Density and current response functions in strongly disordered electron systems: diffusion,electrical conductivity and Einstein relation

We study noninteracting quantum charged particles (electron gas) subject to a strong random potential and perturbed by a weak classical electromagnetic field. We examine consequences of gauge invariance and charge conservation in the space of Bloch waves. We use two specific forms of the Ward identity between the one- and two-particle averaged Green functions to establish exact relations between the density and current response functions. In particular, we find precise conditions under which we can extract the current-current from the density-density correlation functions and vice versa. We use these results to prove a formula relating the density response and the electrical conductivity in strongly disordered systems. We introduce quantum diffusion as a response function that reduces to the diffusion constant in the static limit. We then derive Ficks law, a quantum version of the Einstein relation and prove the existence of the diffusion pole in the quasistatic limit of the zero-temperature electron-hole correlation function. We show that the electrical conductivity controls the long-range spatial fluctuations of the electron-hole correlation function only in the static limit.Received: 10 June 2003, Published online: 22 September 2003PACS: 72.10.Bg General formulation of transport theory - 72.15.Eb Electrical and thermal conduction in crystalline metals and alloys - 72.15.Qm Scattering mechanisms and Kondo effect     

Radiation-induced E″ centers in crystalline SiO2

Electron spin resonance has been used to study three similar, but distinct, S = 1 defects (labelled E″ centers) in high-quality synthetic quartz crystals. These centers are produced by electron irradiation and their concentrations depend on the irradiation temperature, the nature of previous irradiations and thermal anneals, and whether the sample is swept or unswept. The radiation-induced mobility of interstitial alkali ions (Li⁺ and Na⁺) correlates with the production of E″ centers.     

Novel Mn(III) heterochelates: synthesis,thermal, spectroscopic,and coordination aspects

This article describes the synthesis, structural features, and thermal studies of novel Mn(III) heterochelates of the type [Mn(SB _n )(L)(H₂O)]·xH₂O [H₂SB _n  = Nicotinic acid [1-(3-methyl-5-oxo-1-phenyl-4,5 dihydro-1H-pyrazol-4yl)-acylidene]-hydrazide where acyl = acetyl (H₂SB₁); benzoyl (H₂SB₂); propionyl (H₂SB₃); buteryl (H₂SB₄); phenyl acetyl (H₂SB₅); and HL = 5-Chloro-7-iodo-8-hydroxyquinoline (clioquinol)]. The heterochelates have been characterized on the basis of elemental analyses, magnetic susceptibility measurements, cyclic voltammetric studies, (FTIR and electronic) spectra, and thermal studies. The FAB mass spectrum of [Mn(SB₁)(L)H₂O]·3H₂O has been carried out. The cyclic voltammetric studies reveal that quasi-reversible reduction process of Mn(III)/Mn(II) coupled system suggesting that the ligands readily destabilize higher oxidation states of metal ion. Kinetic parameters such as order of reaction (n) and the energy of activation (Ea) were calculated using Freeman–Carroll method. The pre-exponential factor (A), the activation entropy (S*), the activation enthalpy (H*), and the free energy of activation (G*) were calculated using Horowitz–Metzger equations.     

Characterization of quenched-in vacancies in Fe–Al alloys

Physical and mechanical properties of Fe–Al alloys are strongly influenced by atomic ordering and point defects. In the present work positron lifetime (LT) measurements combined with slow positron implantation spectroscopy (SPIS) were employed for an investigation of quenched-in vacancies in Fe–Al alloys with the Al content ranging from 18 to 49 at.%. The interpretation of positron annihilation data was performed using ab-initio   theoretical calculations of positron parameters. Quenched-in defects were identified as Fe-vacancies. It was found that the lifetime of positrons trapped at quenched-in defects increases with increasing Al content due to an increasing number of Al atoms surrounding the Fe vacancies. The concentration of quenched-in vacancies strongly increases with increasing Al content from ≈10⁻⁵$\approx {10}^{-5}$ in Fe₈₂Al₁₈${\mathrm{Fe}}_{82}{\mathrm{Al}}_{18}$ (i.e. the alloy with the lowest Al content studied) up to ≈10⁻¹$\approx {10}^{-1}$ in Fe₅₁Al₄₉${\mathrm{Fe}}_{51}{\mathrm{Al}}_{49}$ (i.e. the alloy with the highest Al content studied in this work).     

Quasiregular mappings to generalized manifolds

We establish the basic analytic and geometric properties of quasiregular maps f: ω → X, where ω ? ? ⁿ is a domain and X is a generalized n-manifold with a suitably controlled geometry. Generalizing the classical Väisälä and Poletsky inequalities, our main theorem shows that the path family method applies to these maps.     

Rapid solidification processing in molten salts chemistry: X-ray analysis of deeply undercooled cryolite-alumina melts

Rapid solidification processing (cooling rate from the interval 10⁵–10⁶ K s⁻¹) was used to prepare deeply undercooled cryolite-alumina melts. Such prepared samples were analyzed by the XRD method. Besides cryolite, XRD patterns belonging to ι-Al₂O₃ were recorded. The influence of annealing on the XRD patterns of deeply undercooled melts was also investigated.     

Arbitrage without borrowing or short selling?

We show that a trader, who starts with no initial wealth and is not allowed to borrow money or short sell assets, is theoretically able to attain positive wealth by continuous trading, provided that she has perfect foresight of future asset prices, given by a continuous semimartingale. Such an arbitrage strategy can be constructed as a process of finite variation that satisfies a seemingly innocuous self-financing condition, formulated using a pathwise Riemann–Stieltjes integral. Our result exemplifies the potential intricacies of formulating economically meaningful self-financing conditions in continuous time, when one leaves the conventional arbitrage-free framework.