Nonequilibrium Green’s function method for quantum thermal transport

This review deals with the nonequilibrium Green’s function (NEGF) method applied to the problems of energy transport due to atomic vibrations (phonons), primarily for small junction systems. We present a pedagogical introduction to the subject, deriving some of the well-known results such as the Laudauer-like formula for heat current in ballistic systems. The main aim of the review is to build the machinery of the method so that it can be applied to other situations, which are not directly treated here. In addition to the above, we consider a number of applications of NEGF, not in routine model system calculations, but in a few new aspects showing the power and usefulness of the formalism. In particular, we discuss the problems of multiple leads, coupled left-right-lead system, and system without a center. We also apply the method to the problem of full counting statistics. In the case of nonlinear systems, we make general comments on the thermal expansion effect, phonon relaxation time, and a certain class of mean-field approximations. Lastly, we examine the relationship between NEGF, reduced density matrix, and master equation approaches to thermal transport.     

Solutions of Two Kinds of Non-Isospectral Generalized Nonlinear Schrodinger Equation Related to Bose-Einstein Condensates

Two non-isospectral generalized nonlinear Schrodinger （ONLS） equations, which are two important models of nonlinear excitations of matter waves in Bose-Einstein condensates, are studied. Two novel transformations are constructed such that these two GNLS equations are transformed to the well-known nonlinear Schr6dinger （NLS） equation, which is an isospectral equation. Therefore, once one solution of the NLS equation is provided, we can immediately obtain one solution for two ONLS equations by these transformations. Thus it is unnecessary to solve these two non-isospectral GNLS equations directly. Soliton solutions and periodic solutions are obtained for them by two transformations from the corresponding solutions of the NLS equation, which are generated by Darboux transformation.     

PROPAGATION OF TWIST SOLITONS IN FULLY INHOMOGENEOUS DNA CHAINS

In the framework of a recently introduced model of DNA torsional dynamics, we argued — on the basis of perturbative considerations — that an inhomogeneous DNA chain could support long-lived soliton-type excitations due to the peculiar geometric structure of DNA and the effect of this on nonlinear torsional dynamics. Here we consider an inhomogeneous version of this model of DNA torsional dynamics, and investigate numerically the propagation of solitons in a DNA chain with a real base sequence (corresponding to the Human Adenovirus 2); this implies inhomogeneities of up to 50% in the base masses and inter-pair interactions. We find that twist solitons propagate for considerable distances (2–10 times their diameters) before stopping due to phonon emission. Our results show that twist solitons may exist in realistic DNA chain models, and on a more general level that solitonic propagation can take place in highly inhomogeneous media. The most relevant feature for general nonlinear dynamics is that we identify the physical mechanisms allowing this behavior and thus the class of models candidate to support long-lived soliton-type excitations in the presence of significant inhomogeneities.     

Testing a New Class of Phonon Operators for RPA-Like Calculations Within an Exactly Solvable Model

Working in a boson formalism, we introduce a phonon operator different from that commonly used in RPA calculations. As a major feature, this new phonon operator has a vacuum carrying only a limited number of particle-hole excitations. Therefore, the form of this vacuum is quite different from the exponential one of the RPA. In addition, multiphonon excitations have a particle-hole structure never exceeding in complexity that of this vacuum, no matter how large is the number of phonons involved. We present the results of some preliminary tests performed within the exactly solvable two-level Lipkin model.     

On the effect of phonon decay on electronic transitions in ionic crystal semiconductors

Generally electronic processes in semiconductors are accompanied by phonon excitations. These excitations themselves influence electronic transitions. On the other hand excited phonons decay by interaction with other impurities in the crystal, which act as a heat-bath. The resulting competition between phonon exciting electronic processes and phonon decay is described by Pauli's master equation. By expansion of its solutions into phonon decay solutions the problem can be separated into different decay equations for phonons and electrons as proposed by Stumpf. Assuming linear phonon-heat-bath coupling the phonon decay equation can be solved exactly by a generating function technique. The appropriate phonon decay frequencies are calculated for a simple heat-bath model.     

声子色散对抛物量子点中极化子基态能量的影响

在声子色散影响下利用压缩态变分法计算了抛物量子点中弱耦合极化子的基态能量。采用的变分方法是基于逐次正则并且利用单模压缩态变换处理通常被我们所忽略的在第一次幺正变换中产生的声子产生湮灭算符的双线性项。计算得出了在考虑声子色散的情况下抛物量子点中弱耦合极化子的基态能量的数学表达式。讨论了抛物量子点中在电子-声子弱耦合情况下,受限长度,电子-声子耦合常数,色散系数与极化子基态能量之间的依赖关系。     

Renormalization of the energy spectrum of quantum dots under vibrational resonance conditions: Persistent hole burning spectroscopy

A theory of photophysical burning of spectral holes in an inhomogeneously broadened light absorption profile of spherical quantum dots under vibrational resonance conditions is developed. The energy spectrum and the eigenfunctions of polaron-like excitations that arise in a quantum dot when the energy of an optical phonon is close to the energy gap between some pair of levels of the quantum dot electron subsystem are found by the method of canonical transformations. Expressions describing the difference light absorption spectra of quantum dots in the regimes of strong and weak confinement are obtained within a simple kinetic model.     

声子色散和库仑势对量子点中极化子基态能量的影响

本文在声子色散和库仑束缚势的影响下利用压缩态变分法计算了抛物量子点中弱耦合极化子的基态能量。采用的变分方法是基于逐次正则并且利用单模压缩态变换处理通常被我们所忽略的在第一次幺正变换中产生的声子产生湮灭算符的双线性项。计算得出了在考虑声子色散和库仑束缚势的情况下抛物量子点中弱耦合极化子的基态能量的数学表达式。讨论了在弱耦合情况下,受限长度,电子-声子耦合常数,色散系数,库仑结合参数与基态能量之间的依赖关系。     

Geometrical coupling between inhomogeneous strain fields: Application to fluctuations in ferroelastics

The compatibility conditions of elasticity theory are applied to the calculation of strain fluctuations in ferroelastic materials. A ferroelastic transition with an acoustic phonon mode instability and an order-disorder transition with striction are considered in the framework of the Landau-Ginzburg functional. Anisotropy of strain correlation functions and their critical behaviour in the symmetric phase near the transition point are analysed and compared with the results of the Ornstein-Zernike theory of fluctuations. Characteristic shape of the correlation functions (“butterflies”) are predicted.     

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.     

离子晶格非简谐振动引起的光学非线性与增强吸收型光双稳

处理了光场（电磁场）与离子晶体的非简谐性振动之间的相互作用问题。导出了用简正坐标即声子模式所表达的非线性晶格动力学和非线性宏观极化。在旋转波近似下，得到在入射光驱动下光子－声子耦合体系的总的相干性哈密顿算符。通过相应的静态方程证明该耦合系统会出现增强吸收型光学双稳性，这也就证明了光场与各种玻色子型固体元激发，如光频支声子和半导体中激子的非线性耦合可以作为增强吸收型光双稳的机制。     

Interactions Between Solitons and Cnoidal Periodic Waves of the (2+1)-Dimensional Konopelchenko-Dubrovsky Equation

The (2+1)-dimensional Konopelchenko-Dubrovsky equation is an important prototypic model in nonlinear physics, which can be applied to many fields. Various nonlinear excitations of the (2+1)-dimensional Konopelchenko-Dubrovsky equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this paper, with the help of the Riccati equation, the (2+1)-dimensional Konopelchenko-Dubrovsky equation is solved by the consistent Riccati expansion (CRE). Furthermore, we obtain the soliton-cnoidal wave interaction solution of the (2+1)-dimensional Konopelchenko-Dubrovsky equation.     

Spin-P honon Renormalization of the Excitation Energy in a Diluted Two-Dimensional Ferromagnet

The contribution of spin-lattice coupling to the phonon self-energy is calculated for a diluted two-dimensional "soft" ferromagnet. The calculations are based on a bond percolation model. Numerical results are presented for the dampings of phonon excitations. At low temperature, the damping rate is much smaller than the frequency of excitations, leading to well-defined phonons. The overall features of the Г ( q ) curves possess similar characteristics: Г ( q ) has two maximum points at qa ≈ 0.5 and qa ≈ 1.7, the value of the latter is much larger than the former. The temperature-dependent phonon line widths arising from spinlattice coupling are also presented. We point out the sensitivity of the interaction on bond concentration of the network.     

Shocks near jamming

Nonlinear sound is an extreme phenomenon typically observed in solids after violent explosions. But granular media are different. Right when they jam, these fragile and disordered solids exhibit a vanishing rigidity and sound speed, so that even tiny mechanical perturbations form supersonic shocks. Here, we perform simulations in which two-dimensional jammed granular packings are dynamically compressed and demonstrate that the elementary excitations are strongly nonlinear shocks, rather than ordinary phonons. We capture the full dependence of the shock speed on pressure and impact intensity by a surprisingly simple analytical model.     

Two-polaron energy diffusion in a 1D lattice of hydrogen bonded peptide units

A generalized Pauli master equation is established for describing the vibrational energy flow in a 1D lattice of hydrogen bounded peptide units. A Lang-Firsov transformation is applied so that the relevant excitations are small polarons corresponding to vibrational excitons dressed by virtual phonons. A special attention is thus paid to characterize the energy transfer mediated by two polarons. At biological temperature, it is shown that the polaron-phonon coupling is sufficiently strong to prevent any coherent motion. The polaron-polaron interaction occurring in such a nonlinear lattice does not affect the long time behavior of the energy flow which results from the diffusion of two independent polarons. This diffusive motion originates from the competition between two contributions related to phonon mediated transitions (incoherent contribution) and to dephasing limited coherent motion (coherent contribution).     

Spin reorientation and magnon-phonon hybridization in a ferromagnet

A model is presented for the magnetic excitations and magnon-phonon coupling in a localised moment ferromagnet in which spins can reorientate by application of a magnetic field. The model is suitable for those materials which possess a spin wave gap at zero wave vector and therefore the magnon and acoustic phonon branches can intersect. A magnon-phonon coupling linear in both spin and phonon operators is employed which has proved successful for the ferrous salts. The main effect of the applied field is to modify the spin wave gap, and to introduce a critical value for the coupling constant which enables the system to remain stable as the gap goes to zero. Furthermore the wave vector of the anticrossing point decreases as the spin wave gap increases and therefore the value of the sound velocity determined by high resolution inelastic neutron experiments is dependent on the gap.     

Study of Two-Mode Squeezed Magnetopolarons

In this paper, we conduct an investigation into two-dimensional squeezed magnetopolarons. The Hamiltonian of magnetopolarons is dealt with two-mode squeezed states transformation, which is based on the Lee-Low-Pines and Huybrechts （LLP-H） canonical transformations. This method makes it possible to take account of the linear terms, bilinear ones of phonon operators, and the correlation between two longitudinal optical （LO） phonon modes. The energies of the ground state and excited states are evaluated by variational approach, and accurate results are obtained. Furthermore, the renormalized cyclotron masses for some possible transitions are discussed in detail.     

Dispersive effects and correction term in two-mode phonon conduction model for Ge

A complete analysis of the phonon conductivity κ, still lacking in the literature, is presented in the two-mode conduction model for Germanium. First a method is derived from which the correction term κ_c of the Callaway model is separated into its longitudinal and transverse parts and then the effects of strong phonon dispersion and the role of longitudinal and transverse phonons on κ_c are studied. For this purpose we have also proposed some new empirical expressions for the three phonon relaxation rates τ_3ph⁻¹'s which are valid in the entire temperature range. This improvised model, when applied simultaneously to the phonon conductivity data of both normal and enriched Ge, yields some new results. These are (i) κ_c neglected by the earlier workers in the two-mode phonon conduction model, gives a substantial contribution beyond the conductivity maximum and (ii) the longitudinal phonons are the major carriers of heat at high temperature.     

Complete and orthonormal eigenfunctions of excitations to a one-dimensional dark soliton

We study linear excitations to a one-dimensional dark soliton described by a defocusing nonlinear Schödinger equation. By solving an eigenvalue problem for the excitations we obtain all eigenvalues and eigenfunctions and prove rigorously that these eigenfunctions are orthonormal and form a complete set. We then use the eigenfunctions to obtain the exact form of linear excitations for any given initial condition and to investigate the transverse stability of the dark soliton. The rigorous results reported in the present work can be applied to study the dynamics of dark solitons in various nonlinear optical media and Bose-Einstein condensates.