Rate equations in the hopping transport

The rate equation formulation of the hopping transport problem is analyzed in detail. It is shown that the usual form of the rate equations for the system of electrons in localized states interacting with phonons is incorrect in the dc limit. A generalized form of the rate equations is derived. Both usual solution and that one corresponding to the result ofKasuya andKoide for the dc conductivity are shown to solve these equations. However, the former one is shown to be improper from the physical point of view as well as from the point of view of a (for a given model) exact asymptotic identity derived. For high frequencies, both forms of the rate equations are shown to be indistinguishable.     

Rate equations in the hopping transport

The usual kinetic equations for the site occupation probabilities in an external field are solved exactly in a simple one-dimensional periodic model with two kinds of atoms using a) free boundary conditions and order of limitsN, 0 needed for a proper treatment of the dc conductivity here b) boundary conditions with metallic contacts and order of limitsN, 0 and c) the same boundary conditions but reversed order of limiting processes 0,N typical of e.g. numerical and percolation treatments. (N and are the number of sites and frequency.) It is demonstrated that though the bulk dc conductivity is the same in all three cases, local bulk properties of the material are strongly dependent on the régime used. The role of the order of all three limiting processes 0,N+ andn+ (N–n+) for local shifts of the chemical potential _n in the dc limit is examined (n is the number of the relevant site calculated from a boundary of the chain). It is shown especially that the rate equation treatment (régime a) on the one hand and numerical or percolation treatments (régime c) on the other hand never yield the same bulk values of _r.     

An exactly solvable model of the phonon-assisted hopping dc conductivity

The model, which is commonly used to obtain the Mott law for the temperature dependence of the dc conductivity of elemental covalent amorphous semiconductors, is solved exactly in the case of small electron-phonon coupling. Differences between the Mott law and our solution are discussed.     

Polaron effect and the dc phonon-assisted hopping conductivity in amorphous semiconductors

A new small parameterW of off-diagonal electron-phonon matrix elements with respect to diagonal ones is introduced. Limiting ourselves to terms of the second order inW, the dc phonon assisted hopping conductivity is calculated to the infinite order in the electron-phonon coupling constant. Result clearly exhibits the polaron effect which is discussed in detail.     

Phononless hopping in the mobility gap of amorphous semiconductors

Two different theories are analyzed and shown to yield the same result for the phononless contribution to the dc hopping conductivity due to electrons in localized states (with single-electron energies broadened by the electron-phonon interaction) in the mobility gap of amorphous semiconductors. Numerical estimate is then used to show that this mechanism cannot explain experimental data on elemental covalent amorphous semiconductors.     

Variable range hopping and/or phonon-assisted tunneling mechanism of electronic transport in polymers and carbon nanotubes

We review and compare two models recently used to describe electronic transport in polymer fibers/nanotubes and carbon nanotubes including graphene nanoribbons, namely, variable range hopping (VRH) in different versions and their modifications on the one hand and electric-field-induced phonon-assisted tunneling (PhAT) on the other hand. The VRH model is mainly approved on behalf of the results of temperature dependences. However, the field dependencies of the conductivity in the framework of this model remain practically unexplained. At the same time, the PhAT model describes properly not only temperature dependence of conductivity measured in a wide temperature range, but also conductivity/current dependences on field strength using the same set of parameters characterizing the materials     

Spatial correlations and temperature dependence of the phonon-assisted hopping thermoelectric power in amorphous semiconductors

The assumption that the thermoelectric power of amorphous elemental semiconductors remains constant (in the hopping regime) down to zero temperature (which accords with some experiments on e.g. amorphous Ge performed above 100 K) is shown to be incompatible with the lowest order single-phonon hopping theory until the spatial interlevel correlations are taken into account.     

Separation of variables in the Klein-gordon equations. III

This paper supplements [1] and [2]. All kinds of external electromagnetic fields are found which contain arbitrary functions admitting complete separation of variables in the Klein-Gordon equations by using one first and two second order differential symmetry operators. The curvilinear coordinates in which the variables separate are presented, and equations in the separated variables are written down.     

A new interpretation of the Ψ-resonances

Recent experimental discoveries favor speculations that there may be several new “flavors” of tricolored quarks. We interpret the Ψ(3095) and Ψ′(3684) resonances as bound states composed of the two new quark flavors of electric charge 2/3 required by the minimal vectorlike theory of the weak interactions. Implications for e⁺e^?-annihilation and neutrino production are discussed.     

The density of states in the mobility gap of amorphous-silicon films computed by a new analytical method

Summary The field effect technique has been used to measure the density of states in the mobility gap of silicon films. We used a new method to compute the density of states distribution. The method is based on an analytical solution of the Fredholm integral equation, which relates the space charge density to the density of states. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

A theorem allowing the derivation of deterministic evolution equations from stochastic evolution equations. III The Markovian-non-Markovian mix

The proof of a theorem that allows one to construct deterministic evolution equations from a set, with two subsets, containing two types of discrete stochastic evolution equation is developed. One subset evolves Markovianly and the other non-Markovianly. As an illustrative example, the deterministic evolution equations of quantum electrodynamics are derived from two sets of Markovian and non-Markovian stochastic evolution equations, of different type, after an average over realization, using the theorem. This example shows that deterministic differential equations that contain both first-order and second-order time derivatives can be derived after a Taylor series expansion of the dynamical variables. It is shown that the derivation of such deterministic differential equations can be done by solving a set of linear equations. Two explicit examples, the first containing updating rules that depend on one previous time step and the second containing updating rules that depend on two previous time steps, are given in detail in order to show step by step the linear transformations that allow one to obtain the deterministic differential equations.     

A new interpretation of the fundamental exciton region in LiF

We have reanalyzed LiF optical data between 12 and 15 eV. We show that the conductivity spectrum can be fitted using effective mass theory for excitons with asymmetric Lorentzian lineshapes. We find the band gap is about 14.5 eV. The determination of the effective rydberg is not accurate enough to give the short-range correction to the hydrogenic energy for the n=1 state.     

On the variation of hopping transport in amorphous silicon with preparation conditions

Thedc conductivity of amorphous silicon prepared by two successive ion bombardments at different temperatures has been measured as a function of temperature. The results may be expressed in terms of a generalized hopping formula =₀ exp [–(T ₀/T) ⁿ where the parameter set {n,T ₀, ₀} varies with the irradiation conditions. In particular, the hopping exponent has been found to assume the limiting values ofn1/4 at irradiation temperatures ofT _i100 K and ofn1/2 atT _i500 K, whereas intermediate values ofn have been observed for temperatures inbetween. It is concluded that thermally activated redistribution processes of radiation defects control the final state of disorder in the irradiated samples, which in turn determines the particular hopping characteristics. Within the framework of existing theories the two limiting cases can be explained to be due to a disordered solid of homogeneous and granular structure, respectively.     

A new interpretation of the special theory of relativity

Assuming the “Big Bang” theory as well as the usual axioms in the Special Theory of Relativity, the time dilations and length contractions are treated as real physical effects. This becomes possible by relating everything to the hypothetical frame,S _a , at rest relative to the “Big Bang” event. This frame in many senses plays the role of the classical aether frame. A clock's real ryhthm, as opposed to its rhythm observed by restricted methods, is then a function of its velocity relative toS _a (assuming a uniform gravitational field). It is further assumed that gravitational radiation is composed of “electromagnetic-like” waves. Therefore when a clock changes its velocity in a uniform gravitational field it must receive a different total energy due to the average frequency shift (Doppler effect), the time dilations are then caused by the change in energy due to this frequency shift. That is, not wo clocks can be in the “same” gravitational field unless they have no relative velocity, and therefore the Special Theory of Relativity is a special case of the General Theory from this viewpoint. Two feasible experimental tests, using the Mössbauer effect, are described that would decide on these viewpoints. The principle of equivalence and the “twin paradox” are also discussed.