Josephson and single-particle currents between partially dielectricized superconductors with charge-density waves

The amplitudes of the nonstationary Josephson current I ¹, the interference current I ², and the quasiparticle current J through symmetric and asymmetric tunnel junctions, including superconductors with charge density waves, are calculated. In the symmetric (s) case the dependence of the Josephson current I _s ¹ on the voltage V on the junction has a logarithmic singularity at |eV|=2Δ, Δ+D, and 2D, where , Δ and Σ are the superconducting and dielectric order parameters, and e is the unit charge. At temperatures T≠0 jumps appear in the current-voltage characteristics I _s ¹ (V) at |eV|=D−Δ. Jumps and singularities are observed in the currents I _s ² and J _s at the same voltages at which singularities and jumps appear in I _s ¹ , respectively. In the nonsymmetric (ns) junctions which include an ordinary superconductor, singularities and jumps occur at |eV|=D+Δ_BCS, Δ+Δ_BCS, and (for T≠0) |D−Δ_BCS| and |Δ−Δ_BCS|, where Δ_BCS is the order parameter of an ordinary superconductor. The quasiparticle current J _ns is an asymmetric function of the voltage V and does not depend on the sign of Σ. The results are compared with experiment. Fiz. Tverd. Tela (St. Petersburg) 39, 991–999 (June 1997)     

Mean square number fluctuation for a fermion source and its dependence on neutrino mass for the universal cosmic neutrino background

Using the general formulation for obtaining chemical potentialμ of an ideal Fermi gas of particles at temperature T, with particle rest mass m₀ and average density 〈N〉/V, the dependence of the mean square number fluctuation 〈ΔN ²〉/V on the particle mass m₀ has been calculated explicitly. The numerical calculations are exact in all cases whether rest mass energym ₀c² is very large (non-relativistic case), very small (ultra-relativistic case) or of the same order as the thermal energy k_BT. Application of our results to the detection of the universal very low energy cosmic neutrino background (CNB), from any of the three species of neutrinos, shows that it is possible to estimate the neutrino mass of these species if from approximate experimental measurements of their momentum distribution one can extract, someday, not only the density 〈N _v〉/V but also the mean square fluctuation 〈Δ _v ² 〉/V. If at the present epoch, the universe is expanding much faster than thermalization rate for CNB, it is shown that our analysis leads to a scaled neutrino massm _v instead of the actual massm _0v .     

Influence of quantum fluctuations on the Néel temperature of a dilute two-dimensional anisotropic antiferromagnet

A quantum Monte Carlo procedure is used to calculate the energy, sublattice magnetization, Néel temperature, and the slopes of the S=[1/T _N(x=0)]dT _N(x)/dx curves as functions of the hole concentration and the exchange anisotropy Δ=1−J _x,y/J _z in the Heisenberg model with anisotropic negative interactions between nearest neighbors in a square lattice with dilution among the lattice sites. The slope diverges in the limit Δ→0: S∼ln(6.5/Δ). Fiz. Tverd. Tela (St. Petersburg) 39, 898–900 (May 1997)     

Energy spectrum of excitations in quasi-one-dimensional conductors with a charge-density wave

A well-formed energy gap Δ is observed in the energy spectrum of the quasi-one-dimensional orthorhombic conductor TaS₃ at temperatures much lower than the Peierls transition temperature T _P . As the temperature increases, in the region T>T _P /2 there is a growth of the density of states in the gap and a relative decrease of the density at energies greater than Δ. In addition, absorption lines which probably correspond to soliton states in a charge-density wave are observed in the gap. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 4, 246–250 (25 February 1996)     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

Partial suppression of hydrodynamic mixing in profiled shells

The problems of stability and mixing are important in the physics of high-energy densities. Ablation-induced acceleration of foils and compression of liners entail loss of symmetry and the development of instability. The most destructive instability is the fundamental f ⁻ mode, which conserves the pressure in Lagrangian particles. A means has been proposed to eliminate this dangerous mode, based on special profiling of the mass distribution among the subshells. The presence of this mode has led to novel proposals for limiting the degree of instability and optimization of the shells by profiling in the important case of very large density ratios at the ablation front. The solution is based on a class of new polytropes with an inverted density profile and a negative polytrope index N. In this class the density ρ of the material does not decrease towards the boundary with the vacuum, as for ordinary polytropes with N>0, but rather increases. This permits modeling multilayer distributions of ρ typical of inertial confinement fusion systems in which the high-density subshells form an inner core surrounding a low-pressure cavity, and the outer layers are made from low-density materials (plastic, foam type materials, composites). It is emphasized that the distributions are self-similar, and hence both the linear and the turbulent dynamics are scale-invariant. The spectral problem of perturbations in an incompressible fluid has a hidden symmetry. Isospectral deformations of the density profile I{ρ ₀(_y)} are known that leave the spectrum unchanged. It is of interest to apply the transformation I to the invariant f ^± modes, since they are not tied to any specific profile of ρ ₀(y). This paper analyzes a new type of invariant mode obtained in this way. Zh. éksp. Teor. Fiz. 111, 1347–1368 (April 1997)     

Excess space charge in strontium titanate

An analysis is made of mechanisms of the formation and redistribution of space charge which influence the dielectric hysteresis in SrTiO₃. The excess space charge density in SrTiO₃ at 4.2 K is estimated by comparing calculated and experimental dependences of the initial capacitance and the dielectric hysteresis parameter ΔC/C ₀ as a function of the crystal thickness. Fiz. Tverd. Tela (St. Petersburg) 40, 245–247 (February 1998)     

Observation of Δ+→ pπ0 decay in heavy-ion collisions

Proton-π⁰ coincidences have been measured at the beam energy of 180A MeV in the reaction Ar+Ca studied by TAPS at SIS/GSI. In the proton-π⁰ invariant mass spectrum we observe a significant excess of strength above the background obtained by event mixing. We attribute this signal to the strength distribution N _Δ of the Δ baryonic resonance. No correlation is observed in the case of deuteron-π⁰ coincidences. Assuming isotropic emission of π⁰ and Δ⁺ from a midrapidity thermal source and isospin symmetry, we determined the global N _Δ/N _πratio of 0.79 ±0.30(stat) ±0.2(syst). This value indicates that most pions produced at subthreshold energy in heavy-ion reaction are mediated by the Δ-resonance. Received: 7 April 2000 / Accepted: 29 August 2000     

Dispersion of the Voigt effect in the magnetic semiconductors Cd1−x MnxTe

Spectral measurements of the Voigt birefringence Δn were performed for the cubic magnetic semiconductor Cd_1−x Mn _x Te (0≤x≤0.52) in order to investigate how the exchange interaction of Mn²⁺ ions with itinerant electrons depends on the electron wave vector. It was determined that Δn/x ² is independent of x and the magnetic field direction, i.e., the effect is due to the Mn²⁺ ions and is isotropic. Below the band gap edge the dispersion of the birefringence Δn can be described well in all samples by the unusual dependence Δn∼(E _g −ℏω) ^−3.5. This can be explained by a decrease of the exchange interaction of Mn²⁺ ions with itinerant electrons with increasing distance from the center of the Brillouin zone. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 8, 569–573 (25 April 1998)     

Sigma Terms of Light-Quark Hadrons

A calculation of the current-quark mass dependence of hadron masses can help in using observational data to place constraints on the variation of nature’s fundamental parameters. A hadron’s σ-term is a measure of this dependence. The connection between a hadron’s σ-term and the Feynman-Hellmann theorem is illustrated with an explicit calculation for the pion using a rainbow-ladder truncation of the Dyson-Schwinger equations: in the vicinity of the chiral limit σ_π = m_π/2. This truncation also provides a decent estimate of σ_ρ because the two dominant self-energy corrections to the ρ-meson’s mass largely cancel in their contribution to σ_ρ. The truncation is less accurate for the ω, however, because there is little to compete with an ω → ρπ self-energy contribution that magnifies the value of σ_ω by ≲25%. A Poincaré-covariant Faddeev equation, which describes baryons as composites of confined-quarks and -nonpointlike-diquarks, is solved to obtain the current-quark mass dependence of the masses of the nucleon and Δ, and thereby σ_N and σ_Δ. This “quark-core” piece is augmented by the “pion cloud” contribution, which is positive. The analysis yields σ_N ≃ 60 MeV and σ_Δ ≃ 50 MeV.     

Trajectory attractor of a reaction-diffusion system with a series of zero diffusion coefficients

We study a reaction-diffusion system of N equations with k nonzero and N − k zero diffusion coefficients. More exactly, the first k equations of the system contain the terms a _i Δu _i − f _j (u, v), i = 1, …, k, with the diffusion coefficient a _i > 0. The right-hand sides of the other N − k equations contain only nonlinear interaction functions −h _j (u, v), j = k + 1, …, N, with zero diffusion. Here u = (u ₁, …, u _k ) and v = (υ _k+1, …, υ _N ) are unknown concentration vectors. Under appropriate assumptions on the interaction functions f(·) and h(·), we construct the trajectory attractor of this reaction-diffusion system. We also find the trajectory attractors , δ = (δ ₁, …, δ _k ), for the analogous reaction-diffusion systems having the terms δ _j Δυ _j − h _j (u, v), j = k + 1, …, N, with small diffusion coefficients δ _j ⩾ 0 in the last N − k equations. We prove that the trajectory attractors converge to (in an appropriate topology) as δ → 0+. Dedicated to the memory of Vladimir Borovikov Partially supported by the Russian Foundation for Basic Research (projects nos. 08-01-00784 and 07-01-00500).     

Heat conductivity of a nonlinear β-FPU lattice

In this work, we propose a new approach to the computation of heat conductivity in nonlinear systems. The total heat conductivity process is decomposed into two parts: one part is an equilibrium process at the same temperature T of either end of the lattice, which does not transfer energy and the other is a nonequilibrium process at temperature ΔT of one end and a zero temperature of the opposite end of the lattice. This approach makes it possible to somewhat reduce the time of computation of heat conductivity at ΔT → 0. The threshold temperature T _thr is found to behave as T _thr ∼ N ⁻³, where N is the lattice length. The threshold temperature conventionally separates two mechanisms of heat conductivity: at T < T _thr, phonon heat conductivity is dominant; at T > T _thr, the contribution of soliton heat conductivity increases with increasing temperature. The problem of the computation of heat conductivity in the limit ΔT → 0 reduces to the heat conductivity of a harmonic lattice with time-dependent bond rigidities determined by an equilibrium process at temperature T. An exact expression for the temperature dependence of sound velocity in a lattice with a β-FPU potential at T < 10 is derived. A numerical experiment confirmed the existence of solitons and breathers that correspond to a modified Korteweg-de Vries (KdV) equation. The problem of the quantitative contribution of solitons and breathers to heat conductivity requires further study.     

Melting heat of a nanoparticle

Expressions for the melting point (T _m ), freezing temperature (T _N < T _m ), entropy change per atom (Δs), latent heat (Δh = T _m Δs), and volume change (Δv) for the solid-liquid phase transition are derived from a model of a nanocrystal in the form of a parallelepiped with a variable shape of the surface. These quantities are studied as a function of the number of atoms (N) and the shape of the nanoparticle. Calculations carried out for copper nanoparticles show good agreement with the results of computational experiments. It is shown that functions Δs, Δh, and Δv vanish in a certain range of cluster dimension N ₀ and a hysteresis between the melting point and freezing temperature disappears, T _N (N ₀) = T _m (N ₀). In such a cluster, the phases become physically identical. For nanocopper, this dimension falls into the range N ₀ = 49–309 and grows when the shape of the nanoparticle deviates from the energetically most favorable one.     

Quantum oscillations of resistance and magnetization in the degenerate semiconductor n-HgCr2Se4

In the magnetic field range ΔH=8–60 kOe we observed and studied the anomalous oscillations in the magnetic field dependence of the resistance and magnetization of single crystals of n-HgCr₂Se₄. The absence of periodicity in 1/H in the ΔH=8–20 kOe range can be explained by the non-Fermi-liquid behavior of the electron subsystem and agrees with the theory of the de Haas-van Alphen in systems with intermediate valence. In stronger fields, ΔH=20–60 kOe, the amplitude of the fundamental harmonic decreases, with the number and amplitude of the higher-order harmonics increasing. As a result, noise is superimposed on the signal as magnetic field strength grows. The temperature dependence of the magnetization is the sum of the monotonic spin-wave contribution and the oscillating part. Zh. éksp. Teor. Fiz. 113, 1877–1882 (May 1998)     

Carrier concentration dependence and impurity effects of microwave response in Bi2Sr2CaCu2O8+ y

We report the surface impedance (Z _s ) measurements in high quality single crystals of Bi₂Sr₂CaCu₂O_8+y . At relatively low oxygen content, the change of the penetration depth, Δλ(T) ≡λ(T)-λ(0), of the pure single crystals exhibits linear temperature dependence both parallel to the CuO₂ planes and in thec direction. In contrast to this behavior, by further oxygenation or 0.6% Zn substitution, theT-linear dependence is disrupted andT ² dependence of Δλ is observed. We also found that 0.9% Ni-substitution induces no pairbreaking effect. The present results suggest that the low-lying excitation spectrum of quasiparticles depends on the carrier concentration and is easily changed by a small amount of Zn substitution.     

The sign of interband interaction and stability of the superconducting ground state in the multiband model

Summary It is stressed that the stability of the superconducting ground state in the two-band model is guaranteed for both signs of the leading interband interactionW. Thereby the requirement for the energy minimum fixed the phase differences of two order parameters as |ϕ₁-ϕ₂|=0,2π, … ifW<0 and |ϕ₁-ϕ₂|=π 3π, … ifW>0, and this difference is reflected in the ground-state wave function.     

Modeling a dimer state in CuGeO3 in the two-dimensional anisotropic Heisenberg model with alternated exchange interaction

The two-dimensional Heisenberg spin-1/2 model with alternated exchange interaction along the c axis and an anisotropic distribution of the exchange interaction in the lattice, J _b/J _c=0.1, is examined. A quantum Monte Carlo method is used to calculate the phase diagrams of the antiferromagnet, the dimer state in a plane, the value of the alternation δ of the exchange interaction, and the anisotropy Δ=1−J ^xy/J ^z of the exchange interaction, Δ∼δ ^0.58(6). The following characteristics are calculated for Δ=0.25: the dependence of the temperature of the dimer-state-paramagnet transition on the alternation of the exchange interaction, T _c(δ)=0.55(4)(δ−0.082(6))^0.50(3), the singlet-triplet energy gap, and the dependence of the magnetization on the external field for some values of δ. The value of the exchange interaction, J _c=127 K, the alternation of the exchange interaction, δ=0.11J _c, and the correlation radius along the c axis, ξ _c≈28c, are determined. Finally, it is found that the temperature dependence of the susceptibility and the specific heat are in good agreement with the experimental data. Zh. éksp. Teor. Fiz. 112, 2184–2197 (December 1997)     

Effects of two strong fields in resonant four-wave mixing

An explicit solution is obtained for the four-wave mixing ω₄=ω₁−ω ₂+ω₃ of two strong fields E ₁, E ₃ and two weak fields E ₂, E ₄ in a four-level system with large Doppler broadening. Resonance of the intensity dependence of the mixing coefficient is found around equal Rabi frequencies, E ₁·d ₁=E ₃·d ₃, where d _1,3 are the dipole moments of the corresponding transitions. The effect is interpreted as a crossing of quasi-energy levels. Up to 6 peaks appear in the dependence of the conversion coefficient on the detuning of the probe field E ₂. The unexpected additional pair of peaks is a consequence of averaging over velocities. The results permit interpretation of the saturation behavior found in recent experiments on mixing in sodium vapor. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 12, 777–782 (25 December 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

ΔS = 0 effective weak chiral Lagrangianfrom the instanton vacuum

We investigate the ΔS = 0 effective chiral Lagrangian from the instanton vacuum. Based on the ΔS = 0 effective weak Hamiltonian from the operator product expansion and renormalization group equations, we derive the strangeness-conserving effective weak chiral Lagrangian from the instanton vacuum to order and the next-to-leading order in the 1/N_c expansion at the quark level. We find that the quark condensate and a dynamical term which arise from the QCD and electroweak penguin operators appear in the next-to-leading order in the 1/N_c expansion for the ΔS = 0 effective weak chiral Lagrangian, while they are in the leading order terms in the ΔS = 1 case. Three different types of form factors are employed and we find that the dependence on the different choices of the form factor is rather insensitive. The low-energy constants of the Gasser-Leutwyler type are determined and discussed in the chiral limit. Arrival of the final proofs: 2 December 2005 PACS: 12.40.-y, 14.20.Dh     

<Emphasis Type="Italic">ρρ</Emphasis>N and <Emphasis Type="Italic">ρρ</Emphasis>Δ molecules with J<Superscript>P</Superscript> = 5/2<Superscript>+</Superscript> and J<Superscript>P</Superscript> = 7/2<Superscript>+</Superscript>

The ρρN and ρρΔ three-body systems have been studied within the framework of the fixed center approximation of Faddeev equation. The ρρ interaction in isospin I = 0 , spin S = 2 is strongly attractive, and so are the N ρ, ρΔ interactions. This leads to bound states of both ρρN and ρρΔ. We find peaks of the modulus squared of the scattering matrix around 2227 MeV for ρρN, and 2372 MeV for ρρΔ. Yet, the strength of the peak for the ρρN amplitude is much smaller than for ρρΔ, weakening the case for a ρρN bound state, or a dominant ρρN component. A discussion is made on how these states can be searched for in present programs looking for multimeson final states in different reactions.