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     

Variational wavefunction for multi-species spinful fermionic superfluids and superconductors

We introduce a new fermionic variational wavefunction, generalizing the Bardeen–Cooper–Schrieffer (BCS) wavefunction, which is suitable for interacting multi-species spinful systems and sustaining superfluidity. Applications range from quark matter to the high temperature superconductors. A wide class of Hamiltonians, comprising interactions and hybridization of arbitrary momentum dependence between different fermion species, can be treated in a comprehensive manner. This is the case, as both the intra-species and the inter-species interactions are treated on equally rigorous footing, which is accomplished via the introduction of a new quantum index attached to the fermions. The index is consistent with known fermionic physics, and allows for heretofore unaccounted fermion–fermion correlations. We have derived the finite temperature version of the theory, thus obtaining the renormalized quasiparticle dispersion relations, and we discuss the appearance of charge and spin density wave order.     

Ballistic–diffusive phonon transport and size induced anisotropy of thermal conductivity of silicon nanofilms

The effective thermal conductivity of nanofilms is size dependent due to the diffusive–ballistic transport of phonons. In this paper, we investigate the cross-plane phonon transport from the viewpoint of the phonon Boltzmann equation. A predictive model for the size dependent thermal conductivity is proposed and agrees well with the results of molecular dynamics simulation for silicon nanofilms. The ballistic transport has different effects on the heat conduction in the in-plane or cross-plane directions, which causes the anisotropy of thermal conductivity of nanofilms. Such anisotropy is also size dependent and vanishes with the increase of film thickness.     

Initial state dependence of nonlinear kinetic equations: The classical electron gas

The method of nonequilibrium cluster expansion is used to stydy the decay to equilibrium of a weakly coupled inhomogeneous electron gas prepared in a local equilibrium state at the initial time,t=0. A nonlinear kinetic equation describing the long time behavior of the one-particle distribution function is obtained. For consistency, initial correlations have to be taken into account. The resulting kinetic equation-differs from that obtained when the initial state of the system is assumed to be factorized in a product of one-particle functions. The question of to what extent correlations in the initial state play an essential role in determining the form of the kinetic equation at long times is discussed. To that end, the present calculations are compared with results obtained before for hard sphere gases and in general gases with strong short-range forces. A partial answer is proposed and some open questions are indicated.     

Effect of structural defect on phonon transmission quantization in low-dimensional superlattices

Using the scattering-matrix cascading method, we investigate the effect of structural defect on the acoustic phonon transmission quantization in a low-dimensional superlattice quantum waveguide. In the present system, the phonon transmission exhibits rather complex resonant behaviors. It is found that a lateral defect in an otherwise periodic structure modifies the transversal phonon transmission spectra nontrivially and completely washes away the transmission quantization due to the strong additional scattering by defect. However, the appreciable quantization survives in the presence of a longitudinal defect. Our results also show that by adjusting the geometric parameters of the structural defect, one can control the phonon transport of the structure to match practical requirements in devices.     

Theoretical analysis of higher-order phonon sidebands in semiconductor luminescence spectra

A semiconductor luminescence formula is derived that includes phonon replica of arbitrary order based on a non-perturbative treatment of the electron–phonon interaction. The formula is used to analyze the extraordinarily strong sidebands observed with ZnO nanorods in recent experiments. Sidebands due to free and impurity-bound excitons are compared, and the generic differences between bulk and quantum-well emission are discussed.     

Spectral analysis on a phonon spectral function of a solid-state plasma in a doped semiconductor

We report an analysis on a phonon spectral function of a solid-state plasma formed in a doped semiconductor. Real and imaginary parts of phonon propagators are evaluated including carrier screening effects within a random phase approximation, and finite-temperature spectral behavior of the phonon spectral function is examined in terms of plasmon-phonon coupled modes and quasiparticle excitation mode of the plasma. The results are applied to the case of conduction electrons in a wurtzite GaN considering carrier-phonon coupling channel via polar optical phonons. We show that the dispersion relations of the plasmon-LO phonon coupled (‘upper’ and ‘lower’) modes and the character of the additional modes via single quasiparticle excitations are heavily associated with the nonlocal and dynamic behavior of the energy shift and collisional broadening of the dressed phonon propagator of the plasma.     

Coherent phonon dynamics of normal metal in ultrafast spectroscopy: Non-equilibrium gauge invariant Green's function approach

The phonon dynamics of normal metal in the coherent regime of ultrafast spectroscopy is studied based on the non-equilibrium gauge invariant Green's function method. The non-equilibrium phonon self-energy is computed explicitly as a function of time in a gauge invariant way up to the second order of electric field of applied laser pulse. The extension beyond the coherent regime and the incorporation of correlation effects are discussed.     

Non-interacting dimer kinetics in hypercubic lattices

The exact formulation of the kinetic of dimer in hypercubic lattices is developed in the framework of the kinetic lattice gas model. The so-called local evolution rules are used to obtain the hierarchy of equation of motion for the correlation functions where processes like adsorption and desorption are included. The hierarchy of equations are truncated using a mean field (m, n) closures which allows the analytical treatment of the system. A general expression for non-interacting dimer isotherm and two particle correlation functions are obtained in hypercubic lattices.     

First-principle calculation for the phonon structure on iron-based superconductors

We perform first-principle phonon calculations for three typical iron-based superconductors, i.e., LaFeAsO,BaFe₂As₂, and FeSe. Though those crystals have different structures, we find that the optical modes associated with Fe vibration have almost similar characters. Moreover, we examine the pressure effect on phonons in FeSe. By increasing the external pressure, the phonon mode frequency related to Fe vibration effectively rises up and the electronic density of states at Fermi level also increases. These results may correlate to the critical temperature enhancement under high pressure.     

Entangled Bell states of two electrons in coupled quantum dots—phonon decoherence

We demonstrate coupling and entangling of quantum states in a pair of vertically aligned self assembled quantum dots by studying the dynamics of two interacting electrons driven by external electric field. The present entanglement involves the spatial degree of freedom for the two electrons system. We show that system of two interacting electrons initially delocalized (localized each in one dot) oscillate slowly in response to electric field, since the strong Coulomb repulsion makes them behaving so. We use an explicit formula for the entanglement of formation of two qubit in terms of the concurrence of the density operator. In ideal situations, entangled quantum states would not decohere during processing and transmission of quantum information. However, real quantum systems will inevitably be influenced by surrounding environments. We discuss the degree of entanglement of this system in which we introduce the decoherence effect caused by the acoustic phonon. In this entangled states proposal, the decohering time depends on the external parameters.     

On the lattice Boltzmann method for phonon transport

The lattice Boltzmann method is a discrete representation of the Boltzmann transport equation that has been employed for modeling transport of particles of different nature. In the present work, we describe the lattice Boltzmann methodology and implementation techniques for the phonon transport modeling in crystalline materials. We show that some phonon physical properties, e.g., mean free path and group velocity, should be corrected to their effective values for one- and two-dimensional simulations, if one uses the isotropic approximation. We find that use of the D2Q9 lattice for phonon transport leads to erroneous results in transient ballistic simulations, and the D2Q7 lattice should be employed for two-dimensional simulations. Furthermore, we show that at the ballistic regime, the effect of direction discretization becomes apparent in two dimensions, regardless of the lattice used. Numerical methodology, lattice structure, and implementation of initial and different boundary conditions for the D2Q7 lattice are discussed in detail.     

Predicting mode-dependent phonon thermal conductivity of silicon nanoparticle using Boltzmann transport equation

With the advent of nanotechnology, silicon nanoparticles have shown promising applications in the manufacturing sector. In this letter, we examine the lattice thermal conductivity predictions for a silicon nanoparticle using three popular formulations of the Boltzmann transport equation. The models as proposed by Klemens, Callaway and Holland, essentially differ in the phonon scattering mechanisms and the vibrational modes considered in the respective formulations. At low temperatures, results from all three models show strong agreement with experimental measurements, but deviate significantly with increasing temperatures. Estimates from the Holland model, which explicitly accounts for the normal and Umklapp scattering processes of the transverse and longitudinal modes, concur with the measured values. Similar predictions are obtained from both Holland and Callaway models at high temperatures since phonon transport is dominated by longitudinal modes, as revealed from our analyses of the relaxation times. In conclusion, the letter infers the importance of mode dependent thermal conduction in silicon nanoparticle at elevated temperatures.     

弱相互作用费米气体的相对论顺磁性

通过考虑单粒子的相对论能量并且应用量子统计方法,研究弱磁场中弱相互作用费米气体的相对论顺磁性,求解相对论性的最可几磁化率及平均磁化率,讨论相对论效应对最可几磁化率的影响,给出相对论性的粒子数的临界值. 结果显示, 与非相对论情况比较,当 时, 相对论情况下的最可几磁化率和粒子数的临界值都没有变化. 当 时,相对论效应使系统呈现顺磁性容易,而且相对论效应增加磁化率,同时也放大了相互作用对磁化率的影响.     

Investigation of positively charged acceptor states in Si and Ge under uniaxial stress by phonon induced conduction

We use superconducting Al-tunnel junctions as tunable phonon generators in the meV-range to determine ground state splitting at zero stress of positively charged states associated with single acceptors in Si and double acceptors in Ge. From the stress and energy dependence of the conductivity induced by high frequency phonon irradiation of the corresponding two- and three-hole states we find that the splitting is below 0.1 meV for the ground states of Si:B⁺ and Ge:Be⁺, and 1 meV and 1.2 meV for Si:Ga⁺ and Si:Al⁺, respectively. These level separations are comparable to those found previously for the ground states of the corresponding acceptor bound excitons A⁰X. For the deeper acceptors Si:In⁺, Si:Tl⁺, and Ge:Zn⁺ the results are qualitatively different.     

弱相互作用费米气体的相对论顺磁性

通过考虑单粒子的相对论能量并且应用量子统计方法，研究弱磁场中弱相互作用费米气体的相对论顺磁性，求解相对论性的最可几磁化率及平均磁化率，讨论相对论效应对最可几磁化率的影响，给出相对论性的粒子数的临界值. 结果显示, 与非相对论情况比较，当 时, 相对论情况下的最可几磁化率和粒子数的临界值都没有变化. 当 时，相对论效应使系统呈现顺磁性容易，而且相对论效应增加磁化率，同时也放大了相互作用对磁化率的影响.     

强磁场中超冷费米气体的相对论效应

由单粒子的弱相对论能谱及泊松公式,导出强磁场中费米气体的热力学势函数.在此基础上,运用热力学关系求解低温条件下系统的统计特征量的解析式,分析相对论效应对统计性质的影响机理.研究表明,磁场愈强,相对论效应愈明显.相对论效应引发的单调项与相应的振荡项的振幅相比,对总能,单调项远大于振幅;对化学势及磁矩,单调项与振幅几乎同一量级. 关键词： 强磁场 费米气体 相对论效应