Hall-Koeffizient und spezifischer elektrischer Widerstand flüssiger Metallegierungen

The Hall coefficient and the electrical resistivity of liquid alloys has been measured with an ac current — ac magnetic field method. The experimental Hall coefficients are in agreement with the values given by the free-electron model. If for alloys of the Ag-In type the Fermi wave numbers 2k _F deduced from the experimental Hall coefficients agree with the wave numbersK _p of the first maximum of the partial or total correlation functionsa _AB ora(K), negative temperature coefficients and a maximum of the electrical resistivity are observed for the corresponding concentrations. For alloys of the In-Sn type,K _p is allways smaller than 2k _F, and these alloys do not show any anomalies of the electrical resistivity. The behavior of the electrical resistivity can be explained using the formula for liquid alloys due toFaber andZiman.     

Short-wavelength plasmons in low-dimensional systems

The dispersion of plasma waves in systems of various dimensions is investigated up to the end point of the spectrum. In 2D and 3D systems, the plasmon spectrum still ends (due to Landau damping) within the applicability range of the quasi-classical approximation, i.e., for ?k ? p _F (?k is the plasmon momentum and p _F is the electron Fermi momentum). In 1D systems, the results are qualitatively different, since the Landau damping is concentrated in a region where the quantum effects cannot be ignored. This peculiarity of 1D systems gives rise to undamped branches of acoustic plasmons with a phase velocity lower than the electron Fermi velocity in multicomponent 1D plasmas.     

Quantum quenches in one-dimensional gapless systems

We present a comparison between the bosonization results for quantum quenches and exact diagonalizations in microscopic models of interacting spinless fermions in a one-dimensional lattice. The numerical analysis of the long-time averages shows that density-density correlations at small momenta tend to a non-zero limit, mimicking a thermal behavior. These results are at variance with the bosonization approach, which predicts the presence of long-wavelength critical properties in the long-time evolution. By contrast, the numerical results for finite momenta suggest that the singularities at 2k _F in the density-density correlations and at k _F in the momentum distribution are preserved during the time evolution. The presence of an interaction term that breaks integrability flattens out all singularities, suggesting that the time evolution of one-dimensional lattice models after a quantum quench may differ from that of the Luttinger model.     

Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys

In this short review, we first discuss the results, which are mainly devoted to the generalizations of the famous Kohn–Luttinger mechanism of superconductivity in purely repulsive fermion systems at low electron densities. In the context of repulsive-U Hubbard model and Shubin–Vonsovsky model we consider briefly the superconducting phase diagrams and the symmetries of the order parameter in novel strongly correlated electron systems including idealized monolayer and bilayer graphene. We stress that purely repulsive fermion systems are mainly the subject of unconventional low-temperature superconductivity. To get the high temperature superconductivity in cuprates (with T_C of the order of 100 K) we should proceed to the t–J model with the van der Waals interaction potential and the competition between short-range repulsion and long-range attraction. Finally we note that to describe superconductivity in metallic hydrogen alloys under pressure (with T_C of the order of 200 K) it is reasonable to reexamine more conventional mechanisms connected with electron–phonon interaction. These mechanisms arise in the attractive-U Hubbard model with static onsite or intersite attractive potential or in more realistic theories (which include retardation effects) such as Migdal–Eliashberg strong coupling theory or even Fermi–Bose mixture theory of Ranninger et al. and its generalizations.     

Grundzustand eines Fermi-Gases mit hard-sphere-Wechselwirkung

The decomposition of the ground state wave function of a Fermi gas interacting via hard core potentials into cluster functionsS _n leads to a systematic expansion of wave function and energy in powers of the parameterc=P _F r _c (r _c =hard core radius,P _F =Fermi momentum). For instance,S _n has the order of magnitudec ^n-λ-1, if λ=number of Fermion coordinates with distances smaller thanr _c . The first three energy terms agree with the ones given by other authors. Any occurrence of singular terms in the intermediate steps of the derivation can be avoided     

Fermi Surface Topology in the Case of Spontaneously Broken Rotational Symmetry

The relation between the broken rotational symmetry of a system and the topology of its Fermi surface is studied for the two-dimensional system with the quasiparticle interaction f(p, p') having a sharp peak at |p ? p'| = q₀. It is shown that, in the case of attraction and q₀ = 2p_F the first instability manifesting itself with the growth of the interaction strength is the Pomeranchuk instability. This instability appearing in the L = 2 channel gives rise to a second order phase transition to a nematic phase. The Monte Carlo calculations demonstrate that this transition is followed by a sequence of the first and second order phase transitions corresponding to the changes in the symmetry and topology of the Fermi surface. In the case of repulsion and small values of q₀, the first transition is a topological transition to a state with the spontaneously broken rotational symmetry, namely, corresponding to the nucleation of L ? π(p_F/q₀ ? 1) small hole pockets at the distance p_F ? q₀ from the center and the deformation of the outer Fermi surface with the characteristic multipole number equal to L. At q₀ → 0, when the model under study transforms to the two-dimensional Nozières model, the multipole number characterizing the spontaneous deformation is L → ∞, whereas the infinitely folded Fermi curve acquires the Hausdorff dimension D = 2 which corresponds to the state with the fermion condensate.     

Destruction of the Fermi surface due to pseudogap fluctuations in strongly correlated systems

We generalize the dynamical-mean field theory (DMFT) by including into the DMFT equations dependence on the correlation length of the pseudogap fluctuations via the additional (momentum dependent) self-energy Σ_k. This self-energy describes nonlocal dynamical correlations induced by short-ranged collective SDW-like antiferromagnetic spin (or CDW-like charge) fluctuations. At high enough temperatures, these fluctuations can be viewed as a quenched Gaussian random field with finite correlation length. This generalized DMFT + Σ_k approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with nearest and next nearest neighbor hopping. The effective single impurity problem is solved by using a numerical renormalization group (NRG). Both types of strongly correlated metals, namely, (i) doped Mott insulator and (ii) the case of the bandwidth W ? U (U-value of local Coulomb interaction) are considered. By calculating profiles of the spectral densities for different parameters of the model, we demonstrate the qualitative picture of Fermi surface destruction and formation of Fermi arcs due to pseudogap fluctuations in qualitative agreement with the ARPES experiments. Blurring of the Fermi surface is enhanced with the growth of the Coulomb interaction.     

Polarisations-Korrelations-Messungen am Na24

An arrangement for the measurement of angular correlations betweenβ-particles and circular polarizedγ-radiation is described and a result on Na²⁴ is given. A correlation coefficientA=(+ 0,12± 0,03) was obtained, which indicates a ratio of Gamow-Teller to Fermi matrix elementM _G /M _F > 10.     

Fermion superfluid with hybridized <Emphasis Type="Italic">s</Emphasis>- and <Emphasis Type="Italic">p</Emphasis>-wave pairings

Ever since the pioneering work of Bardeen, Cooper and Schrieffer in the 1950s, exploring novel pairing mechanisms for fermion superfluids has become one of the central tasks in modern physics. Here, we investigate a new type of fermion superfluid with hybridized s- and p-wave pairings in an ultracold spin-1/2 Fermi gas. Its occurrence is facilitated by the co-existence of comparable s- and p-wave interactions, which is realizable in a two-component ⁴⁰K Fermi gas with close-by s- and p-wave Feshbach resonances. The hybridized superfluid state is stable over a considerable parameter region on the phase diagram, and can lead to intriguing patterns of spin densities and pairing fields in momentum space. In particular, it can induce a phase-locked p-wave pairing in the fermion species that has no p-wave interactions. The hybridized nature of this novel superfluid can also be confirmed by measuring the s- and p-wave contacts, which can be extracted from the high-momentum tail of the momentum distribution of each spin component. These results enrich our knowledge of pairing superfluidity in Fermi systems, and open the avenue for achieving novel fermion superfluids with multiple partial-wave scatterings in cold atomic gases.     

M-Zentrenbildung in röntgenbestrahlten KCl-Kristallen

The production of F- and M-centres in KCl by X-irradiation has been studied at temperatures between ?20 °C and 50 °C. The optical absorption measurements could be conducted without interrupting the X-irradiation. The results can be summarized as follows: 1. In Harshaw KCl crystals the number of F-centres created by the so-called fast coloration process was proportional to the height of the absorption band at 204 mμ prior to the irradiation. 2. The F-centres formed by the fast process did not contribute to the formation of M-centres. 3. In crystals with a strong absorption band at 204 mμ unstable M-centres were observed, which decayed rapidly after the cessation of the X-irradiation. Their concentration was found to be independent of the F-centre concentration. 4. At temperatures below 0 °C the relation between the concentration of the stable M-centres and the F-centre concentration could not any longer be represented by [M]=k ₁₂·[F₁]·[F₂]+k ₂₂·[F₂]², F₁ and F₂ referring to the F-centres created respectively by the fast and the slow coloration process. Except at very low F₂-centre concentrations however the relationship [M]=k ₀+k ₂·[F₂]² represented the experimental data at all temperatures between ?20 °C and 50 °C. At constant temperaturek ₂ varied withL, the X-ray energy absorbed per unit time and unit volume, according to 1/k ₂=a+bL+cL ². The temperature dependence ofa ^?1 b ^?1 andc ^?1 could be approximated by Boltzmann factors. The corresponding activation energies wereE _a=0.12 eV,E _b=0.53 eV,E _c=0.97 eV.     

Inflation of the early cold Universe filled with a nonlinear scalar field and a nonideal relativistic Fermi gas

We consider a possible scenario for the evolution of the early cold Universe born from a fairly large quantum fluctuation in a vacuum with a size a ₀ ? l _P (where l _P is the Planck length) and filled with both a nonlinear scalar field φ, whose potential energy density U(φ) determines the vacuum energy density λ, and a nonideal Fermi gas with short-range repulsion between particles, whose equation of state is characterized by the ratio of pressure P(n _F ) to energy density ε(n _F ) dependent on the number density of fermions n _F . As the early Universe expands, the dimensionless quantity ν(n _F ) = P(n _F )/ε(n _F ) decreases with decreasing n _F from its maximum value ν_max = 1 for n _F → ∞ to zero for n _F → 0. The interaction of the scalar and gravitational fields, which is characterized by a dimensionless constant ξ, is proportional to the scalar curvature of four-dimensional space R = κ[3P(n _F )–ε(n _F )–4λ] (where κ is Einstein’s gravitational constant), and contains terms both quadratic and linear in φ. As a result, the expanding early Universe reaches the point of first-order phase transition in a finite time interval at critical values of the scalar curvature R = R _c =–μ²/ξ and radius a _c ? a ₀. Thereafter, the early closed Universe “rolls down” from the flat inflection point of the potential U(φ) to the zero potential minimum in a finite time. The release of the total potential energy of the scalar field in the entire volume of the expanding Universe as it “rolls down” must be accompanied by the production of a large number of massive particles and antiparticles of various kinds, whose annihilation plays the role of the Big Bang. We also discuss the fundamental nature of Newton’ gravitational constant G _N .     

Behavior of Fermi systems approaching the fermion condensation quantum phase transition from the disordered phase

The behavior of Fermi systems that approach the fermion condensation quantum phase transition (FCQPT) from the disordered phase is considered. We show that the quasiparticle effective mass M* diverges as M* ∝ 1/¦x?x_FC¦, where x is the system density and x_FC is the critical point at which FCQPT occurs. Such behavior is of general form and takes place in both three-dimensional (3D) and two-dimensional (2D) systems. Since the effective mass M* is finite, the system exhibits the Landau Fermi liquid behavior. At ¦x? x_FC¦/x_FC?1, the behavior can be viewed as highly correlated, because the effective mass is large and strongly depends on the density. In the case of electronic systems, the Wiedemann-Franz law is valid and the Kadowaki-Woods ratio is preserved. Beyond the region ¦x–x_FC¦/x_FC?1, the effective mass is approximately constant and the system becomes a conventional Landau Fermi liquid.     

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.     

Charge transfer over localized states in a TlS single crystal

It is revealed that TlS single crystals exhibit a variable range hopping conduction along a normal to their natural layers at temperatures T ≤ 230 K in a dc electric field and a nonactivated hopping conduction at low temperatures in strong electric fields. Estimates are made for the density of states near the Fermi level (N _F = 2.8 × 10²⁰ eV^?1 cm^?3 and their energy spread (ΔW = 0.02 eV), the localization radius (a = 33 Å), the average jump distance in the region of activated (R _av(T) = 40 Å) and nonactivated (R _av(F) = 78 Å) hopping conduction, and also the drop in the charge carrier potential energy along the jump distance in an electric field F: eFR = 0.006 and 0.009 eV at F = 7.50 × 10³ and 1.25 × 10⁴ V/cm, respectively.     

On the energy transport velocity in a dissipative medium

An exact definition of the group velocity v _g is proposed for a wave process with arbitrary dispersion relation ω = ω′(k) + iω″(k). For the monochromatic approximation, a limit expression v _g (k) is obtained. A condition under which v _g (k) takes the form of the Kuzelev–Rukhadze expression [1] dω′(k)/dk is found. In the general case, it appears that v _g (k) is defined not only by the dispersion relation ω(k), but also by other elements of the initial problem. As applied to the dissipative medium, it is shown that v _g (k) defines the field energy transfer velocity, and this velocity does not exceed thee light speed in vacuum. An expression for the energy transfer velocity is also obtained for the case where the dispersion relation is given in the form k = k′(ω) + ik″(ω) which corresponds to the boundary problem.     

Pressure dependence of the superconducting state parameters of a binary Ca<Subscript>70</Subscript>Mg<Subscript>30</Subscript> metallic glass superconductor

Theoretical computation of the pressure dependence of superconducting state parameters of a binary Ca₇₀Mg₃₀ metallic glass has been performed using the model potential formalism. Explicit expressions have been derived for the volume dependence of the electron-phonon coupling strength λ and the Coulomb pseudopotential μ*, considering the variation of the Fermi momentum k _F and Debye temperature θ_D with volume. Well-known Ashcroft’s empty core model pseudopotential and five different types of the local-field correction functions, namely, Hartree, Taylor, Ichimaru-Utsumi, Farid et al. and Sarkar et al. have been used for obtaining pressure dependence of transition temperature T _C and the logarithmic volume derivative Φ of the effective interaction strength N ₀ V for the metallic glass superconductor. It has been obtained that T _C of Ca₇₀Mg₃₀ metallic glass decreases rapidly with increasing pressure up to 60% decrease in the volume, for which the μ* and Φ curves show a linear nature. The superconducting phase disappears at about 60% decrease in the volume.     

In-plane torque and gap symmetry of untwinned YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7</Subscript> crystals

The reversible magnetic torque of untwinned YBa₂Cu₃O₇ single crystals shows the four-fold symmetry in thea-b plane. The irreversible torque indicates evidence for a novel intrinsic pinning along thea andb axes. These facts mean that the free energy of the four-fold symmetry has a minimum when the field is applied along thea orb axis. The results are consistent with those expected from thed _x ²?y ² symmetry and rule out the possibility of thed _xy symmetry. The Fermi surface anisotropy is not responsible for the observed anisotropy. This is firstbulk evidence for thek-dependent gap anisotropy on the Fermi surface. The two-fold anisotropy parameter is found as\(\gamma _{ab} = \sqrt {{{m_a } \mathord{\left/ {\vphantom {{m_a } {m_b }}} \right. \kern-\nulldelimiterspace} {m_b }}} = 1.18 \pm 0.14\).     

Negative differential conductivity of metal-insulator-metal tunneling structures

The tunneling characteristics of a metal-insulator-metal junction are calculated in the framework of the two-band model, which takes into account the presence of the valence band for the insulator layer. It is demonstrated that, in the case where the Fermi level E _F of the structure under investigation lies below the middle of the band gap of the insulator, the dependence of the tunneling current on the bias voltage across the junction contains portions with a negative differential resistance at V > E _F/e. The iron-aluminum oxide-iron magnetoresistive junctions are considered as samples in which the effect under discussion can be observed. It is shown that, in the given case, the appearance of a portion with a negative differential resistance should be expected at voltages exceeding the Fermi energy \(E_{F_1 } \) for the spin-up electron band.