Multiple band electron-phonon transport theory: I. Generating functional approach and generalized response

For an electron-phonon system with several equivalent bands a generalized transport and response theory is derived which serves as microscopic justification of a model for the structural phase transition in A15-compounds. By means of a generating functional approach a self-consistent formulation of the theory is achieved. The resulting set of coupled integral equations becomes closed within the ladder approximation. In particular, the functional formalism is used to calculate the generalized response occuring in a coupled electron-phonon system. In a subsequent paper a self-consistent solution of the coupled equation will be given with which the response functions are evaluated and discussed with recourse to the particularities of A15-compounds.     

Statistical theory of electron transport in open electron-phonon systems

Within the framework of general statistical mechanics of irreversible processes the electrical resistivity of an open electron-phonon system is calculated. By means of the projection operator technique an evolution equation for coupled subsystems in a heat bath is derived and specialized for electrons and longitudinal phonons, the latter being coupled to a bath of transverse phonons. The influence of heating of the electron-phonon system is investigated and the question of validity of the linear response theory with or without inclusion of a dissipative mechanism is discussed. In the balance equation for the total electron momentum, terms of only third (and higher) order in the electrical field strength and the current density appear; consequently, the transverse phonons act only as a “momentum bath”. A general resistivity formula is derived containing the Bloch-Grüneisen law as a special case and including corrections due to phonon drag up to infinite order without a partial summation.     

Derivation of the transport equation for electrons moving through random impurities

A single (nonrelativistic, spinless) electron subject to a constant external electric field interacts with impurities located on an infinitely extended lattice by a potential of random strength. The random strength is given by a field of Gaussian random variables. We show the existence of the averaged dynamics and prove that in the weak coupling limit, 0, ₂ t= fixed, one obtains the usual transport equation for the velocity distribution.Work supported by a Max Kade Foundation fellowship.On leave of absence of the Fachbereich Physik der Universität München.     

范德瓦尔斯方程的分子平均场理论推导

利用气体分子动理论和分子平均场理论,导出了真实气体物态方程--范德瓦尔斯方程,并与统计力学严格的理论推导结果作比较,得到了反映真实气体分子作用域大小的一个较为具体的参考值.     

A unified theory of matter. II. Derivation of the fundamental physical law

The equation for the fundamental field quantity ? is obtained. It is Div \(\rho ^\mu (\Omega _1 ) = \operatorname{h} \int {[\rho _\mu (\Omega _1 ),\rho ^\mu (\Omega _2 )]_ - \operatorname{d} \Omega _2 } \) ,where h is an arbitrary function oft andr, and [,]_? is the commutator. The derivation requires the following hypotheses:(1) All of physical reality is completely described by the field ?.(2) Relativistic covariance of the equations governing ?.(3) Principle of continguous action.(4) Conservation of total amount of ?. The equation appears to be unique. It is suggested that the physical world corresponds to ? being a2×2 matrix. A close correspondence between the basic equation and Maxwell's equation is displayed. The electromagnetic vector potential A^μ is identified with ε ρ^μ dΩ. Conservation laws on various measures of ? are obtained. The symmetry groups of the basic equation are derived. A preliminary attempt to connect the field ? to the metric is made via Einstein's gravitational equation G_μυ =_KT_μυ.     

Quantum theory as a description of robust experiments: Derivation of the Pauli equation

It is shown that the Pauli equation and the concept of spin naturally emerge from logical inference applied to experiments on a charged particle under the conditions that (i) space is homogeneous (ii) the observed events are logically independent, and (iii) the observed frequency distributions are robust with respect to small changes in the conditions under which the experiment is carried out. The derivation does not take recourse to concepts of quantum theory and is based on the same principles which have already been shown to lead to e.g. the Schrödinger equation and the probability distributions of pairs of particles in the singlet or triplet state. Application to Stern–Gerlach experiments with chargeless, magnetic particles, provides additional support for the thesis that quantum theory follows from logical inference applied to a well-defined class of experiments.     

Field theory onR×S 3 topology. II: The Weyl equation

A Weyl-type equation onR×S ³ topology is derived, as a generalization to previously obtained Klein-Gordon- and Schrödinger-type equations for the same topology. The general solution of the new equation is given as an expansion in the matrix elements of the irreducible representations of the groupSU ₂. The properties of the solutions are discussed.Supported in part by the Colgate Research Council.     

Derivation of the Simon equation

The form of the empirical Simon equation describing the dependence of the phase-transition temperature on pressure is shown to be asymptotically strict when the system tends to absolute zero of temperature, and then only for crystalline phases.     

Generalized Fokker-Planck equation: Derivation and exact solutions

We derive the generalized Fokker-Planck equation associated with the Langevin equation (in the Ito sense) for an overdamped particle in an external potential driven by multiplicative noise with an arbitrary distribution of the increments of the noise generating process. We explicitly consider this equation for various specific types of noises, including Poisson white noise and Lévy stable noise, and show that it reproduces all Fokker-Planck equations that are known for these noises. Exact analytical, time-dependent and stationary solutions of the generalized Fokker-Planck equation are derived and analyzed in detail for the cases of a linear, a quadratic, and a tailored potential.     

Renormalization of the electron-phonon interaction: a reformulation of the BCS-gap equation

A recently developed renormalization approach is used to study the electron-phonon coupling in many-electron systems. By starting from an Hamiltonian which includes a small gauge symmetry breaking field, we directly derive a BCS-like equation for the energy gap from the renormalization approach. The effective electron-electron interaction for Cooper pairs does not contain any singularities. Furthermore, it is found that phonon-induced particle-hole excitations only contribute to the attractive electron-electron interaction if their energy difference is smaller than the phonon energy.     

Derivation of non-Markovian transport equations for trapped cold atoms in nonequilibrium thermal field theory

The non-Markovian transport equations for the systems of cold Bose atoms confined by a external potential both without and with a Bose-Einstein condensate are derived in the framework of nonequilibrium thermal field theory (Thermo Field Dynamics). Our key elements are an explicit particle representation and a self-consistent renormalization condition which are essential in thermal field theory. The non-Markovian transport equation for the non-condensed system, derived at the two-loop level, is reduced in the Markovian limit to the ordinary quantum Boltzmann equation derived in the other methods. For the condensed system, we derive a new transport equation with an additional collision term which becomes important in the Landau instability.     

A fluctuation problem in particle transport theory II

A balance equation is formulated for the probability that a particle injected into an infinite, amorphous medium will have suffered N collisions and have given rise to n new particles in a given energy range at time t. The method of regeneration points has been employed and this leads, in the case of two particle production, to a non-linear, integro-differential equation for the probability generating function. This equation is solved for the case of foreign particles slowing down, in which case it becomes linear and results are obtained which include the effects of electronic stopping and absorption, thus generalizing the work in part I. In the cascade problem, a single particle gives rise to two new particles in every collision and it is shown, for a simple hard-sphere model with 1/v scattering and absorption, how the non-linear equation may be solved. The probability for the number of particles and the number of collisions suffered to absorption is obtained in the case of zero absorption, the probability law is shown to obey a Furry distribution. The limitations of the method described in part I for dealing with cascades are highlighted.     

Dynamical properties of colloidal systems: 1. Derivation of stochastic transport equations

To describe dynamical properties of a system of interacting Brownian particles stochastic transport equations are derived for the positions of the particles and their concentration fluctuations. This is achieved by an expansion of the Langevin equation for the momenta in terms of the reciprocal of the friction coefficient. As a by-product this procedure gives a new derivation of the generalized Smoluchowski equation. Using a local equilibrium approximation for the configurational distribution function a mode-mode coupling equation is derived for the local concentration, which still depends on the random forces of the solvent. For the interaction free case the relation to the ordinary diffusion approach is established.     

Complex quasiparticle band structure induced by electron-phonon interaction: band splitting in the 1x1H/W110 surface

We show that the self-consistent solution of the complex Dyson equation for the electron-phonon (EP) problem introduces many body effects which are often observed in photoemission experiments. The formalism is applied to the H covered W(110) surface, using first-principles results for the electronic and vibrational structure. We demonstrate that the measured spin-polarized surface band splitting [Phys. Rev. Lett. 84, 2925 (2000)10.1103/PhysRevLett.84.2925; 89, 216802 (2002)] can be traced back to different quasiparticle (QP) states induced by EP coupling. Despite the breakdown of the single QP picture, the spectral functions are very well represented by the predicted multiple QP structure.     

The complete system of algebraic invariants for the sixteen-vertex model: II. Derivation by means of the theory of algebraic invariants

The construction of a complete system of basic invariants for the sixteen-vertex model on an M x N lattice as described in part I is repeated by means of an alternative method based on the theory of algebraic invariants. We use a generalization of a theorem by Cayley and Sylvester to determine the characteristics of the covariants belonging to the basic system. In this way we arrive at the same set of 21 invariants that was found in part I. The present method offers the possibility of a generalization to the three-dimensional 64-vertex model and the vertex model on a triangular lattice.     

Quark-gluon transport theory I. The classical theory

A classical relativistic kinetic theory for a plasma with non-Abelian gauge interactions is formulated. After the local equilibrium solutions for the quark distribution function are found, the associated moment equations and their near-equilibrium expansion, leading to a set of relativistic chromohydrodynamical equations for viscous colored fluids, are studied.     

Ga和Sb纳米线声子结构和电子-声子相互作用的第一性原理研究

基于密度泛函理论的第一性原理方法,系统研究了Ga和Sb纳米线的电子能带结构和声子结构以及电子-声子耦合(EPC)作用.通过对声子的完整Brillouin区分析来研究纳米线的结构稳定性.结果表明,所考察的纳米线显示出不稳定性,不稳定声子波矢远离Brillouin区中心.与通常的Peierls变形机理相比,不稳定的横向声子模会导致一种无开口带隙的相变.Sb比Ga纳米线的EPC要强很多,并且横向变形导致的锯齿形结构使纳米线中的电子-声子相互作用增加了几个数量级.     

Derivation of transport equations for anharmonic lattices

Non-equilibrium properties of dielectric crystals are described using a Green function approach which represents transport phenomena by correlation functions of the equilibrium system. The equation which is equivalent to a Boltzmann equation for phonons is the integral equation for the vertex part corrections. Including all irreducible diagrams quadratic in the cubic and linear in the quartic anharmonicities the vertex part equation is reduced to a form which could be used as a starting point for numerical studies of microscopic models. The vertex part is also used to express the space and time variation of the phonon density and the frequency change of the phonons in response to an external displacement field. We also relate the integral equation for the vertex part to a form of the transport equation which is used in Landau's theory of quantum liquids.