A topological theory of the electromagnetic field

It is shown that Maxwell equations in vacuum derive from an underlying topological structure given by a scalar field which represents a map S ³×RS ² and determines the electromagnetic field through a certain transformation, which also linearizes the highly nonlinear field equations to the Maxwell equations. As a consequence, Maxwell equations in vacuum have topological solutions, characterized by a Hopf index equal to the linking number of any pair of magnetic lines. This allows the classification of the electromagnetic fields into homotopy classes, labeled by the value of the helicity. Although the model makes use of only c-number fields, the helicity always verifies A·Bd³ r=n, n being an integer and an action constant, which necessarily appears in the theory, because of reasons of dimensionality.     

On the discrete spectrum of the negative hydrogen ion with a homogeneous magnetic field

The asymptotics of the discrete spectrum is obtained for the Hamiltonian of the negative hydrogen ion with a homogeneous magnetic field on the subspace of the functions having a symmetry of the weightm of the SO(2) group, when m .     

The Role of Radial Electric Fields in the Tokamaks TEXTOR-94, CASTOR, and T-10

Radial electric fields (E _r) and their role in the establishment of edge transport barriers and improved confinement have been studied in the tokamaks TEXTOR-94 and CASTOR, where E _r is externally applied to the plasma in a controlled way using a biased electrode, as well as in the tokamak T-10 where an edge transport barrier (H-mode) is obtained during electron-cyclotron resonance heating (ECRH) of the plasma.The physics of radial currents was studied and the radial conductivity in the edge of TEXTOR-94 (R = 1.75 m, a = 0.46 m) was found to be dominated by recycling (ion-neutral collisions) at the last closed flux surface (LCFS) and by parallel viscosity inside the LCFS. From a performance point of view (edge engineering), such electrode biasing was shown to induce a particle transport barrier, a reduction of particle transport, and a concomitant increase in energy confinement. An H-mode-like behaviour can be induced both with positive and negative electric fields. Positive as well as negative electric fields were shown to strongly affect the exhaust of hydrogen, helium, and impurities, not only in the H-mode-like regime.The impact of sheared radial electric fields on turbulent structures and flows at the plasma edge is investigated on the CASTOR tokamak (R = 0.4 m, a = 0.085 m). A non-intrusive biasing scheme that we call "separatrix biasing" is applied whereby the electrode is located in the scrape-off layer (SOL) with its tip just touching the LCFS. There is evidence of strongly sheared radial electric field and E×B flow, resulting in the formation of a transport barrier at the separatrix. Advanced probe diagnosis of the edge region has shown that the E×B shear rate that arises during separatrix biasing is larger than for standard edge plasma biasing. The plasma flows, especially the poloidal E×B drift velocity, are strongly modified in the sheared region, reaching Mach numbers as high as half the sound speed. The corresponding shear rates ( 5×10⁶ s^-1) derived from both the flow and electric field profiles are in excellent agreement and are at least an order of magnitude higher than the growth rate of unstable turbulent modes as estimated from fluctuation measurements.During ECRH in the tokamak T-10 (R = 1.5 m, a = 0.3 m), a regime of improved confinement is obtained with features resembling those in the H-mode in other tokamaks. Using a heavy ion beam probe, a narrow potential well is observed near the limiter together with the typical features of the L-H transition. The time evolution of the plasma profiles during L-H and H-L transitions is clearly correlated with that of the density profile and the formation of a transport barrier near the limiter. The edge electric field is initially positive after the onset of ECRH. It changes its sign during the L-H transition and grows till a steady condition is reached. Similar to the biasing experiments in TEXTOR-94 and CASTOR, the experimentally observed transport barrier is a barrier for particles.     

Transport Equation Evaluation of Coupled Continuous Time Random Walks

The transport behavior of a migrating particle in a disordered medium is exhibited in the solution of a transport equation derived from a coupled continuous time random walk (CTRW). A core aspect of CTRW is the spectrum of transitions in displacement s and time t, ψ(s,t), that characterizes the disordered system, which determine the transport. In many applications the CTRW approach has successfully accounted for the anomalous or non-Fickian nature of the particle plume propagation based on a power-law dependence ψ(t) in a decoupled p(s)ψ(t) approximation to ψ(s,t). For example, this power-law dependence in t derives from the complex Darcy flow fields in geological formations. Recently, the fully coupled CTRW was analyzed using a particle tracking approach, demonstrating that the decoupled approximation is valid only for a compact distribution of s. In this paper we solve the nonlocal-in-time transport equation with a ψ(s,t) containing a power-law dependence in both s (a Lévy-like distribution) and t, which necessitates the strong s,t coupling. We show enhanced transport behavior (relative to the plume propagation behavior reported in the literature) that derives from the rare large displacements in s (limited by the transition t). The interplay between the two coupled power laws is clearly shown in the changes in the breakthrough curves in the arrival times, dispersion and dependence on the velocity (v=s/t) distribution. Similar enhancements are exhibited in the particle tracking results.     

Predictability of ion transport properties from the structure of solid electrolytes

The concept of bond valence (BV) is widely used in crystal chemical considerations, e.g. to assess equilibrium positions of atoms in crystal structures from an empirical relationship between bond lengthR _M−X and bond valenceS _A−X =exp [(R ₀ −R _M−X ) /b] as sites where the BV sumV(A)=∑ s _M−X equals the formal valenceV _id of the cationM ⁺ . Our modified BV approach that systematically accounts for the softness of the bond may then be effectively used to study the interplay between structure and properties of solid electrolytes. This is exemplified for correlations to experimental data from IR, NMR, and impedance spectroscopy. Combining the bond valence approach with reverse Monte Carlo (RMC) modeling or molecular dynamics (MD) simulations provides a deeper understanding of ion transport mechanisms, especially in highly disordered or amorphous solids. Local structure models for crystalline electrolytes are derived by combining crystallographic structure information with simulations. A method for the prediction of the activation energy of the ionic conductivity from the bond valence analysis of the crystal structure is proposed. Taking into account the mass dependence of the conversion factor from bond valence mismatch into an activation energy scale, we could establish a correlation that holds for different types of mobile ions. The strong coupling of the H⁺ transfer to the anion motion in proton conductors requires a special treatment. For glassy solid electrolytes RMC structure models are BV-analyzed to assess the total number of equilibrium sites and to identify transport pathways for the mobile ions. Recently, we have reported a correlation between the pathway volume fraction and the transport properties that permits to predict both absolute value and activation energy of the dc ionic conductivities of disordered solids (including mixed alkali glasses) directly from their structural models. Here we discuss a corresponding BV analysis of molecular dynamics simulation trajectories that allows quantifying the evolution of pathways in time and the influence of temperature on the transport pathways. Paper presented at the Patras Conference on Solid State Ionics — Transport Properties, Patras, Greece, Sept. 14 — 18, 2004.     

H-mode in tokamaks attributed to absence of trapped ions in poloidally rotating plasma

It is proposed that the suppression of transport in the H-mode in tokamaks is caused by the absence of trapped ions in the transport barrier. If the poloidal Mach number M=v _θ B/(v _TiB_θ) is large there are exponentially few trapped ions. This criterion agrees with experimental observations of H-mode plasmas. The recently observed transport suppression by reversed shear also points to the dominant role of trapped particles in turbulent transport. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 427–430 (25 March 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Resonant charge and spin transport in a $\mathcal T$-stub coupled to a superconductor

We study transport through a single channel T\mathcal T-stub geometry strongly coupled to a superconducting reservoir. In contrast to the standard stub geometry which has both transmission resonances and anti-resonances in the coherent limit, we find that due to the proximity effect, this geometry shows neither a T = 1 resonance (T is the transmission probability for electrons incident on the T\mathcal T-stub) nor a T = 0 anti-resonance as we vary the energy of the incident electron. Instead, we find that there is only one resonant value at T = 1/4, where charge transport vanishes while the spin transport is perfect.     

Electrical and optical properties of amorphous Te40As38Ge10Si12 thin films

Electrical, optical and structural, properties, of Te₄₀As₃₈Ge₁₀Si₁₀ thin films were studied. X-ray diffraction patterns indicate that these films are in an amorphous state. The dark electrical resistivity of Te₄₀As₃₈Ge₁₀Si₁₂ films was measured at room temperature and at elevated temperature. The thermal activation energy E was determined. The optical constants (refractive index n and absorption index k) of such films were determined in the spectral range of 0.5–2.0 m. The absorption coefficient () of this system was also determined using the known equation =4k/. The refractive index n has anomalous behaviour near the absorption edge. Analysis of the absorption spectrum reveals indirect optical transitions. The corresponding forbidden-band width was determined. Its value is approximately twice the thermal activation energy.     

Temperature dependence of electric resistance and magnetoresistance of pressed nanocomposites of multilayer nanotubes with the structure of nested cones

Bulk samples of carbon multilayer nanotubes with the structure of nested cones (fishbone structure) suitable for transport measurements, were prepared by compressing under high pressure (∼25 kbar) a nanotube precursor synthesized through thermal decomposition of polyethylene catalyzed by nickel. The structure of the initial nanotube material was studied using high-resolution transmission electron microscopy. In the low-temperature range (4.2–100 K) the electric resistance of the samples changes according to the law ln R ∝ (T ₀/T)^1/3, where T ₀∼7 K. The measured magnetoresistance is quadratic in the magnetic field and linear in the reciprocal temperature. The measurements have been interpreted in terms of two-dimensional variable-range hopping conductivity. It is suggested that the space between the inside and outside walls of nanotubes acts as a two-dimensional conducting medium. Estimates suggest a high value of the density of electron states at the Fermi level of about 5×10²¹ eV⁻¹ cm⁻³. Zh. éksp. Teor. Fiz. 113, 2221–2228 (June 1998)     

Theoretical design of azaacene-based non-fullerene electron transport material used in inverted perovskite solar cells

ABSTRACT

Inverted perovskite solar cells (PSCs) have attracted much attention due to their low-temperature and solution-based process. Electron transport layers are important components in inverted PSCs. Non-fullerene n-type organic small molecules seem to be more attractive as electron transport layers, because their structures are easy to be synthesised and modified. In this paper, density functional theory and semi-classical Marcus electron transfer theory were used to explore the electron transport properties in three azaacene derivatives, including one experimentally reported molecule, 1,4,9,16-tetrakis((triisopropylsilyl)ethynyl)quinoxalino[2^?,3^?:4^″,5^″]cyclopenta[1^″,2^″,3^″:5^′,6^′]acenaphtho[1^′,2^′:5,6]pyrazino[2,3-b]phenazine (1), and two theoretically designed molecules (2 and 3). Compound 2 is formed by substituting i-Pr groups in compound 1 with H atoms, which is designed to evaluate the effect of i-Pr groups on the electron transport properties. Compound 3 is designed by adding one more benzopyrazine group to the conjugation structure of compound 1. It shows that i-Pr group can increase HOMO and LUMO energy levels and improve solubility in organic solvent and hydrophobicity. Enlarging conjugation can not only decrease LUMO energy level and electron reorganisation energy, but also can increase solubility and electron mobility. So our designed compound 3 is expected to be a potential electron transport material in inverted PSCs.     

量子点调制的一维量子波导中声学声子输运和热导

利用散射矩阵方法,比较了被一维凸形量子点、凹形量子点调制的量子线中膨胀模的声子输运和热导性质. 研究结果表明: 声子的输运概率与热导受制于量子点几何结构,具有凸形量子点结构的量子线中声子输运概率与热导K_CV大于具有凹形量子点结构的量子线中声子输运概率与热导K_CC. 两者热导之比K_CV/K_CC依赖于一维量子点的具体结构,且随着温度及主量子线与量子点横截面的边长差Δ_SL的增加而增加. 两种具有不同散射结构的一维量子线中热输运性质的区别在于凸形量子点结构中膨胀模数量总是大于凹形量子点结构中膨胀模数量的缘故. 关键词： 声学声子输运 热导 量子结构     

Role of rational surfaces on fluctuations and transport in the plasma edge of the TJ-II stellarator

It has been shown that transport barriers in toroidal magnetically confined plasmas tend to be linked to regions of unique magnetic topology such as the location of a minimum in the safety factor, rational surfaces or the boundary between closed and open flux surfaces. In the absence ofE×B sheared flows, fluctuations are expected to show maximum amplitude near rational surfaces, and plasma confinement might tend to deteriorate. On the other hand, if the generation ofE×B sheared flows were linked to low order rational surfaces, these would be beneficial for confinement. Experimental evidence ofE×B sheared flows linked to rational surfaces has been obtained in the plasma edge region of the TJ-II stellarator. Presented at the Workshop on the Role of Electric Fields in Plasma Confinement and Exhaust, Budapest, 18–19 June, 2000.     

Transmission spectra of thin CdS and CdSe crystals near higher-order isotropic points

Summary For photon energies below the absorption edge in CdS, CdSe and other II–VI crystals the polariton dispersion curves forE⊥c andE‖c (c-axis in a wurtzite crystal) corss at some points called isotropic points (IP). The occurrence of isotropic points provides the possibility of mode coupling between ordinary and extraordinary waves. Since the consequences of mode coupling on the optical properties for photon energies near the lowest IP lying much below the first excitonic state were widely discussed in recent years, more attention is now paid to isotropic points lying near the band gap and related to then=2,3, … excitonic states (?higher isotropic points?). Making use of Stahl's real density matrix approach we derive the polariton dispersion relationsk _⊥ (ω), andk _‖ (ω), for CdS and CdSe bulk crystals and determine the positions of IP's due to the crossing of theB-polariton with higherA-excitonic resonances. By the method of multiple internal reflection we calculate the transmission spectra for various crystal thicknesses (between 3 μm and 0.5 mm) and coupling mechanisms. The calculated transmission shows sharply peaked structures centred at the isotropic points.     

Insulator-metal transition shift related to magnetic polarons in La<Subscript>0.67-x</Subscript>Y<Subscript>x</Subscript>Ca<Subscript>0.33</Subscript>MnO<Subscript>3</Subscript>

The magnetic transport properties have been measured for La_0.67-xY_xCa_0.33MnO₃ ( 0 ⩽ x ⩽ 0.14) system. It was found that the transition temperature T _p almost linearly moves to higher temperature as H increases. Electron spin resonance confirms that above T _p , there exist ferromagnetic clusters. From the magnetic polaron point of view, the shift of T _p vs. H was understood, and it was estimated that the size of the magnetic polaron is of 9.7 ∼ 15.4 ? which is consistent with the magnetic correlation length revealed by the small-angle neutron-scattering technique. The transport properties at temperatures higher than T _p conform to the variable-range hopping mechanism. Received 27 August 2002 / Received in final form 2 December 2002 Published online 14 March 2003     

Sodium profiles in β″-alumina crystals: Modifications induced by argon bombardment

Abstract

Sodium depth profiles in implanted sodium β″-alumina single crystals have been measured by the nuclear resonance technique. A systematic investigation of the depth profile modifications as function of the implanted ion energy has been done using argon-ion (E = 50–600 keV) irradiation at fixed dose (Φ = 4 × 10¹⁶ions/cm²) and beam current (I = 1 μA/cm²). Argon doses were checked by Rutherford backscattering spectrometry. The changes in the sodium profiles are discussed in terms of transport equations which include three main processes: radiation enhanced transport, electric field assisted migration, and preferential surface sputtering of the alkali element. Special attention is devoted to the discussion of sputtering processes.     

Counting statistics of collective photon transmissions

We theoretically study cooperative effects in the steady-state transmission of photons through a medium of N radiators. Using methods from quantum transport, we find a cross-over in scaling from N to N² in the current and to even higher powers of N in the higher cumulants of the photon counting statistics as a function of the tunable source occupation. The effect should be observable for atoms confined within a nano-cell with a pumped optical cavity as photon source.     

Spin exchange in iodine-doped polydiacetylene

It is shown that the observed transformation of the ESR spectrum in polydiacetylene films upon doping with iodine agrees with an exchange interaction between the spin systems of localized paramagnetic centers (S) and polaron states (P) by means of which current-carrier transport occurs. The data obtained indicate carrier transport in the form of uncorrelated hops with probability determined by the lifetime of an exchange-coupled (S-P) pair. Fiz. Tverd. Tela (St. Petersburg) 41, 1879–1881 (October 1999)     

Metastable phases in vapour-quenched Al78Cu22 film

The structure and structural changes of an Al₇₈Cu₂₂ (at%) alloy film produced by coevaporation onto a cooled substrate have been investigated with transmission electron microscopy. A series of metastable phase transitions were observed during the crystallization from the as-deposited amorphous phase to the final equilibrium state. The deposit structure at room temperature consists of a mixture of fine grained α' crystallites (fcc, α = 4.81 Å) with an amorphous phase, and some welldefined crystals with an fcc lattice (a = 7.18 Å, namely α₁). The subsequent annealing led to the grown crystals transforming to an ordered α′ phase. It is argued that the development of such a transition is the result of a gradual atomic rearrangement – first topologically then a chemically predominant disorder-order transition.