Topological Invariants in Terms of Green's Function for the Interacting Kitaev Chain

A one-dimensional closed interacting Kitaev chain and the dimerized version are studied. The topological invariants in terms of Green's function are calculated by the density matrix renormalization group method and the exact diagonalization method. For the interacting Kitaev chain, we point out that the calculation of the topological invariant in the charge density wave phase must consider the dimerized configuration of the ground states. The variation of the topological invariant is attributed to the poles of eigenvalues of the zero-frequency Green functions. For the interacting dimerized Kitaev chain, we show that the topological invariant defined by Green's functions can distinguish more topological nonequivalent phases than the fermion parity.     

First-passage Monte Carlo algorithm: diffusion without all the hops

We present a novel Monte Carlo algorithm for N diffusing finite particles that react on collisions. Using the theory of first-passage processes and time dependent Green's functions, we break the difficult N-body problem into independent single- and two-body propagations circumventing numerous diffusion hops used in standard Monte Carlo simulations. The new algorithm is exact, extremely efficient, and applicable to many important physical situations in arbitrary integer dimensions.     

含有五边形—七边形缺陷的单壁纳米碳管的输运性质研究

运用第一性原理的密度泛函理论结合非平衡格林函数研究了含有五边形—七边形拓扑缺陷的纳米碳管异质结的输运性质.结果发现：拓扑缺陷对碳管的输运性质有很大影响；另外，不同类型的碳管形成的异质结的输运性质也有明显的差异. 关键词： 纳米碳管 输运性质 异质结 透射系数     

Observation of restricted diffusion in the presence of a free diffusion compartment: Single- and double-PFG experiments

Theoretical and experimental studies of restricted diffusion have been conducted for decades using single pulsed field gradient (s-PFG) diffusion experiments. In homogenous samples, the diffusion–diffraction phenomenon arising from a single population of diffusing species has been observed experimentally and predicted theoretically. In this study, we introduce a composite bi-compartmental model which superposes restricted diffusion in microcapillaries with free diffusion in an unconfined compartment, leading to fast and slow diffusing components in the NMR signal decay. Although simplified (no exchange), the superposed diffusion modes in this model may exhibit features seen in more complex porous materials and biological tissues. We find that at low q-values the freely diffusing component masks the restricted diffusion component, and that prolongation of the diffusion time shifts the transition from free to restricted profiles to lower q-values. The effect of increasing the volume fraction of freely diffusing water was also studied; we find that the transition in the signal decay from the free mode to the restricted mode occurs at higher q-values when the volume fraction of the freely diffusing water is increased. These findings were then applied to a phantom consisting of crossing fibers, which demonstrated the same qualitative trends in the signal decay. The angular d-PGSE experiment, which has been recently shown to be able to measure small compartmental dimensions even at low q-values, revealed that microscopic anisotropy is lost at low q-values where the fast diffusing component is prominent. Our findings may be of importance in studying realistic systems which exhibit compartmentation.     

Localized partial traps in diffusion processes and random walks

Reaction-diffusion equations, in which the reaction is described by a sink term consisting of a sum of delta functions, are studied. It is shown that the Laplace transform of the reactive Green's function can be analytically expressed in terms of the Green's function for diffusion in the absence of reaction. Moreover, a simple relation between the Green's functions satisfying the radiation boundary condition and the reflecting boundary condition is obtained. Several applications are presented and the formalism is used to establish the relationship between the time-dependent geminate recombination yield and the bimolecular reaction rate for diffusion-influenced reactions. Finally, an analogous development for lattice random walks is presented.     

The asymptotic behaviour of the exact and approximative ν = 1/2 Chern-Simons Green's functions

We consider the asymptotic behaviour of the Chern-Simons Green's function of the ν = 1/ system for an infinite area in position-time representation. We calculate explicitly the asymptotic form of the Green's function of the interaction free Chern-Simons system for small times. The calculated Green's function vanishes exponentially with the logarithm of the area. Furthermore, we discuss the form of the divergence for all τ and also for the Coulomb interacting Chern-Simons system. We compare the asymptotics of the exact Chern-Simons Green's function with the asymptotics of the Green's function in the Hartree-Fock as well as the random-phase approximation (RPA). The asymptotics of the Hartree-Fock Green's function correspondence well with the exact Green's function. In the case of the RPA Green's function we do not get the correct asymptotics. At last, we calculate the self consistent Hartree-Fock Green's function. Received 5 July 2001 and Received in final form 30 November 2001     

Diffusion along the Grain Boundaries in Crystals with Dislocations

A generalization of the Fisher model of the grain boundary diffusion is suggested, which takes into account the diffusion along short circuit diffusion paths (i.e., dislocations) in the bulk of crystalline grains. For the B-regime of the grain boundary diffusion, three different penetration modes have been found: at the short times the penetration depth of the element diffusing along the grain boundary is given by the Whipple solution of the Fisher model, but with the pipe diffusion coefficients along the dislocation cores instead of the volume diffusivities; at the intermediate times the penetration depth is a weak function of time, and at the large times the penetration depth again increases with time according to the Whipple solution, however, the rate of this increase is much smaller than in the initial period of time. The applications of the model for diffusion in nanomaterials are discussed.     

Simultaneous diffusion of a radio-isotope by two different modes: Sulfur-35 in nickel oxide crystals

Anomalous diffusion behavior may occur when the same diffusing species can occupy two different lattice sites in the base compound. In an ionic crystals, the same diffusing species may occupy two different lattice sites and become positively or negatively ionized. When the reaction rate is negligibly small between these two oppositely charged diffusing ions, the diffusion proceeds by a double mode independent diffusion mechanism. An application is given to sulphur tracer diffusion in nickel oxide. The ionization status of sulfur in nickel oxide is also discussed.     

Point source of polarized resonance radiation in an unbounded medium

The diffusion of polarized resonance radiation is considered. An explicit expression is given for the Green's function of the corresponding equation for an unbounded uniform space.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 53–58, April, 1974.     

Efficient Evaluation of the Green's Function for an Array of Magnetic-Current Sheets Periodically Located on the Surface of a Metal Cylinder

We propose an effective method for calculating the Green's function of an array of identical magnetic-current sheets periodically located on the surface of a circular metal cylinder. The idea of our approach consists in that we explicitly isolate the field singularity at the source by improving the convergence in the Green's function representation. As a result, the residual part of the Green's function can efficiently be calculated numerically. We present numerical results showing the behavior of the Green's function. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 4, pp. 331–339, April 2005     

The Motion of Repulsive Brownian Particles in Quenched Disorder

Brownian motion of the particles with repulsive interaction is investigated. When the potential condition is satisfied, the eigenvalue problem of interaction Fokker-Planck equation under certain conditions can be transformed to that of a many-particle Schrödinger equation. Using the Green's function method, we obtain the effective single-variable Fokker-Planck equation in the low density limit. We find that the diffusion of coupled Brownian particles in quenched disorder media is also anomalous in 2D. The Mittag-Leffler relaxation of pancake vortices is investigated by fractional Fokker-Planck equation.     

Topological order parameters for interacting topological insulators

We propose a topological order parameter for interacting topological insulators, expressed in terms of the full Green's functions of the interacting system. We show that it is exactly quantized for a time-reversal invariant topological insulator, and it can be experimentally measured through the topological magneto-electric effect. This topological order parameter can be applied to both interacting and disordered systems, and used for determining their phase diagrams.     

Comparison between radiative transfer theory and the simplified spherical harmonics approximation for a semi-infinite geometry

In this study, the third-order simplified spherical harmonics equations (SP3), an approximation of the radiative transfer equation, are solved for a semi-infinite geometry considering the exact simplified spherical harmonics boundary conditions. The obtained Green's function is compared to radiative transfer calculations and the diffusion theory. In general, it is shown that the SP3 equations provide better results than the diffusion approximation in media with high absorption coefficient values but no improvement is found for small distances to the source.     

Nonlocal transport of passive scalars in turbulent penetrative convection

We present a Green's function approach for quantifying the transport of a passive scalar (tracer) field in three-dimensional simulations of turbulent convection. Nonlocal, nondiffusive behavior is described by a transilient matrix (the discretized Green's function), whose elements contain the fractional tracer concentrations moving from one subvolume to another as a function of time. The approach was originally developed for and applied to geophysical flows, but here we extend the formalism and apply it in an astrophysical context to three-dimensional simulations of turbulent compressible convection with overshoot into convectively stable bounding regions. We introduce a novel technique to compute this matrix in a single simulation by advecting labeled particles rather than solving the passive scalar equation for a large number of different initial conditions. The transilient matrices thus computed are used as a diagnostic tool to quantitatively describe nonlocal transport via matrix moments and transport coefficients in a generalized, multiorder diffusion equation. Results indicate that transport in both the vertical and horizontal directions is strongly influenced by the presence of coherent velocity structures, generally resembling ballistic advection more than diffusion. The transport of a small fraction of tracer particles deep into the underlying stable region is reasonably efficient, a result which has possible implications for the problem of light-element depletion in late-type stars.     

The Kinetics of the Coordination Transformation for Preparation of Nanosized CdS in a PVA Film

Research on the preparation kinetics of nanosized materials is considered. The layered diffusion model (LDM) for S^2? diffusing in a polymer–metal complex film, used for preparation of nanosized semiconductor metal sulfide by a coordination transformation method, is briefly introduced. An indirect measurement was employed to determine the concentration of residual S^2? in the solution during the diffusion in a PVA–Cd²⁺ complex film. The relationship between the diffusion amount and the diffusion time shows that the diffusion curves are independent of the amount of Cd²⁺ in the film when the total amount of S^2? is less than that of Cd²⁺. The experimental phenomena coincide basically with the theoretical curves deduced from LDM; thus they provide a proof for the LDM and the diffusion equations. The diffusion constant of S^2? diffusing in PVA–Cd²⁺ complex film is about 1.7×10^?3 cm²/s.     

A diffusion problem in a region with a moving boundary

We consider the first linear diffusion problem in a semiinfinite region with a boundary moving in accordance with a quadratic law. For the case of uniformly decelerating motion of the boundary, the solution of the problem is obtained by the Green's function, method under the most general boundary conditions; the solution of the problem for the case of uniformly accelerated motion of the boundary is obtained by an operator method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 102–110, December, 1970.     

Multiple scattering of light in superdiffusive media

Light transport in superdiffusive media of finite size is studied theoretically. The intensity Green's function for a slab geometry is found by discretizing the fractional diffusion equation and employing the eigenfunction expansion method. Truncated step length distributions and complex boundary conditions are considered. The profile of a coherent backscattering cone is calculated in the superdiffusion approximation.     

Time-dependent electromagnetic perturbations in a magnetized plasma with relaxing conductivity

The problem of one-dimensional propagation of a time-dependent electromagnetic perturbation in a homogeneous ionospheric plasma with relaxing conductivity in the presence of a horizontal geomagnetic field is considered. The approximate Green's function is constructed assuming that the dynamics of electromagnetic perturbations is determined by the diffusion mechanism if the diffusion is due to the sound wave motion. It is found that the relaxation of plasma conductivity may result in a solitary perturbation precursor preceding the arrival of the sound wave front.State University, St. Petersburg. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 7, pp. 668–677, July, 1995.     

Universality of the edge-tunneling exponent of fractional quantum Hall liquids

In a microscopic model of fractional quantum Hall liquids with electron-electron interactions and confinement, we calculate the edge Green's function via exact diagonalization. Our results for nu=1/3 and 2/3 suggest that, in the presence of Coulomb interaction, "external" parameters such as the sharpness of the edge and the strength of the edge confining potential, which can lead to edge reconstruction, may cause deviations from universality in the edge-tunneling I-V exponent. In particular, we do not find any direct dependence of this exponent on the range of the interaction potential as suggested by recent calculations in contradiction to the topological nature of the edge.