Extremal Theory for Spectrum of Random Discrete Schrödinger Operator. III. Localization Properties

In this paper, we study the asymptotic localization properties with high probability of the Kth eigenfunction (associated with the Kth largest eigenvalue, K?1 fixed) of the multidimensional Anderson Hamiltonian in torus V increasing to the whole of lattice. Denote by z _K,V ∈V the site at which the Kth largest value of potential is attained. It is well-known that if the tails of potential distribution are heavier than the double exponential function and satisfies additional regularity and continuity conditions at infinity, then the Kth eigenfunction is asymptotically delta-function at the site z _τ(K),V (localization centre) for some random τ(K)=τ _V (K)?1. We study the asymptotic behavior of the index τ _V (K) by distinguishing between three cases of the tails of potential distribution: (i) for the “heavy tails” (including Gaussian), τ _V (K) is asymptotically bounded; (ii) for the light tails, but heavier than the double exponential, the index τ _V (K) unboundedly increases like |V|^o(1); (iii) finally, for the double exponential tails with high disorder, the index τ _V (K) behaves like a power of |V|. For Weibull’s and fractional-double exponential types distributions associated with the case (ii), we obtain the first order expansion formulas for logτ _V (K).     

The πd scattering length from Kα X-rays

X-rays from the K_α transition (2P → 1S) of the π^?d mesic atom have been observed. Their energy, 2592.8 _?2.0^+1.6, has been measured by the critical absorber technique, using the M_V absorption edge in bismuth. The strong interaction shift in the 1S state is ?4.8 eV, corresponding to a scattering length a(πd) = ?(0.052_?0.017^+0.022)m_π^?1, in agreement with recent calculations. The intensity ratio K_α/K_total = 0.548 ± 0.015.     

Mesoscopic spin-flip transport through a hybrid system with a single molecular dot system applied with ac magnetic fields

We have investigated the current for the system of vibrating quantum dot irradiated with a rotating magnetic field and an oscillating magnetic field by nonequilibrium Green's function. The rotating magnetic field rotates with the angular frequency ωr around the z-axis with the tilt angle ?, and the time-oscillating magnetic field is located in the z-axis with the angular frequency ω. Different behaviors have been shown in the presence of electron-phonon interaction (EPI) which plays a significant role in the transport. The current displays asymmetric behavior as the source-drain bias eV=0, novel side peaks or shoulders can be found due to the phonon absorption and emission procedure, and the negative differential resistance becomes stronger as the parameter g increases. Furthermore, the strong EPI also destroys the quasiperiodic oscillations of current in the region μ₀B₁>2.5Δ. The electron transport properties are also significantly influenced by the linewidth function Γ.     

Observation of a narrowK s 0 K s 0 π+π− state at 1.97 GeV produced inK + p interactions at 32 GeV/c

Evidence is provided for a new resonance in theK _s ⁰ K _s ⁰ π⁺π^? system with a mass of 1.97±0.01 GeV and width 40±20 MeV. It is produced with an inclusive cross section of ～6μb in the beam fragmentation process of 4-prongK ⁺ p interactions with at least 2 associatedV ⁰'s at 32 GeV/c and decays dominantly into theK ^{* ±} (892)K _s ⁰ π^? mode.     

Semiempirical determination of the atom-surface interaction

We discuss three methods of determining V(z), the lateral average (G = 0 Fourier component) of the atom-surface interaction, from the bound state spectrum found in beam scattering. One method uses the Rydberg-Klein-Rees technique, which yields the width of the potential (i.e., separation of classical turning points) as a function of energy. This method incorporates also the known asymptotic form V ～ ?C₃z^?3, whereC₃ is derived from the polarizability and dielectric function of atom and solid, respectively. The second method uses a hybrid potential, constructed from a Morse potential with shifted zero of energy connected to the asymptotic form,?C₃z^?3, requiring continuity of V and $\text{d}\text{V}\text{d}\text{z}$. The third potential is a Lennard-Jones 3–9 interaction. Results are presented for H and He scattering from LiF and NaF.     

αS(KT2) versus αS(K2) in QCD jet development: Some quantitative remarks

Properties of QCD jets for two proposed choices of the variable appearing in the QCD running coupling constant, α_S(K²) or α_S(K_T²) with K_T²=z(1?z)K², have been studied in detail by the use of Monte Carlo techniques. Contrary to expectations based on approximate analytic calculations it is found that when substituting K² with K_T² in α_S the growth with energy of the multiplicity of the quanta is not sensibly altered, and it is even slowed down for extreme values of the non-perturbative cutoff, which delimits the minimum virtual mass of the quanta. It appears, therefore, that the analysis of subleading effects may be totally misleading if phase-space constraints are not taken into account exactly, which is possible to do in Monte Carlo calculations.     

Kinetic Green's functions

It is shown that the theory of kinetic Green's functions coincides completely with the theory of vacuum Green's functions after the choice of the operatorO ^?1 in its overall part. An expression for the energy of the system is obtained directly in terms of the mass operators. An equation is given that is a generalization of the Boltzmann equation and has the same mathematical structure.     

Longitudinal sound in impure jellium for small frequency and wavevector

The behaviour of long wavelength (q ?k _F ) and low frequency (ω ? ε _f ) longitudinal sound in jellium containing a small concentration of defects (τ^?1?ε _f ) is discussed without making use of the unitary transformation to a frame moving with the ion velocity. The relevant contributions for the phonon Green's function are formulated in terms of diagrams within a laboratory-frame perturbation theory. As a special result Pippard's formula for sound-damping is rederived within this formalism.     

Study of meson systems with isospin I = 3/2 at the VES setup

Preliminary results obtained by studying K ^? π ^?, K ^? π ^? π ⁰, and K ^? π ^? η systems in the VES experiment are presented. No statistically significant signals from possible resonances were observed in two- and three-particle mass spectra of doubly charged (sub)systems.     

Evidence for higher twist effects in fast π− production by antineutrinos in neon

Evidence for a significant higher twist contribution to highz π^? production in antineutrino scattering is presented. In events withW>3 GeV andQ ²>1 GeV² in our data, it accounts for (51 ±8)% of all π^? withz above 0.5. It is consistent with thez?Q ² correlations of Berger's higher twist prediction. The data are inconclusive concerning the predictedy?z correlation andp _T dependence. Thez ?Q ² correlation is not adequately described by the Lund Monte-Carlo.     

Two and three body equations in quantum field models

In each pure phase of a ?(φ)₂ quantum field model, we establish local regularity of the Green's functions and exponential decay for noncritical models. We establish the existence of two-particle and three-particle Bethe-Salpeter kernels in the Euclidean region.     

Thermal expansion of CuGaSe2

The thermal expansion coefficients of CuGaSe₂ are measured in the temperature range from 300 to 670 K by an X-ray technique and are found to be α_a = 13.1 × 10^?6K^?1 and α_c = 5.2 × 10^?6K^?1 for the lattice parameters a and c, respectively. Some general trends in the temperature dependence of the tetragonal distortion of the I-III-VI₂ and II-IV-V₂ compounds are considered.     

Study of quasi two-body final states in K−n reactions at 8.25 GeV/c

Cross sections for various channels in 3 prong + V₀ final states of K^?n interactions are obtained at 8.25 GeV/c. An energy dependence study of the quasi two-body reactions Σ^?(1385) + vector meson and ΛB^? seem to imply the presence of cuts in the Regge exchange formalism, whereas the reaction Δ(1236) $\text{K}$¹ (890) does not require such cuts. Upper limits of 1 and 2 μb are found for the reactions K^?n → ΛA₁ and K^?n → ΛA₂.     

Relativistic nuclear and neutron matter at finite temperatures

Nuclear matter as well as neutron matter is studied in the framework of a relativistic nuclear field theory at finite temperature. A spectral representation for the two-point Green's function at finite temperature and finite density is constructed. The bulk properties of the interacting system are calculated in the Hartree and Hartree-Fock approach. In additionσ ³- andσ ⁴-self-interactions have been taken into account. We present and discuss the results of hot and dense matter for temperaturesT≦ 50 MeV and densitiesθ≦6θ ₀ (ρ ₀≈0.17 fm^?3) using six different model parameter sets.     

Direct transfer reactions derived from the green's functions method

Direct transfer reactions are extracted from the general many body theory of nuclear reactions. Especially the case of ground state transitions is considered explicitly for single- and two-nucleon transfer reactions. For this the two- and the three-particle Green's functions respectively are to be used. In deriving theT-matrices of scattering theory plausible assumptions on the energy dependence of the correspondingK-matrices are made. Expressions for direct reactions are obtained which look similar to DWBA. The resultingT-matrices contain microscopic many body expressions for the effective interaction and the optical potentials instead of the phenomenological ones of DWBA.     

Transport properties of dilute magnetic alloys

The electrical resistivity, thermopower, and the electronic part of the thermal resistivity of dilute magnetic alloys are calculated in the framework of the Suhl-Nagoaka theory. Using Bloomfield's and Hamann's solution of the Nagaoka equations, we derive expressions for the transport quantities in the limitT? ¯ T_K andT?¯ T_K to order (In ¯T _K /T)^?4 where ¯T _K is the Kondo temperature which may depend on the spin independent scattering. We find that the thermopower and deviations from the Wiedemann-Franz law in this limit decrease as ¦In ¯T_K/T¦^?3 if one neglects a trivial temperature dependence of the thermopower due to the electron-phonon interaction.     

The penetration parameter λ of the anomalousM1-conversion of the 482 keV transition in181Ta

Byγ- e _K ^? ande _K ^? -γ TDPAC measurements with the 133 keV–482 keV cascade of¹⁸¹Ta in a polycrystalline beryllium matrix theA ₂(e _K ^? )-coefficient of the 482 keV transition was determined as: A₂(482e _K ^? )=?0.095±0.015. The theoretical value is 6.0 times larger. A remeasurement of the E2/M1 mixing ratio of the same transition by integralγ- γ angular correlation measurements with a system of three 20 ccm Ge(Li)-detectors gave the result:δ(482)=4.96±0.25. Theα _K -coefficient was redetermined as:α _K (482)=0.0246±0.0018. From these data the penetration parameter:λ=157±11 is derived and compared with previously published values and theoretical estimates.     

The dispersion force of physical adsorption: II. Nonlocal theory

We present a nonlocal theory of the dispersion force of physisorption for non-polar atoms or molecules. The calculation uses linear response theory and the surface impedance method. The results generalize those presented previously, which relied on a local theory of the dielectric response. Also included in the treatment is the role of diffuseness of the interface between substrate and vacuum. Adatom dipole and quadrupole fluctuations are treated. Several diverse contributions to the potential are thus calculated, giving rise to a substantial modification of the conventional expression V ? -C₃(z-z₀)^?3, especially at small separation z.     

Investigation on native defects of α-MgAgSb and its effects on thermoelectric properties using first principles calculations

α-MgAgSb is a promising thermoelectric materials having good performance at medium temperature. Native defects in α-MgAgSb are frequently reported experimentally and are tightly involved in the thermoelectric properties of α-MgAgSb. In this paper, all possible native defects in α-MgAgSb are calculated as well as detailed results are given and discussed. The concentrations of several dominant native defects, for example, V_Ag and Ag_Sb, could reach up to 10^?4 cm^?3 at 540 K. Furthermore, the electronic structure and transport properties of α-MgAgSb with dominant native defects are investigated. Results show that the introduction of Ag_Mg and V_Ag contributes to a much lower inertial mass and slight decrease in Seebeck coefficient. The lattice thermal conductivity is greatly reduced with the introduction of native defects. For α-MgAgSb with V_Ag, the peak ZT could reach up to 1.84 at 420 K. Our calculation demonstrates that defect engineering is an effective strategy to enhance thermoelectric performance of the materials.