NMR dynamics in disordered magnets

The excitation dynamics of site diluted magnets can be described at low energies (long length scales) by magnons, and above a crossover frequency, ω_c, (short length scales) by fractons. The density of fracton states is given by , where is the fracton dimensionality. Dilution gives rise to a characteristic length ξ∝(p−p _c)^ν, wherep _c is the critical concentration for (magnetic) percolation. The crossover frequency ω_c is proportional to ξ^-1[1+(θ/2)], where θ is the rate at which the diffusion constant decays with distance for diffusion on an equivalent network. A fractal dimensionD describes the density of magnetic sites on the infinite network, and . For percolating networks, for all dimensions ≥2. Neutron scattering structure factor measurements by Uemura and Birgeneau compare well with calculations using fracton concepts. Magnons are extended at low energies, while the fracton states are geometrically localized, with a wave function envelope proportional to exp . Here, is the fracton length scale at frequency ω. The exponentd _ϕ lies between 1 andd _min, the chemical length index (of the order of 1.6 in three dimensions). The localization of the magnetic excitations causes a spread in the NMR relaxation rates. A given nuclear moment will experience only a limited set of fracton excitations, resulting in an overall non-exponential decay of the NMR relaxation signal. When strong cross-relaxation is present, the relaxation will be exponential, but the temperature dependence will be strongly altered from the concentrated result.     

Vision of a fully laser-driven ${\sf n\gamma}{-}{\sf m\gamma}$ collider

The use is suggested of a laser-accelerated dense electron sheet with an energy of (E=[(g)\tilde] mc²E=\tilde{\gamma} mc^2) as a relativistic mirror to reflect coherently a second laser with photon energy ħω, generating by the Doppler boost high-energy γ photons with $ \hbar \omega ' = 4\tilde \gamma ^2 \hbar \omega $ \hbar \omega ' = 4\tilde \gamma ^2 \hbar \omega and short duration [A. Einstein, Annalen der Physik 17, 891 (1905); D. Habs et al., Appl. Phys. B 93, 349 (2008)]. Two of these counter-propagating γ beams are focused by the parabolically shaped electron sheets into the interaction region with small, close to diffraction-limited, spot size. Comparing the new nγ-mγ collider with former proposed γγ collider schemes we achieve the conversion of many photon-pairs in a small space-time volume to matter-antimatter particles, while in the other discussed setups only two isolated, much more high-energetic photons will be converted, reaching in the new approach much higher energy densities and temperatures. With a γ-field strength somewhat below the Schwinger limit we can reach this complete conversion of the γ bunch energy into e⁺e^- or quark-antiquark q[`(q)]q\bar{q}-plasmas. For a Bose-Einstein condensate (BEC) [A. Einstein, Physikalisch-mathematische Klasse (Berlin) 22, 261 (1924); A. Einstein, Physikalisch-mathematische Klasse (Berlin) 22, 3 (1925); A. Griffin, D.W. Snoke, S. Stringari, Bose-Einstein Condensation (Cambridge University Press, 1995)] final state or for the Cooper pair ground state at higher densities [A.J. Leggett, Quantum Liquids, Oxford Graduate Texts (Oxford University Press, 2006)] the strong induced transition into this coherent state is of special interest for single-cycle γ pulses. Due to annihilation these cold coherent states are very short-lived. For γ beams with photon energies of 1–10 keV the rather cold e<sup>+</sup>e<sup>-</sup>-plasma or e<sup>+</sup>e<sup>-</sup>-BEC expands to a cold dense aggregate of positronium (Ps) atoms, where the production of Ps molecules is discussed. For photon energies of 1–10 MeV we discuss the production of a cold induced π<sup>0</sup>-BEC followed by the formation of molecules. For the direct population of higher q[`(q)]q\bar{q} densities we can study condensates of color-neutral mesons with enhanced population. For a γγ collider with several-cycle laser pulses the following cycles heat up the fermion-antifermion f[`(f)]f\bar{f} system to a certain temperature. Thus we can reach high energy densities and temperatures of an e⁺e^-γ plasma, where the production of hadrons in general or the quark-gluon phase transition can be observed. Within the long-term goal of very high photon energies of about 1 GeV in the nγ-mγ-collider, even the electro-weak phase transition or SUSY phase transition could be reached.     

Quantum phase fluctuations in an array of mesoscopic Josephson junctions

The effects of macroscopic ordering in a system of mesoscopic Josephson junctions are investigated by the quantum Monte Carlo simulation technique (using path integrals). The phase diagram of the system in the T-q plane (q is the dimensionless quantum parameter , where J is the Josephson coupling constant and C ₀ is the self-capacitance of the granules) is investigated in detail. An analysis of the behavior of the relative root-mean-square phase shifts, as well as the helicity and vorticity moduli, demonstrates the need to employ these two quantities as the parameters which most completely reflect the character of the topological phase transition in the quantum system under consideration. Two methods are proposed for calculating the vorticity modulus: 1) a modification of the Gibbs-Bogolyubov variational principle for calculating the free energy change in response to alteration of the type of boundary conditions; 2) calculation of the response to the introduction of an infinitesimal magnetic flux at some point in the system. The calculations confirm the absence of reentrant melting and phase transitions of a non-Kosterlitz-Thouless type in the region of strong quantum phase fluctuations q>1. Fiz. Tverd. Tela (St. Petersburg) 39, 1513–1519 (September 1997)     

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)     

Superconductor-insulator duality for an array of Josephson wires

A novel model system is proposed for the study of superconductor-insulator transitions that is a regular lattice whose each link consists of a Josephson-junction chain of N ≫ 1 junctions in sequence. The theory of such an array is developed for the case of semiclassical junctions with the Josephson energy E _J larger compared to the Coulomb energy E _C = e ²/2C of the junctions. An exact duality transformation is derived that transforms the Hamiltonian of the proposed model into a standard Hamiltonian of a JJ array. The nature of the ground state is controlled (in the absence of random offset charges) by the parameter q ≈ N ² exp with the superconductive state corresponding to small q < q _c . The values of q _c are calculated for magnetic frustrations f = 0 and f = 1/2. The temperature of the superconductive transition T _c (q) and q < q _c is estimated for the same values of f. In the presence of strong random offset charges, the T = 0 phase diagram is controlled by the parameter ; the critical value and the critical temperature at zero magnetic frustration are estimated. The text was submitted by the authors in English.     

Optical-absorption anomalies near magnetic phase transitions in copper oxide

The optical absorption coefficient in the region of a wide charge-transfer band in copper oxide CuO (ℏω=3.19 eV) exhibits sharp and anomalously large (up to 8% (!)) changes near two magnetic phase transition temperatures . It is shown that the wide fundamental absorption bands can be used for optical detection of magnetic phase transitions, the parameters of long-and short-range magnetic order, and the effects of a magnetic-impurity state. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 4, 251–255 (25 February 1996)     

Harness Processes and Non-Homogeneous Crystals

We consider the Harmonic crystal, a measure on with Hamiltonian H(x)=∑ _i,j J _i,j (x(i)−x(j))²+h∑ _i (x(i)−d(i))², where x, d are configurations, x(i), d(i)∈ℝ, i,j∈ℤ ^d . The configuration d is given and considered as observations. The ‘couplings’ J _i,j are finite range. We use a version of the harness process to explicitly construct the unique infinite volume measure at finite temperature and to find the unique ground state configuration m corresponding to the Hamiltonian.     

Effective Lagrangians and IG(JPC)=1?(1?+) exotic resonance state in the VP and the PP channel

For I ^G (J ^PC)=1⁻(1⁻⁺) exotic waves in the reactions ρπ → ρπ, ρπ → ηπ, ρπ → η′π, and ρπ → and in allied reactions, a model is constructed that satisfies the conditions of unitarity and analyticity and which employs, as an input, an “anomalous” nondiagonal VPPP interaction relating the ρπ, ηπ, η′π, and channels. The possibility of obtaining, within this simple field-theoretical model, a resonance behavior of the I ^G(J ^PC)=1⁻(1⁻⁺) amplitudes corresponding to the {10} − and {8} representations of the SU(3) group and their mixing is demonstrated explicitly in the mass range 1.3–1.6 GeV, where data of present-day experiments suggest a rich exoticism. __________ Translated from Yadernaya Fizika, Vol. 65, No. 3, 2002, pp. 579–588. Original Russian Text Copyright ? 2002 by Achasov, Shestakov.     

Electron impact excitation of the<Emphasis Type="Italic">D</Emphasis> states of Mg,Ca and Sr atoms: Complete experiment results

We have used non-relativistic and relativistic distorted wave approximation methods to study the excitation of then ¹ D states of magnesium (n = 3), calcium (n = 4) and strontium (n = 5) from the ground n¹ S state. Calculations have been performed for the complete set of parameters (σ, ). The results are presented for electron impact energies of 20 and 40 eV. We compare our results obtained from both the non-relativistic and relativistic methods with each other. Good agreement is found on comparison and the importance of relativistic effects is also explored.     

Effect of low-level Ge additions on the superconducting transition in PbTe:Tl

A study is reported of the effect of low-level germanium additions (∼0.01–0.1 at. %) on the parameters of the superconducting transition, viz. the critical temperature T _c, the second critical magnetic field H _c2, and in PbTe doped with 2 at. % Tl, which are derived from the dependence of the electrical resistivity of a sample on temperature (0.4–4.2 K) and magnetic field (0–1.3 T). The discontinuity revealed by experimental data is related to the onset of a Ge-induced structural phase transition. Fiz. Tverd. Tela (St. Petersburg) 40, 1204–1205 (July 1998)     

The insulating and conducting crystal states. Localization and delocalization of electronic states

An ab initio analysis is made of the localized (in Mott’s sense) and delocalized (band) states of an electron in a crystal. The criterion of a difference between these states is the behavior of the off-diagonal elements in the one-particle electronic density matrix for T=0. Localization can be related to its exponential falloff for |r−r′|→∞, and delocalization, to its power-law decay. This corresponds to the analyticity of the density matrix in k space of the Brillouin zone in the first case, and to a singularity (Fermi step) in the second. This analyticity gives rise also to a power-law decay of the correlation functions. In a normal system, localization can be identified with the insulating state, and delocalization, with the conducting state. It is shown that the above localization criterion is applicable to disordered systems as well. Electron localization in superconductors is also discussed. It is pointed out that the above criterion of localization is met also in the BCS superconducting state and in the localized-pair model. The reason for the considerable difference between the properties of the insulating and superconducting states lies in that there are no static fluctuations in the number of electrons, 〈(ΔN)²〉₀, in the ground state of an insulator whereas in a superconductor ODLRO results in nonzero fluctuations of N of a quantum nature. Fiz. Tverd. Tela (St. Petersburg) 41, 1582–1592 (September 1999)     

On the effect of a magnetic field on the yield point and kinetics of macroplasticity in LiF crystals

A strong effect of a static magnetic field B on active deformation kinetics ( =const) in LiF crystals is observed. This is a threshold effect with respect to B and ; it is observed only for B> B _c (B≃0.4 T) and . Magnetic sensitivity is exhibited by the yield stress τ _y , which decreases by approximately a factor of 1.5 for B=0.48 T, and by the stage-II and stage-III hardening coefficients θ_II and θ _III, the former decreasing and the latter increasing in a magnetic field. A physical interpretation is proposed for the observed behavior. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 6, 470–474 (25 March 1997)     

Critical current calculations for long 0-π Josephson junctions

A zigzag boundary between a $d_{x^2 - y^2}$ and an s-wave superconductor is believed to behave like a long Josephson junction with alternating sections of 0 and π symmetry. We calculate the field-dependent critical current of such a junction, using a simple model. The calculation involves discretizing the partial differential equation for the phase difference across a long 0-π junction. In this form, the equations describe a hybrid ladder of inductively coupled small 0 and π resistively and capacitively shunted Josephson junctions (RCSJ's). The calculated critical critical current density J_c(H_a) is maximum at non-zero applied magnetic field H_a, and depends strongly on the ratio of Josephson penetration depth λ_J to facet length L_f. If λ_J/L_f ≫1 and the number of facets is large, there is a broad range of H_a where J_c(H_a) is less than 2% of the maximum critical current density of a long 0 junction. All of these features are in qualitative agreement with recent experiments. In the limit λ_J/L_f →∞, our model reduces to a previously-obtained analytical superposition result for J_c(H_a). In the same limit, we also obtain an analytical expression for the effective field-dependent quality factor Q_J(H_a), finding that . We suggest that measuring the field-dependence of Q_J(H_a) would provide further evidence that this RCSJ model applies to a long 0-π junction between a d-wave and an s-wave superconductor.     

Quark-Antiquark states and their radiative transitions in terms of the spectral integral equation: Bottomonia

In the framework of the spectral integral equation, we consider the states and their radiative transitions. We reconstruct the interaction on the basis of data for the levels of the bottomonium states with J ^PC = 0⁻⁺, 1⁻⁻, 0⁺⁺, 1⁺⁺, 2⁺⁺ as well as the data for the radiative transitions γ (3S) → _γχbJ(2P) and γ(2S) → _γχbJ(1P) with J = 0, 1, 2. We calculate bottomonium levels with the radial quantum numbers n ≤ 6, their wave functions, and corresponding radiative transitions. The ratios Br[_χbJ(2P) → _γγ(2S)]/Br[_χbJ(2P) → _γγ(1S)] for J = 0, 1, 2 are found to be in agreement with data. We determine the component of the photon wave function using the data for the e ⁺ e ⁻ annihilation, e ⁺ e ⁻ → γ(9460), γ(10 023), γ(10 036), γ(10 580), γ(10 865), γ(11 019), and predict partial widths of the two-photon decays ηb0 → γγ, χb0 → γγ, χb2 → γγ for the radial excitation states below the threshold (n ≤ 3). The text was submitted by the authors in English.     

Excitonic light-absorption and amplification bands in the presence of laser radiation

We examine the absorption and amplification bands of a weak probe signal in the presence of Bose-Einstein condensation of excitons that emerges in nonequilibrium conditions in the field of coherent laser radiation with a wave vector k ₀. We assume that the detuning from resonance between the energy ħω _ex (k ₀)+L ₀ of the exciton level, which is shifted because of exciton-exciton interaction, and the laser photon energy ħω _L , is generally nonzero. The elementary excitation spectrum consisting of the quasiexcitonic and quasienergy branches determines the optical properties of the system. When there is real induced Bose-Einstein condensation, at the two branches touch, as they do in spontaneous Bose-Einstein condensation. In virtual induced Bose-Einstein condensation, when , instabilities emerge in the spectrum in certain regions of the k-space. These instabilities are caused by a real transformation of two laser photons into two extracondensate particles. Nonequilibrium extracondensate excitons strongly affect the absorption and amplification of the probe light signal. We show that light absorption is due to the quantum transition from the ground state of the crystal to the quasiexcitonic branch of the spectrum. On the other hand, amplification of the signal is caused by the transition from the quasienergy branch to the ground state of the crystal. The same transition can be explained by a real transformation of two laser photons into a vacuum photon of frequency ħcq and a crystal exciton with a wave vector 2k ₀−q. Finally, we show that the excitonic absorption and light-amplification bands are essentially anisotropic at and depend on the orientation of the vectors q and k ₀. Zh. éksp. Teor. Fiz. 112, 167–179 (July 1997)     

Magnetic susceptibility of multilayered carbon nanotubes

A theoretical study of the magnetic susceptibility of multilayered carbon nanotubes in fields both parallel, H _∥, and perpendicular, H _⊥, to the tube axis has been carried out disregarding electron-electron interaction. The temperature dependences of the magnetic susceptibility obtained exhibit a nontrivial form for H _∥, which is related to the quasi-one-dimensionality of such a system as the nanotube. The dependences of the magnetic susceptibility on chemical potential χ(μ) have also been derived. At low temperatures, χ(μ) has sharp peaks in fields H _∥, which is connected with the presence of singularities in the density of states of nanotubes. The effect of interlayer coupling on magnetic susceptibility of small-radius tubes has been investigated numerically. Fiz. Tverd. Tela (St. Petersburg) 40, 1950–1954 (October 1998)     

Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane

We consider the Edwards-Anderson Ising spin glass model on the half-plane \mathbbZ ×\mathbbZ⁺{\mathbb{Z} \times \mathbb{Z}^+} with zero external field and a wide range of choices, including mean zero Gaussian for the common distribution of the collection J of i.i.d. nearest neighbor couplings. The infinite-volume joint distribution K(J,a){\mathcal{K}(J,\alpha)} of couplings J and ground state pairs α with periodic (respectively, free) boundary conditions in the horizontal (respectively, vertical) coordinate is shown to exist without need for subsequence limits. Our main result is that for almost every J, the conditional distribution K(a | J){\mathcal{K}(\alpha\,|\,J)} is supported on a single ground state pair.     

High resolution study of AsHD2: Ground state and the three bending fundamental bands ν3, ν4, and ν6

For the first time the infrared spectrum of the AsHD₂ molecule has been measured in the region of the bending fundamental bands ν₃, ν₄, and ν₆ on a Fourier transform spectrometer with a resolution of 0.0024 cm⁻¹ and analyzed. More than 5500 transitions with J^max = 26 have been assigned and used both to obtain “ground state combination differences” and for the determination of upper state ro-vibrational energies of the triad (001000), (000100), and (000001). Rotational parameters including centrifugal distortion coefficients up to octic terms of the ground vibrational state were calculated by fitting more than 500 “ground state combination differences” with J^max and . The obtained set of 24 parameters provides a rms-deviation of 0.00011 cm⁻¹. The upper energies were fitted with 52 parameters of an effective Hamiltonian which takes into account strong resonance interactions between all vibrational states of the triad (001000), (000100), and (000001). The rms-deviation for the energy levels considered in the fit is 0.00014 cm⁻¹.