Correlations in one-dimensional quantum impurity problems with an external field

We study response functions of integrable quantum impurity problems with an external field at T = 0 using non-perturbative techniques derived from the Bethe ansatz. We develop the first steps of the theory of excitations over the new, field-dependent ground state, leading to renormalized (or “dressed”) form factors. We obtain exactly the low-frequency behaviour of the dynamical susceptibility χ″ (ω) in the double-well problem of dissipative quantum mechanics (or equivalently the anisotropic Kondo problem), and the low-frequency behaviour of the AC noise S_t(ω) for tunnelling between edges in fractional quantum Hall devices. We also obtain exactly the structure of singularities in χ″ (ω) and S_t (ω). Our results differ significantly from previous perturbative approaches.     

“Missing moment” and perturbative methods for polynomial iterated function systems

An iterated function system (IFS) over a compact metric space X is defined by a set of contractive maps w_i: X → X, i = 1,…,N, with associated nonzero probabilities p_i > 0, p_i = 1. The “parallel” action of the maps defines a unique compact invariant attractor set A X which supports an invariant measure μ and which is balanced with respect to the p_i. For linear , the invariance of μ yields a relation between the moments g_n = ∫ χⁿ dμ which permits their recursive computation from the initial value g₀ = 1. For nonlinear w_i, however, the moment relations are incomplete and do not permit a recursive computation. This paper describes two methods of obtaining accurate estimates of the moments when the IFS maps w_i are polynomials: (i) application of the necessary Hausdorff conditions on the g_i to obtain convergent upper and lower bounds and (ii) a perturbation expansion approach. The methods are applied to some model problems.     

“Gluelump” spectrum and adjoint source potential in lattice QCD3

We calculate the potential between “quarks” which are in the adjoint representation of SU(2) color in the three-dimensional lattice theory. We work in the scaling region of the theory and at large quark separations R. We also calculate the masses M_Qg of color-singlet bound states formed by coupling an adjoint quark to adjoint glue (“gluelumps”). Good scaling behavior is found for the masses of both magnetic (angular momentum J = 0) and electric (J = 1) gluelumps, and the magnetic gluelump is found to be the lowest-lying state. It is naively expected that the potential for adjoint quarks should saturate above a separation R_scr where it becomes energetically favorable to produce a pair of gluelumps. We obtain a good estimate of the naive screening distance R_scr. However we find little evidence of saturation in the potential out to separations R of about 1.5R_scr.     

Kondo screening in gapless magnetic alloys

The low-energy physics of a spin- Kondo impurity in a gapless host, in which the density of band states ρ₀(ε)=|ε|^r/(|ε|^r+β^r) vanishes at the Fermi level ε=0, is studied by the Bethe ansatz. It is shown that the growth of the parameter Γ_r=βg^−1/r (where g is an exchange coupling constant) drives the ground state of the system from the Kondo regime with a screened impurity spin to the Anderson regime, where the impurity spin is unscreened. However, in a weak magnetic field H, the impurity spin exceeds its free value, , due to a strong coupling to a band.     

Duality and quantum-algebra symmetry of the AN−1 open spin chain with diagonal boundary fields

We show that the transfer matrix of the A_N−1⁽¹⁾ open spin chair with diagonal boundary fields has the symmetry U_q(SU(l)) × U_q(SU(N−l)) × U(1), as well as a “duality” symmetry which maps l ↔ N − l. We exploit these symmetries to compute exact boundary S-matrices in the regime with q real.     

Landau damping in degenerate solid state plasmas

Helicon waves are found useful for studying Landau damping in degenerate plasmas. The damping is analyzed as the phase velocity of the wave is increased from ω/q v_F to ω/q v_F. There is no first-orderlike transition at ω/q = V_F. In the collisionless limit, the damping tends to zero as ω/q → v_F. For finite collision times τ it does not vanish for ω/q > v_F. Nonlocal corrections to the wavelength exhibit a peak at ω/q = V_F, which degenerates into a shoulder for ωτ 100.     

Yb (Ba, Sr)2Cu4O8: a “124” phase superconductor with a reduced unit cell volume

Yb(Ba_1−xSr_x)₂Cu₄O₈ (0.1x0.3) superconductors of the YBa₂Cu₄O₈(“124”) structure were successfully synthesized using an O₂-hot-isostaticc-pressing (HIP) technique. The samples were characterized with respect to the crystal structure and superconducting properties. The lattice parameters of the samples decreased as the substitution of Sr for Ba proceeded. The superconducting transition temperatures of all the Yb-“124” samples were more or less the same, being around 80 K.     

Ising spin glass on a D = 3 hierarchical lattice: Effects of tailed coupling distributions

Within a real-space renormalization-group framework, we approach the cubic lattice through a D = 3 diamond-like hierarchical lattice. The model is a standard, nearest-neighbor, Ising spin glass with coupling constants {J_ij} distributed according to the family of continuous probability distributions P_q(J_ij) ∝ 1/[1 + (q − 1)J_ij²/2J²]^{1/(q − 1)} (if 1 + (q − 1) J_ij²/2J² > 0, and zero otherwise; q ). Such distributions, which arise naturally in the treatment, within the recently proposed nonextensive thermostatistics, of anomalous diffusion, reproduce the usual, Gaussian case, for q → 1. Moreover, they present a second moment J_ij² proportional to (5 − 3q)⁻¹ for q < 5/3, diverging for q ≥ 5/3, but keeping a finite width at midheight. In the limit q → 3, P_q(J_ij) collapses with the abscissa, and so the width at midheight diverges. We compute the q-dependence of the spin-glass critical temperature T_c. We show numerically that T_c does not scale with J_ij^21/2 (contrary to the usual belief), but rather with the width at midheight of P_q(J_ij). Our results suggest that T_c vanishes as −1/q when q → −∞; furthermore, we verified that T_c diverges exponentially when q approaches 3 from below.     

The algebraic Bethe ansatz for the Izergin–Korepin model with open boundary conditions

We present the procedure of exactly solving the Izergin–Korepin model with open boundary conditions by using the algebraic Bethe ansatz, which include constructing the multi-particle state and achieving the eigenvalue of the transfer matrix and corresponding Bethe equations. We give a proof about our conclusions on the multi-particle state based on an assumption. When the model is U_q(su(2)) quantum invariant, our results agree with that obtained by analytic Bethe ansatz method.     

A relation between the atomic charge of carbon and the C1s core electron binding energy estimated from a comparison of gas phase and solid state data and the molar polarizabilities of the investigated molecules

A method for internal calibration of ESCA (XPS ) spectra is described that permits the use of a simple relation between binding energy (E_b) and atomic charge (q) : E_b = kq + E_b0. This relation has been shown to hold for a large number of elements. So far the relation for carbon has, however, not been very well established. A method is now described that allows the use of carbon charges determined from E_b, vs. q correlations for other elements and has also made it possible to establish a linear relation for carbon. The method does not use carbon charges determined directly from quantum chemical calculations.

As an essential part of this procedure we investigated empirically the possible relation between the difference between the gas phase calibration standard and that for the same element in the solid state, “a”, and the molar polarizability of the substance, P. It was found that “a” decreases with increasing polarizability, tentatively as a=4.15+8.30 P^−1/3. Therefore, knowledge of the polarizability of carbon-containing molecules from the literature made it possible to determine “a” and then the charge of all other atoms in the molecule. In this way a set of E_b and qc date was obtained. These data were complemented by another set using theoretical q_c snd solid state E_b of phenyl compounds previously made.

The results of the investigation show a linear relation between E_b(Cls) and q_c valid for the solid state: E_b,(Cls) = 4.68 q_c + 286.2 eV with a correlation coefficient of 0.945. This brings the previously obtained k value for carbon, which seemed anomalously high, down to a value of similar magnitude as for other light elements.     

Photoproduction of Θ and other pentaquark states

We present constraints on the relative photoproduction cross sections of positive parity pentaquark states, Σ₅, Λ₅, and N₅, based on a minimum phenomenology gained in and their baryon–meson couplings as in the work of Close and Dudek. The possibility of anomalous signals in γp→K⁰_S(Θ⁺;Σ_d⁺) is discussed. We emphasize the importance of comparing with “conventional” states such as γN→KΣ(1660).     

Charge susceptibility and charge correlation function in the d---p model

The properties of the charge fluctuation are investigated in the d---p model with the repulsion U_pd between holes on the nearest-neighbor Cu and O sites and the infinite on-site repulsion U_d at the Cu site. We calculate the charge susceptibility χ^c(q, iω_n) and the charge correlation function S^c(q) = TΣ_ωn χ^c(q, iω_n). It is found that S^c(q) has a peak at the Γ point and a maximum in a ring around the Γ point. The former is due to Tχ^c(q, 0). Its intensity is proportional to temperature T and strongly enhanced by U_pd. The latter is due to TΣ_{ωn ≠ 0} χ^c(q, iω_n) and shows a weak T and U_pd dependence. The intensity of the diffuse X-ray scattering on taking the charge fluctuation into account is also calculated. The result is consistent with the experiments in La_2−δSr_δCuO₄.     

High field magnetization in Pr(Ni1-xCox)5 single crystals

Magnetization measurements in fields up to 38 T performed at low temperature on single crystals of the hexagonal Pr(Ni_1-xCo_x)₅ compounds for x = 0, 0.05, 0.10 and 0.20 are presented. In PrNi₅ we observe highly original behaviour predicted by the knowledge of the Crystalline Electric Field parameters and arising from the existence of a non-magnetic singlet ground state; namely transitions associated with the field induced “anticrossing” and “crossing” of the two lowest states along the [100] and [120] directions, respectively. The measurements performed on the other compounds have allowed us to study the dependence of this behaviour on Co substitutions.     

Incommensurate magnetic structure of CeSi as observed by neutron diffraction

The magnetic ordering of the orthorhombic compound CeSi (Pama space group, FeB type of structure, Z = 4) T_n = 5.6 K was investigated by means of powder neutron diffraction in the temperatures 1.5 and 10 K. Our results show that the magnetic ordering is associated with a three dimensionally amplitude-modulated phase which is incommensurate with the crystal lattice with wave vector q = (q_χ,q_y,q_z). The ordered Ce³⁺ moments are confined to the plane (a,b) at an angle of 16.7° with the b direction. It follows from the present data analysis that the dominant wave vector component is q_z, which approximately corresponds to a transversal modulation, however the incommensurateness involves also the q_x and q_y components. The amplitude of the sine wave is μ⁰_j = 1.667μ_B at 1.5 K which corresponds to quite a reduced ordered moment value compared to the Ce³⁺ free ion value gJ = 2.14μ_B.     

Scattering-controlled recombination of Δ2-light-hole indirect excitons and apparently enhanced quantum confined Stark effect in tensilely strained Si1−yCy/Si (0 0 1) quantum wells

Anomalies are found in the near-band-edge luminescence properties of Δ₂-light-hole indirect excitons in Si_1−yC_y-based tensilely strained quantum wells (QWs). The experimental spectra exhibit a clear signature of phonon-assisted transitions on the lower energy side of the “no-phonon” transition, which indicates the relevance of “virtual” indirect valleys and in-plane k-dispersion, as opposed to the theoretical prediction that the zone-centered Δ₂ valleys take over the conduction band edge. Intervalley scattering between [0 0 1]-Δ₂ valleys and in-plane Δ₄ valleys is suggested as the underlying mechanism. On the other hand, the experimental evidence was found for “apparently enhanced” quantum-confined Stark red shifts for Si_1−yC_y-based QWs. However, quantitative estimates are in conflict with the experimental results and predict a blue shift due to exciton weakening which masks the Stark effect as in the case of Δ₄-heavy hole excitons in Si_1−xGe_x-based QWs.     

The Hadron to quark-gluon transition in relativistic heavy-ion collisions

In this paper we construct a scenario for the QCD transition from the hadron phase to the quark/gluon phase using physical models for these phases. The hadron phase is modeled by a spectrum of hadrons with masses which drop (with a common scaling factor) towards zero at chiral symmetry restoration. The number of hadronic effective degrees of freedom is limited by the number of microscopic degrees of freedom in the quark/gluon phase. This limitation can be imposed either by fiat or through the introduction of a temperature-dependent excluded volume. Given that the number of degrees of freedom in hadrons and in quarks and gluons are roughly equal, the QCD phase transition is inhibited by the bag constant. The only phase transition seen in lattice-gauge calculations, once low-mass quarks are included, is the restoration of chiral symmetry which occurs at the relatively low temperature of ˜ 150 MeV. At present, lattice gauge calculations do not have the resolution to determine the properties of the higher hadronic states accurately. They do, however, demonstrate that chiral restoration takes place in the (ρ. a₁), ( +)), ( −)) and (π, σ) systems by yielding “screening masses” for chiral partners which are distinct for T < T _xSR and identical for T>T _xSR. Further, within numerical accuracy, these “screening masses” are consistent with pure thermal energies and show no evidence of remaining bare masses once chiral symmetry is restored. These, and other lattice-gauge results, will be discussed in the light of our scenario. We shall also consider the consequences of our picture for relativistic heavy-ion experiments.     

The pion velocity at chiral restoration and the vector manifestation

We study the effects of Lorentz non-invariance on the physical pion velocity at the critical temperature T_c in an effective theory of hidden local symmetry (HLS) with the “vector manifestation” fixed point. We match at a “matching scale” Λ_M the axial-vector current correlator in the HLS with the one in the operator product expansion for QCD, and present the matching condition to determine the bare pion velocity. We find that the physical pion velocity, which is found to be one at T=T_c when starting from the Lorentz invariant bare HLS, remains close to one with the Lorentz non-invariance, v_π(T_c)=0.83–0.99. This result is quite similar to the pion velocity in dense matter.     

The ΔNγ electromagnetic transition form factors GM(q) and GE(q)

A parameter-free, nonperturbative calculation of the ΔNγ electromagnetic transition amplitudes GM*(q2), GE*(q2), and the resonant multipole ratio REM(q2)≡E1+3/2(q2)/M1+3/2(q2) is performed in terms of the well-known nucleon isovector Sachs form factor GMV. Our methods are fully relativistic with conservation of the electromagnetic current guaranteed. We find that GM*(q2) decreases more rapidly than the nucleon dipole form factor when −q21 GeV2/c2 and that REM(q2) remains small even for very high four-momentum transfer implying that the perturbative QCD prediction REM(q2)→1 is purely asymptotic and is valid only for extremely high |q2|.