic and Fermi–Pasta–Ulam–Tsingou-β (FPUT-β) types, we find two crossovers of relaxation in general, i.e. a first crossover from the stretched-exponential to the regular exponential relaxation occurring in a short timescale, and a further crossover from the exponential to the power-law relaxation taking place in a long timescale. The first and second relaxations are universal, but the final power-law relaxation is strongly influenced by the properties of DBs, e.g. the scattering processes of DBs with phonons and boundaries in the FPUT-β type systems make the power-law decay relatively faster than that in the counterparts of the harmonic type systems under the same coupling. Our results present new information and insights for understanding the slow energy relaxation in cooling the lattices.     

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.     

Temperature dependence of heat conduction coefficient in nanotube/nanowire networks

Studies on heat conduction are so far mainly focused on regular systems such as the one-dimensional(1D) and twodimensional(2D) lattices where atoms are regularly connected and temperatures of atoms are homogeneously distributed.However, realistic systems such as the nanotube/nanowire networks are not regular but heterogeneously structured, and their heat conduction remains largely unknown. We present a model of quasi-physical networks to study heat conduction in such physical networks and focus on how the network structure influences the heat conduction coefficient κ. In this model,we for the first time consider each link as a 1D chain of atoms instead of a spring in the previous studies. We find that κ is different from link to link in the network, in contrast to the same constant in a regular 1D or 2D lattice. Moreover, for each specific link, we present a formula to show how κ depends on both its link length and the temperatures on its two ends.These findings show that the heat conduction in physical networks is not a straightforward extension of 1D and 2D lattices but seriously influenced by the network structure.     

Cooling nonlinear lattices toward energy localization

We describe the energy relaxation process produced by surface damping on lattices of classical anharmonic oscillators. Spontaneous emergence of localized vibrations dramatically slows down dissipation and gives rise to quasistationary states where energy is trapped in the form of a gas of weakly interacting discrete breathers. In one dimension, strong enough on-site coupling may yield stretched-exponential relaxation which is reminiscent of glassy dynamics. We illustrate the mechanism generating localized structures and discuss the crucial role of the boundary conditions. For two-dimensional lattices, the existence of a gap in the breather spectrum causes the localization process to become activated. A statistical analysis of the resulting quasistationary state through the distribution of breathers' energies yield information on their effective interactions.     

Heat conduction in a three-dimensional momentum-conserving anharmonic lattice

Heat conduction in three-dimensional anharmonic lattices was numerically studied by the Green-Kubo theory. For a given lattice width W, a dimensional crossover is generally observed to occur at a W-dependent threshold of the lattice length. Lattices shorter than W will display a 3D behavior while lattices longer than W will display a 1D behavior. In the 3D regime, the heat current autocorrelation function was found to show a power-law decay as a function of the time lag τ as τ^{β} with β=-1.2. This indicates normal heat conduction. However, the decay exponent deviates significantly from the conventional theoretical value of β=-1.5. A flat power spectrum S(ω) of the global heat current in the low-frequency limit was also observed in the 3D regime. This provides not only an alternative verification of normal heat conduction but also a clear physical insight into its origin.     

Full current statistics of incoherent "cold electrons"

We evaluate the full current statistics (FCS) in the low-dimensional (1D and 2D) diffusive conductors in the incoherent regime eV>E(Th)=D/L(2), E(Th) being the Thouless energy. It is shown that the Coulomb interaction substantially enhances the probability of big current fluctuations for short conductors with E(Th)>1/tau(E), tau(E) being the energy relaxation time, leading to the exponential tails in the current distribution. The current fluctuations are most strong for low temperatures, provided E(Th) approximately [(eV)(2)/Dnu(2)(1)](1/3) for 1D and E(Th) approximately (eV/g)ln(g for 2D, where g is a dimensionless conductance and nu(1) is a 1D density of states. The FCS in the "hot electron" regime is also discussed.     

Heat conduction in low-dimensional quantum magnets

Transport properties provide important information about the mobility, elastic and inelastic of scattering of excitations in solids. Heat transport is well understood for phonons and electrons, but little is known about heat transport by magnetic excitations. Very recently, large and unusual magnetic heat conductivities were discovered in low-dimensional quantum magnets. This article summarizes experimental results for the magnetic thermal conductivity κ_mag of several compounds which are good representations of different low-dimensional quantum spin models, i.e. arrangements of S=1/2 spins in the form of two-dimensional (2D) square lattices and one-dimensional (1D) structures such as chains and two-leg ladders. Remarkable properties of κ_mag have been discovered: It often dwarfs the usual phonon thermal conductivity and allows the identification and analysis of different scattering mechanisms of the relevant magnetic excitations.     

声子气的状态方程和声子气运动的守恒方程

根据爱因斯坦的狭义相对论中质能的等效关系，把固体(本文指非导体)晶格(原子)的质量分为晶格(原子)的静质量和晶格热振动能量的等效质量两个部分，后者就是固体中声子气的等效质量.晶格(原子)热振动的能量则分为晶格(原子)静质量具有的热能以及声子气质量具有的热能.基于固体的状态方程，导得了晶格静质量热振动的状态方程和声子气的状态方程.声子气在固体介质中的宏观运动就是热量在固体中的传递过程.建立了声子气运动的守恒方程组，分析表明，忽略惯性力时声子气的动量守恒方程就退化为傅里叶导热定律，阐明了傅里叶导热定律的物理本质是声子气驱动力与阻力的平衡方程.当热流密度很大惯性力不能忽略时，傅里叶导热定律不再适用. 关键词： 非傅里叶导热 声子气 声子气质量 状态方程 守恒方程     

The Ising Model on Pure Husimi Lattices: A General Formulation and the Critical Temperatures

We consider the Ising spin 1/2 model on arbitrary pure Husimi lattices. An effective representation for the recursion relations is found which allows to write the general solution of the model in an fluent unified way for all pure Husimi lattices. In this respect, explicit expressions for the spontaneous magnetization, for the susceptibility, for the free energy, and for the specific heat are found. Besides, it is shown that this representation allows also to determine exactly the position of the critical temperature on arbitrary pure Husimi lattice. It is found that the critical temperatures for all pure Husimi lattices are driven by a single polynomial equation with coefficients given by parameters that uniquely describe the lattices.     

Size Dependent Heat Conduction in One-Dimensional Diatomic Lattices

We study the size dependency of heat conduction in one-dimensional diatomic FPU-β lattices and establish that for low dimensional material,contribution from optical phonons is found more effective to the thermal conductivity and enhance heat transport in the thermodynamic limit N →∞.For the finite size,thermal conductivity of 1D diatomic lattice is found to be lower than 1D monoatomic chain of the same size made up of the constituent particle of the diatomic chain.For the present 1D diatomic chain,obtained value of power divergent exponent of thermal conductivity0.428±0.001 and diffusion exponent 1.2723 lead to the conclusions that increase in the system size,increases the thermal conductivity and existence of anomalous energy diffusion.Existing numerical data supports our findings.     

Higher-order surface solitons in one-dimensional Bessel optical lattices

We demonstrate the existence of higher-order solitons occurring at an interface separating two one-dimensional (1D) Bessel optical lattices with different orders or modulation depths in a defocusing medium. We show that, in contrast to homogeneous waveguides where higher-order solitons are always unstable, the Bessel lattices with an interface support branches of higher-order structures bifurcating from the corresponding linear modes. The profiles of solitons depend remarkably on the lattice parameters and the stability can be enhanced by increasing the lattice depth and selecting higher-order lattices. We also reveal that the interface model with defocusing saturable Kerr nonlinearity can support stable multi-peaked solitons. The uncovered phenomena may open a new way for soliton control and manipulation.     

Exciton formation and annihilation during 1D impact excitation of carbon nanotubes

Near-infrared electroluminescence was recorded from unipolar single-wall carbon nanotube field-effect transistors at high drain-source voltages. High resolution spectra reveal resonant light emission originating from the radiative relaxation of excitons rather than heat dissipation. The electroluminescence is induced by only one carrier type and ascribed to 1D impact excitation. An emission quenching is also observed at high field and attributed to an exciton-exciton annihilation process and free carrier generation. The excitons' binding energy in the order of 270 meV for 1.4 nm SWNTs is inferred from the spectral features.     

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).     

Studies of bosons in optical lattices in a harmonic potential

We present a theoretical study of Bose condensation and specific heat of non-interacting bosons in finite lattices in harmonic potentials in one, two, and three dimensions. We numerically diagonalize the Hamiltonian to obtain the energy levels of the systems. Using the energy levels thus obtained, we investigate the temperature dependence, dimensionality effects, lattice size dependence, and evolution to the bulk limit of the condensate fraction and the specific heat. Some preliminary results on the specific heat of fermions in optical lattices are also presented. The results obtained are contextualized within the current experimental and theoretical scenario.     

Ground states for lattices of ferromagnetic granules with dipolar magnetic interaction

The magnetic phase diagrams of 2D and 3D regular lattices formed by nonspherical single-domain ferromagnetic granules featuring a dipolar magnetic interaction are studied. The energy of a magnetic state of such systems is calculated using an approximate expression for the pair interaction of nonspherical granules. The character of the magnetic ground state of the system is determined by three geometric parameters: (i) the eccentricity of granules; (ii) the ratio of periods of the rectangular (2D) or tetragonal (3D) lattice; and (iii) the ratio of a lattice period to a granule size. In contrast to the case of lattices formed by point (or spherical) magnetic moments, in which the ground state is always antiferromagnetic or frustrated (for triangular lattices), the ground state of a 2D lattice composed of nonspherical granules can be ferromagnetic. The magnetic phase diagrams of the systems studied are constructed in the space of the above geometric parameters.     

Topological phase transition and electrically tunable diamagnetism in silicene

The movement and relaxation of the localized energy on FPU lattices have been studied by using Wavelet transforms methods. The energy relaxation mechanism for nonlinear chains involves the degradation of higher frequency excitations into lower frequencies. It is shown that low frequency modes decay more slowly in nonlinear chains. The wavelet spectrum exhibits a behavior involving the interplay of phonon modes and breather modes.     

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.     

Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrödinger lattices

We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schrödinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities. Several species of stationary solutions are constructed, and bifurcations linking their families are investigated using parameter continuation starting from the anti-continuum limit, and also with the help of a variational approximation. In particular, a species of hybrid solitons, intermediate between the site- and bond-centered types of the localized states (with no counterpart in the 1D model), is analyzed in 2D and 3D lattices. We also discuss the mobility of multi-dimensional discrete solitons that can be set in motion by lending them kinetic energy exceeding the appropriately defined Peierls-Nabarro barrier; however, they eventually come to a halt, due to radiation loss.     

荷电膜渗透传质过程的计算机模拟：一价离子的传递

以渗透理论的方法研究一价离子通过荷电膜的传质机理,用计算机编程模拟一价带电离子通过荷电膜的过程以研究荷电膜中导电性能和荷电组分含量的关系.模拟结果表明,对于二维格栅体系在荷电组分含量为0.4～0.6时,膜导电性能存在渗透突跃现象;而对于三维格栅体系则在0.1～0.2时存在渗透突跃现象,此结果和MontoCarlo的二维、三维随机模拟结果比较接近.由于实际的荷电膜也可看作为三维格栅体系,因此,可用三维格栅体系程序对不同荷电分率膜的电导数据进行拟合,结果表明,对于实际的磺化聚苯硫醚(SPPS)/聚醚砜(PES)共混膜,当荷电组分SPPS的分率达到0.144时,共混膜即会从不良导体变为良导体,显然该值落在理论值0.1～0.2,因此,理论模拟结果与实际荷电膜传质的实验数据相吻合.     

Impurity dipole interactions in alkali halides at low temperature

Calculations of dipole correlations and internal-energy densities are reported for dilute dipole systems in the NaCl and CsCl lattices. The tensorial dipole interaction potential is used in thermal averaging in a two-dipole approximation. Actual lattice geometries are taken into account in the three-dimensional spatial averages. The dipoles are assumed to have equilibrium orientations along [100] in the NaCl lattice, and along either [100] or [111] in the CsCl lattice. It is found thatlocal antiparallel ordering is favored in both lattices at low temperatures. Comparison with recent, low-temperature dielectric data indicates that relaxation mechanisms are as important as local antiparallel ordering in limiting theT ^?1 increase of (??1)/(?+2) with decreasing temperature for OH^? doped KCl. A simplified, nonequilibrium mechanism is studied whereby parallel-correlated dipoles with interaction energies greater than2 kT in absolute value become nonalignable and do not contribute to?. This mechanism together with antiparallel ordering are found to describe the experimental data satisfactorily; but additional relaxation mechanisms are indicated. The contribution of the dipole interactions to the specific heat is also calculated, and is in qualitative agreement with measured specific heat data for OH^? doped KCl.