Solutions of Eliashberg equations for an electron-phonon coupling with a cutoff

In this paper we discuss the Eliashberg equations for the case of an electron-phonon coupling with an energy cutoff. This cutoff is imposed either for the energy difference by means of a strip function, or for both energies, with a Cooper-like expression. The strip function cutoff requires explicit calculation of not only the frequency renormalization functionZ but also the energy renormalizationX. The physical origin of such cutoffs might lie in the very strong electron-electron interaction which seems typical for highT _c superconductivity. If such cutoffs are admitted, the hypothesis thatT _c is caused at least in part by a strong electron-phonon interaction can be reconsidered. We find that the combination of strong coupling and low-energy cutoff could produce highT _c with only small isotope effect and with little damping or pulling of the phonon modes. Correlation with other physical properties, such as specific heat, is reexamined in view to estimate the coupling constant . Some objections to the model using strong electron phonon interaction are removed and better agreement with observed properties is obtained     

Similarity renormalization of the electron-phonon coupling

We study the problem of the phonon-induced electron-electron interaction in a solid. Starting with a Hamiltonian that contains an electron-phonon interaction, we perform a similarity renormalization transformation to calculate an effective Hamiltonian. Using this transformation singularities due to degeneracies are avoided explicitly. The effective interactions are calculated to second order in the electronphonon coupling. It is shown that the effective interaction between two electrons forming a Cooper pair is attractive in the whole parameter space. For a simple Einstein model we calculate the renormalization of the electronic energies and the critical temperature of superconductivity.     

Eliashberg theory with the external pair potential

Based on BCS model with the external pair potential formulated in a work Grigorishin (2017) [1], analogous model with electron-phonon coupling and Coulomb coupling is proposed. The generalized Eliashberg equations in the regime of renormalization of the order parameter are obtained. High temperature asymptotics and effect of Coulomb pseudopotential on them are investigated: as in the BCS model the order parameter asymptotically tends to zero as temperature rises, but the accounting of the Coulomb pseudopotential leads to existence of critical temperature. The effective Ginzburg-Landau theory is formulated for such model.     

Direct extraction of the Eliashberg function for electron-phonon coupling: a case study of Be(10(-)10)

We propose a systematic procedure to directly extract the Eliashberg function for electron-phonon coupling from high-resolution angle-resolved photoemission measurement. The procedure is successfully applied to the Be(10(-)10) surface, providing new insights into electron-phonon coupling at this surface. The method is shown to be robust against imperfections in experimental data and suitable for wider applications.     

An Asymptotic Preserving scheme for the Euler equations in a strong magnetic field

This paper is concerned with the numerical approximation of the isothermal Euler equations for charged particles subject to the Lorentz force (the ‘Euler–Lorentz’ system). When the magnetic field is large, or equivalently, when the parameter ε$\epsilon$ representing the non-dimensional ion cyclotron frequency tends to zero, the so-called drift-fluid (or gyro-fluid) approximation is obtained. In this limit, the parallel motion relative to the magnetic field direction splits from perpendicular motion and is given implicitly by the constraint of zero total force along the magnetic field lines. In this paper, we provide a well-posed elliptic equation for the parallel velocity which in turn allows us to construct an Asymptotic-Preserving (AP) scheme for the Euler–Lorentz system. This scheme gives rise to both a consistent approximation of the Euler–Lorentz model when ε$\epsilon$ is finite and a consistent approximation of the drift limit when ε→0$\epsilon \to 0$. Above all, it does not require any constraint on the space and time-steps related to the small value of ε$\epsilon$. Numerical results are presented, which confirm the AP character of the scheme and its Asymptotic Stability.     

On the microscopic derivation of mode-mode coupling equations

Alternative results derived on a microscopic basis for the mode-mode coupling kinetic equations are shown to be identical. It is also emphasized that nonlinear kinetic equations for the gross variables describing the system are only suggested but not implied by the corresponding equations obeyed by their dynamical variables. Finally an equivalent closed form for the renormalized transport coefficients is shown to hold in mode-mode coupling theory.Miembro del Colegio Nacional. On sabbatical leave from UAM—Iztapalapa, Mexico.     

Optical spectra of organic quantum dots in the strong coupling regime

We analyze the emission spectrum of a single organic quantum dot coupled to a microcavity in the strong coupling regime. We take into account non-linearities arising from both exciton–exciton interactions and the Pauli exclusion principle. We apply the recently developed Pade approximation for regular truncation of Green functions to calculate the emission spectrum. We show that as the number of excitations in the quantum dot increases the Rabi doublet evolves into a more complicated triplet structure.     

On the critical temperature of a superconducting system

Based on the assumption that in the groundbcs state the net gain in energy is equivalent to the repulsive electron-ion and electron-electron Darwin interactions, an expression forT _c has been obtained which depends on only a few atomic parameters. The theory provides a criterion for the occurrence of superconductivity and yields satisfactory values ofT _c for metals and alloys, and ternary chalcogenides and borides. It explains the difference inT _c in the crystalline and amorphous states as well as the pressure dependence ofT _c . The possibility of occurrence of high temperature superconductivity has been explored.     

Analytical computation of amplification of coupling in relativistic equations with Yukawa potential

The approximate analytic solutions to the Klein-Gordon and Dirac equations with the Yukawa potential were derived by using the quasilinearization method (QLM). The accurate analytic expressions for the ground state energies and wave functions were presented. These high-precision approximate analytic representations are obtained by first casting the proper relativistic equation into a nonlinear Riccati form and then solving that nonlinear equation in the first QLM iteration. The choice of zero iteration is based on general features of the exact solutions near the origin and infinity. To estimate the accuracy of the QLM solutions, the exact numerical solutions were found, as well. The analytical QLM solutions are found to be extremely accurate for a small exponent parameter w of the Yukawa potential. The reasonable accuracy is kept for the medium values of w. When w approaches the critical values, the precision of the QLM results falls down markedly. However, the approximate analytic QLM solution to the Dirac equation corresponding to the maximum relativistic effect turned out to be very accurate even for w close to the exact critical , whereas the QLM calculations yield . This effect of “amplification” in compare with the Schrödinger equation critical parameter was investigated earlier [S. De Leo, P. Rotelli, Phys. Rev. D 69 (2004) 034006]. In this work, it was found that the “amplification” for the Klein-Gordon equation became all the more evident. The exact numerical value is , whereas the QLM approximation yields .     

Direct evidence for the decomposition of YBa2Cu3O7−x into orthorhombic and tetragonal phases at 200°C

The variations of room temperature resistivity (ρ ₃₀₀), powder a.c. susceptibility (χ′) and x-ray diffraction (XRD) line profiles of (013), (103) and (110); (003), (010) and (100) reflections in the step scanning mode were investigated on single phase samples of Y₁Ba₂Cu₃O_7−x (YBCO), as a function of ageing at 200°C up to 860 h. The average off-stoichiometryx=0.22 remained constant throughout the experiment.ρ ₃₀₀ showed a monotonic increase while the superconducting transition curves showed increasing sharpening with ageing time. XRD of the reflections investigated developed satellite structures or additional intensities at 2θ values different from those of main reflections. The results are consistent with the prediction and earlier observation of the decomposition of the off-stoichiometric YBCO into oxygen ordered orthorhombic and vacancy ordered tetragonal phases.     

Solution of N-S equations based on the quadtree cut cell method

With the characteristic of the quadtree data structure, a new mesh generation method, which adopts square meshes to decompose a background domain and a cut cell approach to express arbitrary boundaries, is proposed to keep the grids generated with a good orthogonality easily. The solution of N-S equations via finite volume method for this kind of unstructured meshes is derived. The mesh generator and N-S solver are implemented to study two benchmark cases, i.e. a lid driven flow within an inclined square and a natural convection heat transfer flow in a square duct with an inner hot circular face. The simulation results are in agreement with the benchmark values, verifying that the present methodology is valid and will be a strong tool for two-dimensional flow and heat transfer simulations, especially in the case of complex boundaries. Supported by Japan Society for the Promotion of Science (Grant No. C20560175) and the National Natural Science Foundation of China (Grant Nos. 10872159 and 40675011)     

一类广义强阻尼Sine-Gordon方程的整体解

同时考虑黏性效应及外阻尼作用研究了一类广义强阻尼Sine-Gordon方程-利用Galerkin方法,首先证明了该方程在初值u(x,0)∈H¹₀(Ω),u_t(x,0)∈L²(Ω)的条件下初边值问题存在整体弱解u(x,t),并证明了整体弱解关于初始条件具有 关键词： Sine-Gordon型方程 强阻尼 Galerkin方法 整体解     

Spatially periodic modulation of the level population upon saturation for centers with weak and strong electron-phonon interactions

Simple relationships are derived for describing a spatially periodic modulation of the difference between the diagonal elements of the density matrix for individual orientation groups of quantum systems in anisotropic crystals and for centers of the crystal as a whole. It is revealed that the modulation depth of the level populations upon saturation for centers with a strong electron-phonon interaction in the limit is two times greater than that for centers with pure electronic optical transitions. The effect of doubling of the wave number of the periodic structures induced by excited centers is described using crystals with a rutile structure and a four-fold optic axis as an example.     

An Approximated Solution of the Einstein Equations for a Rotating Body with Negligible Mass

The paper considers the problem of finding the metric of space time around a rotating, weakly gravitating body. Both external and internal metric tensors are consistently found, together with an appropriate source tensor. All tensors are calculated at the lowest meaningful approximation in a power series. The two physical parameters entering the equations (the mass and the angular momentum per unit mass) are assumed to be such that the mass effects are negligible with respect to the rotation effects. A non zero Riemann tensor is obtained. The order of magnitude of the physical effects is discussed.     

Some Comments on a Recently Derived Approximated Solution of the Einstein Equations for a Spinning Body with Negligible Mass

Recently, an approximated solution of the Einstein equations for a rotating body whose mass effects are negligible with respect to the rotational ones has been derived by Tartaglia. At first sight, it seems to be interesting because both external and internal metric tensors have been consistently found, together an appropriate source tensor; moreover, it may suggest possible experimental checks since the conditions of validity of the considered metric are well satisfied at Earth laboratory scales. However, it should be pointed out that reasonable doubts exist if it is physically meaningful because it is not clear if the source tensor related to the adopted metric can be realized by any real extended body. Here we derive the geodesic equations of the metric and analyze the allowed motions in order to disclose possible unphysical features which may help in shedding further light on the real nature of such approximated solution of the Einstein equations.