Comparative study of solute trapping and Gibbs free energy changes at the phase interface during alloy solidification under local nonequilibrium conditions

An analytical model has been developed to describe the influence of solute trapping during rapid alloy solidification on the components of the Gibbs free energy change at the phase interface with emphasis on the solute drag energy. For relatively low interface velocity V < V _D , where V _D is the characteristic diffusion velocity, all the components, namely mixing part, local nonequilibrium part, and solute drag, significantly depend on solute diffusion and partitioning. When V ≥ V _D , the local nonequilibrium effects lead to a sharp transition to diffusionless solidification. The transition is accompanied by complete solute trapping and vanishing solute drag energy, i.e. partitionless and “dragless” solidification.     

Zur Chronologie des alten Ägypten

The velocityv of the propagation of discharge along the anode of a self-quenchingG—M-counter is a function of total pressureP, pressure of the quenching gasP _D, radius of the cathoder _a and of the anoder _i andV _ü the difference between working- and starting-potential. For the mixtures argon-methylal, argon-alcohol and helium-alcohol isv=v ₀·exp[k·(V _ü/V _e)^1/2] withv ₀ the velocity at the starting potentialV _e v ₀=(a+b·P _D/P)·V _n ^1/2 ·exp [(c?d·P_D/P·V _n ^?1/2 ] andV _n=V _e·(lnr _a/r _i)^?1.k, a, b, c andd are characteristical constants of the filling gas.     

Nonlinear Hall effect in a quasi-two-dimensional electron system

The nonlinear electron transport in GaAs double quantum wells with two occupied size-quantization levels has been studied at a temperature of 4.2 K in the magnetic fields B < 1 T. It has been found that a sinusoidal electric current I _ac induces the generation of higher harmonics of both longitudinal V _xx (B) and Hall V _xy (B) voltages in the quasi-two-dimensional electron system under consideration. The Hall voltage oscillating in the magnetic field has been shown to appear in the electron system with two occupied size-quantization levels in the presence of microwave radiation and dc electric current I _dc. The experimental data indicate the independent contributions of the diagonal and off-diagonal components of the conductivity tensor to the nonlinear magnetotransport at high filling factors.     

On wave and rheidity properties of the Earth’s crust

The properties of the Earth’s solid crust have been studied on the assumption that this crust has a block structure. According to the rotation model, the motion of such a medium (geomedium) follows the angular momentum conservation law and can be described in the scope of the classical elasticity theory with a symmetric stress tensor. A geomedium motion is characterized by two types of rotation waves with shortand long-range actions. The first type includes slow solitons with velocities of 0 ≤ V_sol ≤ c0, max = 1–10 cm s^–1; the second type, fast excitons with V₀ ≤ V_ex ≤ V_S–V_P. The exciton minimal velocity (V₀ = 0) depends on the energy of the collective excitation of all seismically active belt blocks proportional to the Earth’s pole vibration frequency (the Chandler vibration frequency). The exciton maximal velocity depends on the velocities of S (V_S ≈ 4 km s^–1) and/or P (V_P ≈ 8 km s^–1) seismic (acoustic) waves. According to the rotation model, a geomedium is characterized by the property physically close to the corpuscular–wave interaction between blocks that compose this medium. The possible collective wave motion of geomedium blocks can be responsible for the geomedium rheidity property, i.e., a superplastic volume flow. A superplastic motion of a quantum fluid can be the physical analog of the geomedium rheid motion.     

Extremal Theory for Spectrum of Random Discrete Schrödinger Operator. II. Distributions with Heavy Tails

We study the asymptotic structure of the first K largest eigenvalues λ _k,V and the corresponding eigenfunctions ψ(?;λ _k,V ) of a finite-volume Anderson model (discrete Schrödinger operator) \(\mathcal{H}_{V}= \kappa \Delta_{V}+\xi(\cdot)\) on the multidimensional lattice torus V increasing to the whole of lattice ? ^ν , provided the distribution function F(?) of i.i.d. potential ξ(?) satisfies condition ?log(1?F(t))=o(t ³) and some additional regularity conditions as t→∞. For z∈V, denote by λ ⁰(z) the principal eigenvalue of the “single-peak” Hamiltonian κΔ _V +ξ(z)δ _z in l ²(V), and let \(\lambda^{0}_{k,V}\) be the kth largest value of the sample λ ⁰(?) in V. We first show that the eigenvalues λ _k,V are asymptotically close to \(\lambda^{0}_{k,V}\). We then prove extremal type limit theorems (i.e., Poisson statistics) for the normalized eigenvalues (λ _k,V ?B _V )a _V , where the normalizing constants a _V >0 and B _V are chosen the same as in the corresponding limit theorems for \(\lambda^{0}_{k,V}\). The eigenfunction ψ(?;λ _k,V ) is shown to be asymptotically completely localized (as V↑?) at the sites z _k,V ∈V defined by \(\lambda^{0}(z_{k,V})=\lambda^{0}_{k,V}\). Proofs are based on the finite-rank (in particular, rank one) perturbation arguments for discrete Schrödinger operator when potential peaks are sparse.     

Effective Heisenberg exchange integrals of diluted magnetic semiconductors determined within realistic multi-band tight-binding models

Diluted magnetic semiconductors (DMS) like Ga_1?x Mn _x As are described by a realistic tight-binding model (TBM) for the (valence) bands of GaAs, by a Zener (J-)term modeling the coupling of the localized Mn-spins to the spins of the valence band electrons, and by an additional potential scattering (V-) term due to the Mn-impurities. We calculate the effective (Heisenberg) exchange interaction between two Mn-moments mediated by the valence electrons. The influence of the number of bands taken into account (6-band or 8-band TBM) and of the potential (impurity) scattering V-term is investigated. We find that for realistic values of the parameters the indirect exchange integrals show a long-range, oscillating (RKKY-like) behavior, if the V-term is neglected, probably leading to spin-glass behavior rather than magnetic order. But by including a V-term of a realistic magnitude the exchange couplings become short ranged and mainly positive allowing for the possibility of ferromagnetic order. Our results are in good agreement with available results of ab initio treatments.     

Percolation and the electron–electron interaction in an array of antidots

A square lattice of microcontacts with a period of 1 μm in a dense low-mobility two-dimensional electron gas is studied experimentally and numerically. At the variation of the gate voltage V _g , the conductivity of the array varies by five orders of magnitude in the temperature range T from 1.4 to 77 K in good agreement with the formula σ(V _g ) = (V _g ?V _g ^* (T))^β with β = 4. The saturation of σ(T) at low temperatures is absent because of the electron–electron interaction. A random-lattice model with a phenomenological potential in microcontacts reproduces the dependence σ(T, V _g ) and makes it possible to determine the fraction of microcontacts x(V _g , T) with conductances higher than σ. It is found that the dependence x(V _g ) is nonlinear and the critical exponent in the formula σ ∝ ? (x - 1/2) ^t in the range 1.3 < t(T, V _g ) < β.     

Drag of ballistic electrons by an ion beam

Drag of electrons of a one-dimensional ballistic nanowire by a nearby one-dimensional beam of ions is considered. We assume that the ion beam is represented by an ensemble of heavy ions of the same velocity V. The ratio of the drag current to the primary current carried by the ion beam is calculated. The drag current turns out to be a nonmonotonic function of velocity V. It has a sharp maximum for V near v _nF/2, where n is the number of the uppermost electron miniband (channel) taking part in conduction and v _nF is the corresponding Fermi velocity. This means that the phenomenon of ion beam drag can be used for investigation of the electron spectra of ballistic nanostructures. We note that whereas observation of the Coulomb drag between two parallel quantum wires may in general be complicated by phenomena such as tunneling and phonon drag, the Coulomb drag of electrons of a one-dimensional ballistic nanowire by an ion beam is free of such spurious effects.     

On the Negative Spectrum of the Two-Dimensional Schrödinger Operator with Radial Potential

For a two-dimensional Schrödinger operator H _{α V}  = ?Δ ?αV with the radial potential V(x) = F(|x|), F(r) ≥ 0, we study the behavior of the number N _?(H _{α V} ) of its negative eigenvalues, as the coupling parameter α tends to infinity. We obtain the necessary and sufficient conditions for the semi-classical growth N _?(H _{α V} ) = O(α) and for the validity of the Weyl asymptotic law.     

Almost mobility edges and the existence of critical regions in one-dimensional quasiperiodic lattices

We study a one-dimensional quasiperiodic system described by the Aubry–André model in the small wave vector limit and demonstrate the existence of almost mobility edges and critical regions in the system. It is well known that the eigenstates of the Aubry–André model are either extended or localized depending on the strength of incommensurate potential V being less or bigger than a critical value V _c , and thus no mobility edge exists. However, it was shown in a recent work that for the system with V < V _c and the wave vector α of the incommensurate potential is small, there exist almost mobility edges at the energy E _c±, which separate the robustly delocalized states from “almost localized” states. We find that, besides E _c±, there exist additionally another energy edges E _c′±, at which abrupt change of inverse participation ratio (IPR) occurs. By using the IPR and carrying out multifractal analyses, we identify the existence of critical regions among |E _c±|?≤?|E|?≤?|E _c′±| with the mobility edges E _c± and E _c′± separating the critical region from the extended and localized regions, respectively. We also study the system with V > V _c , for which all eigenstates are localized states, but can be divided into extended, critical and localized states in their dual space by utilizing the self-duality property of the Aubry–André model.     

Quantum oscillations of rectified dc voltage as a function of magnetic field in an “almost” symmetric superconducting ring

Periodic oscillations in the dependence V _dc(B) of rectified dc voltage on the perpendicular magnetic field have been experimentally observed near the critical temperature in a single superconducting aluminum ring with slight geometric inhomogeneities (without specially formed circular asymmetry), biased by an external ac current (without a dc component). With a change in the external current and temperature, the voltage V _dc(B) behaves like the corresponding voltage on a circularly asymmetric ring but has a much smaller amplitude. The Fourier spectrum of the function V _dc(B) contains the fundamental frequency, corresponding to the ring area, and its highest harmonics. “Satellite” frequencies, dependent on the structure geometry and external parameters, were unexpectedly found in the spectrum.     

Partial pseudospin polarization,latticetronics and Fano resonances in quantum dots based in graphene ribbons: a conductance spectroscopy

In this work we study, as a function of the height V and width L _b of the potentialbarriers, the transport of Dirac quasi-particles through quantum dots in graphene ribbons.We observed, as we increase V, a partial polarization (PP) of the pseudospin due to the participation of the hyperbolic bands. This generates polarizations in the sub-lattices A or B outside the dot regions for single, coupled, and open dots. Thus for energies around the Dirac point, the conductance G at both sides of the dot shows a latticetronics of conductances G _A and G _B as a function ofV and L _b . This fact can be used as a PPspectroscopy which associates hole-type waves with the latticetronics. A periodic enhancement of PP is obtained with the increase of V in dots formed bybarriers that completely occupy the nanoribbon width. For this case, a direct correspondence between G(V) and PP(V) exists. On the other hand, for the open dots, the PP(V) and the G(V) show a complex behavior that exhibit higher intensities when compared to the previous case. In the Dirac limit we have no backscattering signs, however when we move slightly away from this limit the firstsigns of confinement appear in the PP(V) (it freezes in a given sub-lattice). In the last case the backscattering fingerprints are obtained directly fromthe conductance (splittings). The open quantum dots are very sensible to their opening w _d and this generatesFano line-shapes of difficult interpretation around the Dirac point. The PP spectroscopy used here allows us to understand the influence of w _d in the relativistic analogues and to associate electron-type waves with the observed Fano line-shapes.     

Effect of incommensurate potential on the resonant tunneling through Majorana bound states on the topological superconductor chains

We study the transport through the Kitaev chain with incommensurate potentials coupled to two normal leads by the numerical operator method. We find a quantized linear conductance of e ² / h, which is independent to the disorder strength and the gate voltage in a wide range, signaling the Majorana bound states. While the incommensurate potential suppresses the current at finite voltage bias, and then narrows the linear response regime of the I-V curve which exhibits two plateaus corresponding to the superconducting gap and the band edge, respectively. The linear conductance abruptly drops to zero as the disorder strength reaches the critical value 2g _s + 2Δ with Δ the p-wave pairing amplitude and g _s the hopping between neighbor sites, corresponding to the transition from the topological superconducting phase to the Anderson localized phase. Changing the gate voltage also causes an abrupt drop of the linear conductance by driving the chain into the topologically trivial superconducting phase, whose I-V curve exhibits an exponential shape.     

Superconducting properties of superlattices containing ferromagnetic layers

Using the microscopic theory formulated by de Gennes and extended by Takahashi and Tachiki, we calculate the transition temperatureT _c and the pair functionF for the superlattices consisting of superconducting and ferromagnetic layers. Superconducting layers. (s) and ferromagnetic layers (f) are modeled byV _s ≠0 andI _m,s =0 andV _f =0 andI _m,f ≠0, whereV _s .(V _f ) is the BCS coupling constant andI _m,s (I _m,f ) is the molecular field fors (f) layers.     

Structure,ionic conduction,and phase transformations in lithium titanate Li<Subscript>4</Subscript>Ti<Subscript>5</Subscript>O<Subscript>12</Subscript>

The spinel structure of lithium titanate Li₄Ti₅O₁₂ is refined by the Rietveld full-profile analysis with the use of x-ray and neutron powder diffraction data. The distribution and coordinates of atoms are determined. The Li₄Ti₅O₁₂ compound is studied at high temperatures by differential scanning calorimetry and Raman spectroscopy. The electrical conductivity is measured in the high-temperature range. It is shown that the Li₄Ti₅O₁₂ compound with a spinel structure undergoes two successive order-disorder phase transitions due to different distributions of lithium atoms and cation vacancies (□, V) in a defect structure of the NaCl type: (Li)_8a[Li_0.33Ti_1.67]_16dO₄ → [Li□]_16c[Li_1.33Ti_1.67]_16dO₄ → [Li_1.33□_0.67]_16c[Ti_1.67□_0.33]_16dO₄. The low-temperature diffusion of lithium predominantly occurs either through the mechanism ... → Li(8a) → V(16c) → V(8a) → ... in the spinel phase or through the mechanism ... → Li(16c) → V(8a) → V(16c) → ... in an intermediate phase. In the high-temperature phase, the lithium cations also migrate over 48f vacancies: ... Li(16c) → V(8a, 48f) → V(16c) → ....     

Kraus Operator-Sum Solution to the Master Equation Describing the Single-Mode Cavity Driven by an Oscillating External Field in the Heat Reservoir

Exploiting the thermo entangled state approach, we successfully solve the master equation for describing the single-mode cavity driven by an oscillating external field in the heat reservoir and then get the analytical time-evolution rule for the density operator in the infinitive Kraus operator-sum representation. It is worth noting that the Kraus operator M _{l, m} is proved to be a trace-preserving quantum operation. As an application, the time-evolution for an initial coherent state ρ _|β〉 = |β〉〈β| in such an environment is investigated, which shows that the initial coherent state decays to a new mixed state as a result of thermal noise, however the coherence can still be reserved for amplitude damping.     

On a Semiclassical Formula for Non-Diagonal Matrix Elements

Let H(?)=?? ²d²/dx ²+V(x) be a Schrödinger operator on the real line, W(x) be a bounded observable depending only on the coordinate and k be a fixed integer. Suppose that an energy level E intersects the potential V(x) in exactly two turning points and lies below V _∞=lim?inf?_|x|→∞ V(x). We consider the semiclassical limit n→∞, ?=? _n →0 and E _n =E where E _n is the nth eigenenergy of H(?). An asymptotic formula for 〈n|W(x)|n+k〉, the non-diagonal matrix elements of W(x) in the eigenbasis of H(?), has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner.     

Maslov index for power-law potentials

The Maslov index in the semiclassical Bohr–Sommerfeld quantization rule is calculated for one-dimensional power-law potentials V (x) = ?V ₀/x ^s, x > 0, 0 < s < 2 The result for the potential V(x)=-V ₀/x ^1/2 is compared with the recently reported exact solution. The case of a spherically symmetric power-law potential is also considered.