On the lower critical field and phase diagram of a thin cylindrical type-II superconductor

The lower critical field H _c1 ^cyl (T) of a superconducting cylinder with radius r ₀∼ξ(T)≪λ(T) is found on the basis of the Ginzburg-Landau theory with various boundary conditions. These results together with the well-known results for the upper critical field are used to construct phase diagrams in terms of the field versus the reduced radius r ₀∼ξ(T) variables. The jump in the average magnetization at H _c1 ^cyl (T) is calculated as a function of the reduced radius. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 8, 537–542 (25 April 1999)     

Annihilation of nematic point defects: Pre-collision and post-collision evolution

The annihilation of the nematic hedgehog and anti-hedgehog within an infinite cylinder of radius R is studied. The semi-microscopic lattice-type model and Brownian molecular dynamics are used. We distinguish among the i) early pre-collision, ii) late pre-collision, iii) early post-collision, and iv) late post-collision stages. In the pre-collision stage our results agree qualitatively with the existing experimental observations and also continuum-type simulations. The core of each defect exhibits a ring-like structure, where the ring axis is set perpendicular to the cylinder symmetry axis. For ξ⁽⁰⁾_d/(2R) > 1 the interaction between defects is negligible, where ξ⁽⁰⁾_d describes the initial separation of defects. Consequently, the defects annihilate within the simulation time window for ξ⁽⁰⁾_d/(2R) < 1. For close enough defects their separation scales as ξ_d (t_c - t)^0.4±0.1, where t_c stands for the collision time. In elastically anisotropic medium the hedgehog is faster than the anti-hedgehog. In the early pre-collision stage the defects can be treated as point-like particles, possessing inherent core structure, that interact via the nematic director field. In the late pre-collision stage the cores reflect the interaction between defects. After the collision a charge-less ring structure is first formed. In the early post-collision stage the ring adopts an essentially untwisted circular structure of the radius ξ_r. In the late post-collision stage we observe two qualitatively different scenarios. For μ = ξ_r/R < μ_c ∼ 0.25 the ring collapses leading to the escaped radial equilibrium structure. For μ > μ_c the chargeless ring triggers the nucleation growth into the planar polar structure with line defects.     

Lattice Dislocations in a 1-Dimensional Model

The spectral properties of the Schr?dinger operator T(t)=−d ²/dx ²+q(x,t) in L ²(ℝ) are studied, where the potential q is defined by q=p(x+t), x>0, and q=p(x), x<0; p is a 1-periodic potential and t∈ℝ is the dislocation parameter. For each t the absolutely continuous spectrum σ _ac (T(t))=σ _ac (T(0)) consists of intervals, which are separated by the gaps γ _n (T(t))=γ _n (T(0))=(α _n ⁻,α _n ⁺), n≥1. We prove: in each gap γ _n ≠?, n≥ 1 there exist two unique “states” (an eigenvalue and a resonance) λ _n ^±(t) of the dislocation operator, such that λ _n ^±(0)=α _n ^± and the point λ _n ^±(t) runs clockwise around the gap γ _n changing the energy sheet whenever it hits α _n ^±, making n/2 complete revolutions in unit time. On the first sheet λ _n ^±(t) is an eigenvalue and on the second sheet λ _n ^±(t) is a resonance. In general, these motions are not monotonic. There exists a unique state λ₀(t) in the basic gap γ₀(T(t))=γ₀(T(0))=(−∞ ,α₀ ⁺). The asymptotics of λ _n ^±(t) as n→∞ is determined. Received: 5 April 1999 / Accepted: 3 March 2000     

Critical currents in polycrystalline thin films of high-T c superconductors

Summary It is shown that the behaviour of the temperature dependence of the critical current in polycrystalline thin films of high-T _c superconductors depends crucially on the assumption made concerning the nature of the intergranular material. The usual assumption of a superconductor-insulator-superconductor (=SIS) ?sandwich? between each grain leads to a crossover fromI _c∼(1−T/T _c) toI _c∼(1−T/T _c)^3/2, for temperatures nearT _c (whereI _c is the critical current,T the absolute temperature, andT _c the superconducting transition temperature). Instead, for a superconductor-normal metal-superconductor (=SNS) sandwich the dependenceI _c∼(1−T/T _c)² is found for all temperatures. Consideration is given to the effect of self-magnetic field on the analysis. The comparison between expressions for continuous and granular systems is extended. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction.     

Vortex pinning in YBa2Cu3O7?x films

Evidence that pinning on linear or planar defects dominates the vortex dynamics in YBa₂Cu₃O_7−x (YBCO) films is provided by complex impedance measurements at temperature 8 K<T<T _c and magnetic field 0<B<6 T. Below the vortex lattice melting transition B_g(T) but above a threshold field B_p≈8(1-T/T _c ) T, the inductance of vortices increases as B², much less rapidly than predicted for collective pinning of vortices by point defects. Above the vortex melting line, critical scaling persists over the region B_g(T<B<B^*(T) where the vortex correlation length ξ exceeds a characteristic length scale ξ^*≡ξ(B=B^*)≈450?. The value of ξ^* is not sensitive to Al-doping in the Cu sites in the lattice and is close to the size of twin domains in the film. The nature of the observed crossovers is discussed in terms of available theoretical models for a glass-liquid transition at B_g.     

Friedel oscillation about a Friedel-Anderson impurity

The Friedel oscillations in the vicinity of a Friedel-Anderson (FA) impurity are investigated numerically. For an FA impurity in the local moment limit the normalized amplitude A(ξ) is S-shaped, approximately zero at short distances, approaching two at large distances and crossing the value one at the characteristic length ξ _1/2. Surprisingly, the Friedel oscillations of a simple non-interacting Friedel impurity with a narrow resonance at the Fermi level show a very similar behavior of their amplitude A(ξ). A comparison correlates the resonance width and the Kondo energy of the FA impurity with the characteristic length ξ _1/2 of the Friedel oscillations.     

On the Poisson Limit Theorems of Sinai and Major

Let f(ϕ) be a positive continuous function on 0 ≤ϕ≤Θ, where Θ≤ 2 π, and let ξ be the number of two-dimensional lattice points in the domain Π _R (f) between the curves r=(R+c ₁/R)f(ϕ) and r=(R+c ₂/R)f(ϕ), where c ₁<c ₂ are fixed. Randomizing the function f according to a probability law P, and the parameter R according to the uniform distribution μ _L on the interval [a ₁ L,a ₂ L], Sinai showed that the distribution of ξ under P×μ _L converges to a mixture of the Poisson distributions as L→∞. Later Major showed that for P-almost all f, the distribution of ξ under μ _L converges to a Poisson distribution as L→∞. In this note, we shall give shorter and more transparent proofs to these interesting theorems, at the same time extending the class of P and strengthening the statement of Sinai. Received: 15 June 1999 / Accepted: 11 February 2000     

Pseudovector heavy quarkonia in e + e −2 collisions

It is shown that BR(χ _b1(1 P)→e ⁺ e ⁻)≃3.3· 10⁻⁷ and BR(χ _c1(1 P)→e ⁺ e ⁻)≃10⁻⁸. This gives realistic possibilities for searching for the production of χ _b1(1 P) and ξ _c1(1 P) states in e ⁺ e ⁻ collisions, even on the present-day colliders, to say nothing of b and c-τ factories. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 569–574 (25 April 1996)     

Current-voltage characteristics for a Peierls-conducting point contact

Current-voltage (J-V) and differential-conductivity-voltage ( dJ/dV-V) characteristics are analytically calculated at zero temperature for a point contact consisting of: two Peierls conductors P ( = 1, 2) separated by an insulator (I). Here P is a conductor with charge density wave (CDW). The J-V and dJ/dV-V characteristics depend on the CDW phases ( = 1, 2) in the mean field approximation. To calculate them analytically we assumed, = ≡Δ where ( = 1, 2) are the energy gaps of P ( = 1, 2). The current J has a discontinuous jump at eV = 2Δ for ϕ ₁ = ϕ ₂≠ 0. The differential conductivity dJ/dV has a singularity at eV = 2Δ for ϕ ₁ = ϕ ₂≠ 0. The relation J(V,ϕ ₁,ϕ ₂) = - J(- V,ϕ ₁ + π,ϕ ₂ + π) is obtained. Received 4 July 2001 and Received in final form 13 September 2001     

Insulating phases of the one-dimensional t-J model with nearest-neighbor repulsive interaction

Using the deformed Hubbard operator approach, we analytically study weak-coupling phase diagram of the one-dimensional t-J-V model at half filling. In the case of small deformed parameter ζ(≪1), the interactions induced by the no double occupancy constraint are softened, accessible by the bosonization field theory and the renormalization group technique. The ground state exhibits insulating behavior of density-wave correlations. The bond-spin-density-wave (BSDW) and bond-charge-density-wave (BCDW) phases are realized in the whole weak-coupling regime while the charge-density-wave (CDW) and spin-density-wave (SDW) phases depend on V/J > (V/J) _c or V/J < (V/J) _c , where (V/J) _c = 1/4. Furthermore, our results are expected to adiabatically continue back to ζ = 1.     

Pinning of pancake vortices in a three-dimensional Josephson medium and structure of the vortex lattice in the “critical” state

A system of pancake vortices formed near the boundary of a sample in a monotonically increasing external magnetic field is calculated with allowance for pinning due to the cellular structure of the medium for various values of the pinning parameter I, which is proportional to the critical current of the junction and the cell diameter. The shortest distance from the outermost vortex to the nearest neighbor is proportional to I ⁻¹¹. It is shown that the pinning parameter has a critical value I _c separating two regimes with different types of critical states. For I<I _c the external magnetic field has a threshold value H _t(I), above which the field immediately penetrates the interior of the junction to an infinite distance. For I>I _c the magnetic field decays linearly from the boundary into the interior of the junction. The value obtained in the study, I _c=3.369, differs from the value of 0.9716 postulated by other authors. The dependence of the slope of the magnetic field profile near the boundary on I is determined. It is shown that the slope is independent of I in intervals 2πk<I<2πk+π. Fiz. Tverd. Tela (St. Petersburg) 39, 1958–1963 (November 1997)     

Reciprocity relations for the effective electrical conductivity of randomly inhomogeneous media in the fractal regime

An exact relation for the realization-averaged effective conductivities in the fractal region is found for two-dimensional randomly inhomogeneous media. It has the form {σ _e (τ,L)~× {1/σ _e (−τ,L)~⁻¹=σ _e ² (τ=0, L≫ξ), where ξ is the correlation length (the self-averaging scale), L is the size of the system, τ=(p-p _c )/p _c , and p _c is the percolation threshold. For L≫ ξ, the system is self-averaged, and the relation transforms into the Dykhne reciprocity relation, A. M. Dykhne, Zh. éksp. Teor. Fiz. 59, 110 (1970) [Sov. Phys. JETP 32, 63 (1971)] σ _e (τ)σ _e (−τ])=σ _e ² (τ=0)= σ ₁ σ ₂. A similar relation is obtained for media with an exponentially broad distribution of local conductivities, as well as for individual realizations of some deterministic structures. Zh. éksp. Teor. Fiz. 113, 1484–1490 (April 1998)     

Low-energy theorems of QCD and bulk viscosity at finite temperature and baryon density in a magnetic field

The nonperturbative QCD vacuum at finite temperature and baryon density in an external magnetic field has been studied. Relations between the nonperturbative condensates and the thermodynamic pressure at T ≠ 0, μ _q ≠ 0, and H ≠ 0 have been obtained and the low-energy theorems have been derived. Bulk viscosity ζ(T, μ, H) has been described in terms of the main thermodynamic quantities characterizing the quark-gluon matter at T ≠ 0, μq ≠ 0, and H ≠ 0. Various limiting cases have been discussed.     

Low-temperature properties of CePd2In

We report measurements of the specific heatC _p(T), electrical resistivity ϱ(T) and magnetic susceptibility ξ(T) of hexagonal CePd₂In, at low temperatures. Anomalies inC _p(T), χ(T) and ϱ(T) atT=1.23 K, indicate a phase transition, most likely to an antiferromagnetically-ordered phase. The electronic entropy reachesR ln2 per mole Ce at 9.2K, suggesting that the phase transition involves a doublet state. The ordered phase coexists with moderately correlated itinerant electrons.     

Three-dimensional correlated-fermion phase separation from analysis of the geometric mean of the individual susceptibilities

A quasi-Gaussian approximation scheme is formulated to study the strongly correlated imbalanced Fermions thermodynamics, where the mean-field theory is not applicable. The non-Gaussian correlation effects are understood to be captured by the statistical geometric mean of the individual susceptibilities. In the three-dimensional unitary fermions ground state, a universal nonlinear scaling transformation relates the physical chemical potentials with the individual Fermi kinetic energies. For the partial polarization phase separation to full polarization, the calculated critical polarization ratio is δ _C = [1−(1−ξ)^6/5]/[1+(1−ξ)^6/5] ≐ 0.34. ξ = 4/9 gives the ratio of the symmetric ground state energy density to that of the ideal fermion gas. Supported by the National Natural Science Foundation of China (Grant Nos. 10875050 and 10675052), the Fund of Central China Normal University, and the Foundation of Ministry of Education of China (Grant No. IRT0624)     

Penetration of magnetic field into a long periodically modulated Josephson contact

A new approach to magnetic field profiling inside a Josephson contact is suggested. Its essence consists in analyzing continuous variation of a current configuration leading to a decrease in the Gibbs potential. With this approach, one can find a configuration into which the Meissner state turns when an external field slightly exceeds the upper boundary of the Meissner regime and trace the evolution of this configuration with increasing field. Calculations show that there exists critical value I _c of the pinning parameter in the range 0.95–1.00. This critical value separates two possible conditions of magnetic field penetration into the contact. At I > I _c, a near-boundary current configuration completely compensating for the external field inside the contact arises irrespective of the external field strength. At I < I _c, such a situation is observed only until the external field strength exceeds certain value H _max. Higher fields penetrate into the contact indefinitely deep. In nearboundary configurations, the magnetic field drops with increasing depth almost linearly. Its slope k has rational values, which remain constant within finite intervals of I. As I goes beyond a given interval, k rises stepwise and takes on another rational value. When an external magnetic field is switched on adiabatically, configurations with a maximal growth rate of the magnetic field are observed.     

Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Charmonia

Earlier by the authors (Yad. Fiz. 70, 68 (2007)), the bƃ states were treated in the framework of the spectral integral equation, together with simultaneous calculations of radiative decays of the considered bottomonia. In the present paper, such a study is carried out for the charmonium states. We reconstruct the interaction in the c-c sector on the basis of the data for the charmonium levels with J _PC = 0⁻⁺, 1⁻⁻, 0⁺⁺, 1⁺⁺, 2⁺⁺, 1⁺⁻ and radiative transitions ψ(2S) → γχ _c0(1P), γχ _c1(1P), γχ _c2(1P), γχ _c(1S) and χ _c0(1P), χ _c1(1P), χ _c2(1P) → γJ/ψ. The c-c levels and their wave functions are calculated for the radial excitations with n ≤ 6. Also, we determine the c-c component of the photon wave function using the e ⁺ e ⁻-annihilation data: e ⁺ e ⁻ → J/ψ(3097), ψ(3686), ψ(3770), ψ(4040), ψ(4160), ψ(4415) and perform the calculations of the partial widths of the two-photon decays for the n = 1 states η _c0(1S), χ _c0(1P), χ _c2(1P) → γγ and n = 2 states η _c0(2S) → γγ, χ _c0(2P) → γγ. We discuss the status of the recently observed c-c states X(3872) and Y(3941): according to our results, the X(3872) can be either χ _c1(2P) or η _c2(1D), while Y(3941) is χ _c2(2P). The text was submitted by the authors in English.     

The study of two-color excitation upconversion of Pr(0.5)Yb(3):ZBLAN

The excited state absorption upconversion of Pr(0.5)Yb(3):ZBLAN glass material, under two-color excitation of the 960 nm semiconductor laser and the Xe lamp light simultaneously, is reported in this article. It was found that the upconversion emission spectra of 480.1, 519.0, 601.9 and 631.8 nm coincide with the common emission spectra. Meanwhile, the upconversion-excitation spectrum has three obvious peaks under two-color excitation, and they respectively correspond to the 856.0 nm upconversion excitation transition [¹G₄(Pr³⁺)→¹I₆(Pr³⁺) and ¹G₄(Pr³⁺)→³P₁(Pr³⁺)], the 789.0 nm upconversion excitation transition ¹G₄(Pr³⁺)→³P₂(Pr³⁺), and the 803.7 nm upconversion excitation transition ³H₆(Pr³⁺)→¹D₂(Pr³⁺). The upconversion excitation transition ¹G₄(Pr³⁺)→¹I₆(Pr³⁺) is strong because its oscillator strength f = 23.040×10⁻⁶ is large, which results in a large peak appearing in the upconversion excitation spectrum. That is just the new interesting two-color excitation upconversion luminescence phenomenon of Pr(0.5)Yb(3):ZBLAN induced by one laser and one continuous normal light simultaneously.     

Is the Abrikosov model applicable for describing electronic vortices in plasmas?

A new model of electronic vortices in plasma is studied. The model assumes that the profile of the Lagrangian invariant I, equal to the ratio I=Ω/n of the electronic vorticity to the electron density, is given. The proposed approach takes into account the magnetic Debye scale r _B ≃B/4πen, which leads to breakdown of plasma quasineutrality. It is shown that the Abrikosov singular model cannot be used to describe electron vortices in plasmas because of the fundamental limitation on the electron vorticity on the axis of a vortex in a plasma. Analysis of the equations shows that in the model considered for the electronic vorticity, the total magnetic flux decreases when the size r ₀ of the region in which I≠0 becomes less than c/ω_pe (ω_pe is the electron plasma frequency). For ω _pe r ₀/c≪1, an electronic vortex is formed in which the magnetic flux decreases as r ₀ ² and the inertial component predominates in the electronic vorticity. The structure arising as ω _pe r ₀/c⇒0 is a narrow “hole” in the electron density, which can be identified from the spectrum of electromagnetic waves in this region. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 461–466 (10 April 1998)