Diffusion blocking at low particle concentration

The rate equations describing classical particle hopping in periodic lattices are integrated to obtain exact, self-consistent expressions for the occupancy correlation functions at low atomic concentration. The long-wavelength, small-frequency behaviour is analyzed analytically. Exact results for labelled particle diffusion are obtained which properly include the correlation and atomic blocking effects.     

On the solutions of the infinite U Hubbard model through orthofermions

We reinforce our earlier arguments for the soundness of the orthofermion approach to the infinite U Hubbard model by studying the distribution and the partition functions for a system of noninteracting orthofermions as well as for two systems of noninteracting orthofermions coupled through inter system single particle hopping.     

On the approach to kinetic theory due to Gross

A classical kinetic theory introduced by Gross is explored in further detail. The theory consists of a sequence of approximations to the Liouville distribution function, with each approximation leading to a truncation of the BBGKY hierarchy at successively higher order. We formulate the truncation scheme at general order in terms of a set of time-dependent equilibrium correlation functions. It has the correct symmetries and, as is implied by the work of Gross with the first two approximations, is such that the interparticle potential appears only implicitly via static equilibrium correlation functions. We arrange the theory as a sequence of linear kinetic equations for the phase-space density correlation function, and solve for the collision kernels which result in each order. The collision kernel of the second approximation, which involves only binary dynamics, is shown to be a mean-field generalization of the known low-density kernel. The third approximation gives a similar generalization of the triple-collision kernel. The nth approximation also reproduces the frequency moments of S(kω) through order ω²ⁿ. More generally, the approximations are shown to give a continued-fraction expansion of the collision kernel, with the levels governed by the dynamics of successively larger numbers of particles. This is a renormalized kinetic theory in the sense that the potential is eliminated and clusters of particles are never isolated.     

Velocity and diffusion constant of a periodic one-dimensional hopping model

The velocity and the diffusion constant are obtained for a periodic onedimensional hopping model of arbitrary periodN. These two quantities are expressed as explicit functions of all the hopping rates. The velocity and the diffusion constant of random systems are calculated by taking the limit N→Β. One finds by varying the distribution of hopping rates that the diffusion constant and the velocity are singular at different points. Lastly, several possible applications are proposed.     

Parton distribution functions from the precise NNLO QCD fit

We report on the parton distribution functions (PDFs) determined from the NNLO QCD analysis of the world inclusive DIS data with account for the precise NNLO QCD corrections to the evolution equations kernel. The value of the strong coupling constant α _s ^NNLO (M _Z ) = 0.1141 ± 0.0014 (exp.), in fair agreement with the one obtained using the earlier approximate NNLO kernel by van Neerven-Vogt. The intermediate bosons rates calculated in the NNLO using the obtained PDFs are in agreement with the latest Run II results.     

Reply to: “Comment on: ‘Effects of including the counterrotating term and virtual photons on the eigenfunctions and eigenvalues of a scalar photon collective emission theory’ [Phys. Lett. A 372 (2008) 2514]” [Phys. Lett. A 372 (2008) 5732]

We compute the emission amplitude for the collective emission from a sphere of identical atoms in the scalar photon theory for both the cases of the complex kernel (i.e. including virtual photons) and real kernel. We explicitly show that the single mode theory based on the real kernel neglects the effects of the different decay rates and frequency shifts associated with the eigenfunctions belonging to the same angular index but with different radial indices. We show that these effects modify, for k₀R?1, both the time dependence of the emission amplitude and its angular distribution, in clear contradiction to the assertions made by the Comment's authors.     

Field theory of the random flux model

The random flux model (defined here as a model of lattice fermions hopping under the influence of maximally random link disorder) is analysed field theoretically. It is shown that the long range physics of the model is described by the supersymmetric version of a field theory that has been derived earlier in connection with lattice fermions subject to weak random hopping. More precisely, the field theory relevant for the behaviour of n-point correlation functions is of non-linear σ model type, where the group GL(n|n) is the global invariant manifold. It is argued that the model universally describes the long range physics of random phase fermions and provides further evidence in favour of the existence of delocalised states in the middle of the band in two dimensions. The same formalism is applied to the study of non-Abelian generalisations of the random flux model, i.e. N-component fermions whose hopping is mediated by random U(N) matrices. We discuss some physical applications of these models and argue that, for sufficiently large N, the existence of long range correlations in the band centre (equivalent to metallic behaviour in the Abelian case) can be safely deduced from the RG analysis of the model.     

Source Identities and Kernel Functions for Deformed (Quantum) Ruijsenaars Models

We consider the relativistic generalization of the quantum A _N-1 Calogero–Sutherland models due to Ruijsenaars, comprising the rational, hyperbolic, trigonometric and elliptic cases. For each of these cases, we find an exact common eigenfunction for a generalization of Ruijsenaars analytic difference operators that gives, as special cases, many different kernel functions; in particular, we find kernel functions for Chalykh–Feigin–Veselov–Sergeev-type deformations of such difference operators which generalize known kernel functions for the Ruijsenaars models. We also discuss possible applications of our results.     

Ferromagnetism in the two-dimensional Hubbard model with long-range hopping

The combination of small-cluster exact-diagonalization calculations and the quantum Monte Carlo method is used to examine ferromagnetism in the two-dimensional Hubbard model with a generalized type of hopping. It is found that the long-range hopping with exponentially decaying hopping amplitudes t _ij ～ ? q ^Ri?Rj stabilizes the ferromagnetic state for a wide range of electron interactions U and electron concentrations n > 1. The critical value of the hopping parameter q _c above which the ferromagnetic state becomes stable is calculated numerically and the ground-state phase diagram of the model is discussed for physically the most interesting cases.     

Low-temperature hopping conduction over the upper Hubbard band in p-GaAs/AlGaAs multilayered structures

The low-temperature 2D variable range hopping conduction over the states of the upper Hubbard band is investigated in detail for the first time in multilayered Be-doped p-type GaAs/AlGaAs structures with quantum wells of 15-nm width. This situation was realized by doping the layer in the well and a barrier layer close to the well for the upper Hubbard band (A ⁺ centers) in the equilibrium state filled with holes. The conduction was of the Mott hopping type in the entire temperature range (4?0.4 K). The positive and negative magnetoresistance branches as well as of non-Ohmic hopping conduction at low temperature are analyzed. The density of states and the localization radius, the scattering amplitude, and the number of scatterers in the upper Hubbard band are estimated. It is found that the interference pattern of phenomena associated with hopping conduction over the A ⁺ band is qualitatively similar to the corresponding pattern for an ordinary impurity band, but the tunnel scattering is relatively weak.     

Diffusion-limited annihilation in inhomogeneous environments

We study diffusion-limited (on-site) pair annihilation A + A → 0 and (on-site) fusion A + A → A which we show to be equivalent for arbitrary space-dependent diffusion and reaction rates. For one-dimensional lattices with nearest neighbour hopping we find that in the limit of infinite reaction rate the time-dependent n-point density correlations for many-particle initial states are determined by the correlation functions of a dual diffusion-limited annihilation process with at most 2n particles initially. Furthermore, by reformulating general properties of annihilating random walks in one dimension in terms of fermionic anticommutation relations we derive an exact representation for these correlation functions in terms of conditional probabilities for a single particle performing a random walk with dual hopping rates. This allows for the exact and explicit calculation of a wide range of universal and non-universal types of behaviour for the decay of the density and density correlations.     

Fourier-Gauss transforms of bilinear generating functions for the continuous q-Hermite polynomials

The classical Fourier-Gauss transforms of bilinear generating functions for the continuous q-Hermite polynomials of Rogers are studied in detail. Our approach is essentially based on the fact that the q-Hermite functions have simple behavior with respect to the Fourier integral transform with the q-independent exponential kernel.     

Controlled delocalization of electronic states in a multi-strand quasiperiodic lattice

Finite strips, composed of a periodic stacking of infinite quasiperiodic Fibonacci chains, have been investigated in terms of their electronic properties. The system is described by a tight binding Hamiltonian. The eigenvalue spectrum of such a multi-strand quasiperiodic network is found to be sensitive on the mutual values of the intra-strand and inter-strand tunnel hoppings, whose distribution displays a unique three-subband self-similar pattern in a parameter subspace. In addition, it is observed that special numerical correlations between the nearest and the next-nearest neighbor hopping integrals can render a substantial part of the energy spectrum absolutely continuous. Extended, Bloch like functions populate the above continuous zones, signalling a complete delocalization of single particle states even in such a non-translationally invariant system, and more importantly, a phenomenon that can be engineered by tuning the relative strengths of the hopping parameters. A commutation relation between the potential and the hopping matrices enables us to work out the precise correlation which helps to engineer the extended eigenfunctions and determine the band positions at will.     

Coarse-grained kinetic equations for quantum systems

The nonequilibrium density matrix method is employed to derive a master equation for the averaged state populations of an open quantum system subjected to an external high frequency stochastic field. It is shown that if the characteristic time τ_stoch of the stochastic process is much lower than the characteristic time τ_steady of the establishment of the system steady state populations, then on the time scale Δt ～ τ_steady, the evolution of the system populations can be described by the coarse-grained kinetic equations with the averaged transition rates. As an example, the exact averaging is carried out for the dichotomous Markov process of the kangaroo type.     

A model of hopping and band DC photoconduction in doped crystals

Expressions for the screening length and the ambipolar diffusion length are derived, for the first time, for the case where hopping conduction and band conduction coexist in semiconductors with hydrogen-like impurities. A method is proposed for calculating the diffusion coefficient of electrons (holes) hopping between impurity atoms from data on the Hall effect, in the case where the hopping and band conductivities are equal. An interpretation is given of available experimental data on hopping photoconduction between acceptors (Ga) and donors (As) in p-Ge at T=4.2 K doped by a transmutation method. It is shown that the relative magnitude of the mobilities of electrons hopping between donors and holes hopping between acceptors can be found from the hopping photoconductivity measured as a function of the intensity of band-to-band optical carrier excitation.     

A.C. hopping conductivity in VO2

The a.c. hopping conductivity is investigated in VO₂ between 25 kHz and 10⁹ Hz as a function of temperature. The ω^s law with 0.7 < s < 1 is observed over a large range of frequencies, which is interpreted in terms of electron hopping among a wide distribution of localized levels. A detailed analysis of the results leads to the conclusion that two hopping processes are involved: a low frequency process, thermally excited with an activation energy of 30 meV, with a cutoff frequency of about 10⁸ Hz, and a high frequency process, extending to very high frequencies and nearly temperature independent.     

Constant dielectric loss in disordered ionic conductors: Theoretical aspects

Cooperative charge relaxation within a random system of electrostatically interacting defect centers provides a mechanism for a “nearly constant dielectric loss” (NCL) response in structurally disordered ionic conductors. Pertinent models based on statistical mechanics are reviewed briefly. In addition, we present a theoretical frame for the problem of how two kinds of ionic motion, hopping migration and NCL-type local charge relaxation, are superimposed in the total ac-response. Using renewal theory, the modification of NCL-spectra due to hopping is calculated in terms of the waiting time distribution for ionic hops. In the special case of Poissonian hops with average rate λ the modified complex dielectric susceptibility in the NCL-regime is obtained by analytic continuation from the corresponding susceptibility in the absence of hops. Implications with respect to the crossover between hopping transport and NCL-behavior are discussed.     

Effect of Cd on the structural, magnetic and electrical properties of nanostructured Mn-Zn ferrite

Nanoparticles of Mn_0.5Zn_0.5−xCd_xFe₂O₄ (x=0.0, 0.1, 0.2 and 0.3) have been synthesized by a chemical co-precipitation method. The lattice constant increases with increasing Cd content. X-ray calculations indicate that there is deviation in the cation distribution in the nanostructured spinel ferrite. The dielectric constant and dielectric loss decrease for the samples with Cd content up to x=0.2. However the dielectric constant rises for x=0.3. This is due to an increase in the hopping process at the octahedral (B sites). The dielectric constant increases with increase in temperature, indicating a thermally activated hopping process. The DC resistivity increases with Cd content up to x=0.2 and decreases for Cd content x=0.3. The maximum magnetization of all the samples decreases with increase in Cd content.     

Exact phase space localized projectors from energy eigenstates

In investigations of the emergence of classicality from quantum theory, a useful step is the construction of quantum operators corresponding to the classical notion that the system resides in a region of phase space. The simplest such constructions are approximate projection operators. Here, we show how to construct exact projection operators which are localized on regions of phase. We elucidate the properties of such operators and explore their time evolution. For the harmonic oscillator we find sets of phase space localized histories which are exactly decoherent for any initial state and have probability 1 for classical evolution.     

Classical density functional theory meets Monte-Carlo simulations

ABSTRACT

Typically the quality of an approximate density functional is evaluated by a direct comparison of its predictions in a given test case to exact data obtained by computer simulations. An important example for such an approach is the test of equilibrium structure of a simple fluid as measured by the pair distribution function g(r) or the cavity correlation function y(r). However, the combination of exact density profiles and the analytical structure of density functional theory allows one to determine and potentially improve the quality of a functional in a more sophisticatedway.