Renormalization of a Hard-Core Guest Charge Immersed in a Two-Dimensional Electrolyte

This paper is a continuation of a previous one [L. Šamaj, J. Stat. Phys. 120:125 (2005)] dealing with the renormalization of a guest charge immersed in a two-dimensional logarithmic Coulomb gas of pointlike ± unit charges, the latter system being in the stability-against-collapse regime of reduced inverse temperatures 0 ≤ β < 2. In the previous work, using a sine-Gordon representation of the Coulomb gas, an exact renormalized-charge formula was derived for the special case of the pointlike guest charge Q, in its stability regime β |Q| < 2. In the present paper, we extend the renormalized-charge treatment to the guest charge with a hard core of radius σ, which allows us to go beyond the stability border β|Q| = 2. In the limit of the hard-core radius much smaller than the correlation length of the Coulomb-gas species and at a strictly finite temperature, due to the counterion condensation in the extended region β|Q| > 2, the renormalized charge Q _ren turns out to be a periodic function of the bare charge Q with period 1. The renormalized charge therefore does not saturate at a specific finite value as |Q| →∞, but oscillates between two extreme values. In the high-temperature Poisson-Boltzmann scaling regime of limits β→ 0 and Q→∞ with the product β Q being finite, one reproduces the Manning-Oosawa type of counterion condensation with the uniform saturation of β Q _ren at the value 4/π in the region β|Q| ≥ 2. The obtained results disprove the “regularization hypothesis” of the previous work about the possibility of an analytic continuation of the formula for Q _ren from the stability region β |Q| < 2 to β |Q| ≥ 2.     

Fermilab top mass and modified Fritzsch mass matrices

Fritzsch like mass matrices with non-zero 22-elements both in U sector and D sector have been investigated in the context of latest data regardingm _t ^phys , |V _ub|, |V _cb|, |V _td| and |V _ts|. Unlike several other phenomenological models, the present model not only accommodates the value ofm _t ^phys in the range 150–240 GeV, encompassing the CDF and D0 values, but is also able to reproduce |V _cb| ≊0.040 and |V _ub/V_cb| = 0.08±0.02 and |V _td| is predicted to lie in the range 0.005–0.014. Further, the angles of the unitarity triangle, related to the CP-violating asymmetries, are calculated to be in the ranges −1.0⩽sin2α⩽−0.1, 0.6 ⩽sin2α⩽1.0 and 0.48⩽sin2β⩽0.56, which are in agreement with other recent calculations.     

| m | Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

The symmetry and |m| partial-wave analysis for two-dimensional (2D) Coulomb-scattering is investigated. As a function of energyE, the |m| partial-wave scattering amplitudef _|m|(θ) is analytically continuated to the, negativeE (complexk) plane, and it is found that the bound state energy eigenvalues (E<0) are just located at the poles off _|m|(θ) on the positive imaginaryk axis as is expected. In addition, as a function of |m|,f _|m|(θ) is analytically continuated to the complex |m| plane, the bound state energy eigenvalues are just located at the poles off _|m|(θ) on the positive real |m| axis.     

Damping of zero sound in Luttinger liquids

We calculate the damping γ_q of collective density oscillations (zero sound) in a one-dimensional Fermi gas with dimensionless forward scattering interaction F and quadratic energy dispersion k² / 2 m at zero temperature. Using standard many-body perturbation theory, we obtain γ_q from the expansion of the inverse irreducible polarization to first order in the effective screened (RPA) interaction. For wave-vectors | q| /k_F ≪F (where k_F = m v_F is the Fermi wave-vector) we find to leading order γ_q ∝| q |³ /(v_F m²). On the other hand, for F ≪| q| /k_F most of the spectral weight is carried by the particle-hole continuum, which is distributed over a frequency interval of the order of q²/m. We also show that zero sound damping leads to a finite maximum proportional to |k - k_F | ^{-2 + 2 η} of the charge peak in the single-particle spectral function, where η is the anomalous dimension. Our prediction agrees with photoemission data for the blue bronze K_0.3MoO₃. We comment on other recent calculations of γ_q.     

Bulk singularities at critical end points: a field-theory analysis

A class of continuum models with a critical end point is considered whose Hamiltonian [φ,ψ] involves two densities: a primary order-parameter field, φ, and a secondary (noncritical) one, ψ. Field-theoretic methods (renormalization group results in conjunction with functional methods) are used to give a systematic derivation of singularities occurring at critical end points. Specifically, the thermal singularity ∼ | t|^{2 - α} of the first-order line on which the disordered or ordered phase coexists with the noncritical spectator phase, and the coexistence singularity ∼ | t|^{1 - α} or ∼ | t|^β of the secondary density <ψ> are derived. It is clarified how the renormalization group (RG) scenario found in position-space RG calculations, in which the critical end point and the critical line are mapped onto two separate fixed points _CEP ^* and _λ ^*, translates into field theory. The critical RG eigenexponents of _CEP ^* and _λ ^* are shown to match. _CEP ^* is demonstrated to have a discontinuity eigenperturbation (with eigenvalue y = d), tangent to the unstable trajectory that emanates from _CEP ^* and leads to _λ ^*. The nature and origin of this eigenperturbation as well as the role redundant operators play are elucidated. The results validate that the critical behavior at the end point is the same as on the critical line. Received 18 January 2001     

Search for exotic contributions to atmospheric neutrino oscillations

The energy spectrum of neutrino-induced upward-going muons in MACRO has been analyzed in terms of effects of violating relativity principles, keeping standard mass-induced atmospheric neutrino oscillations as the dominant source of ν _μ → ν _τ transitions. The data disfavor these exotic possibilities even at a subdominant level, and stringent 90% C.L. limits are placed on the Lorentz invariance violation parameter |Δυ| < 6 × 10⁻²⁴ at sin(2ϑ_υ) = 0 and |Δυ| < (2.5–5) × 10⁻²⁶ at sin(2ϑ_υ) = ±1. These limits can also be reinterpreted as upper bounds on the parameters describing violation of the equivalence principle. The text was submitted by the author in English.     

Random quantum magnets with broad disorder distribution

We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that P(ln J) ∼ | ln J|^{-1 - α}, α > 1, for large | ln J| (Lévy flight statistics). For sufficiently broad distributions, α < , the critical behavior is controlled by a line of fixed points, where the critical exponents vary with the Lévy index, α. In one dimension, with = 2, we obtained several exact results through a mapping to surviving Riemann walks. In two dimensions the varying critical exponents have been calculated by a numerical implementation of the Ma-Dasgupta-Hu renormalization group method leading to ≈ 4.5. Thus in the region 2 < α < , where the central limit theorem holds for | ln J| the broadness of the distribution is relevant for the 2d quantum Ising model. Received 6 December 2000 and Received in final form 22 January 2001     

A first experimental approach to the 15O + α elastic scattering

The ¹⁵O(α,α)¹⁵O elastic scattering is investigated using a ¹⁵O radioactive beam and a He gas cell limited by Mylar windows. The width of a ¹⁹Ne state at an excitation energy of 5.35MeV is measured as Γ_α = 3.2±1.6keV, in agreement with charge symmetry estimate.     

The Asymptotic Limits of Zero Modes of Massless Dirac Operators

Asymptotic behaviors of zero modes of the massless Dirac operator H = α · D + Q(x) are discussed, where α = (α₁, α₂, α₃) is the triple of 4 × 4 Dirac matrices, , and Q(x) = (q _jk (x)) is a 4 × 4 Hermitian matrix-valued function with | q _jk (x) | ≤ C 〈x〉^−ρ, ρ > 1. We shall show that for every zero mode f, the asymptotic limit of |x|² f (x) as |x| → + ∞ exists. The limit is expressed in terms of the Dirac matrices and an integral of Q(x) f (x).      

Time Quasi-Periodic Unbounded Perturbations¶of Schrödinger Operators and KAM Methods

We eliminate by KAM methods the time dependence in a class of linear differential equations in ℓ² subject to an unbounded, quasi-periodic forcing. This entails the pure-point nature of the Floquet spectrum of the operator H ₀+εP(ωt) for ε small. Here H ₀ is the one-dimensional Schr?dinger operator p ²+V, V(x)∼|x|^α, α <2 for |x|→∞, the time quasi-periodic perturbation P may grow as |x|^β, β <(α−2)/2, and the frequency vector ω is non resonant. The proof extends to infinite dimensional spaces the result valid for quasiperiodically forced linear differential equations and is based on Kuksin's estimate of solutions of homological equations with non-constant coefficients. Received: 3 October 2000 / Accepted: 20 December 2000     

Critical Rotational Speeds in the Gross-Pitaevskii Theory on a Disc with Dirichlet Boundary Conditions

We study the two-dimensional Gross-Pitaevskii theory of a rotating Bose gas in a disc-shaped trap with Dirichlet boundary conditions, generalizing and extending previous results that were obtained under Neumann boundary conditions. The focus is on the energy asymptotics, vorticity and qualitative properties of the minimizers in the parameter range |log ε|≪Ω≲ε ⁻²|log ε|⁻¹ where Ω is the rotational velocity and the coupling parameter is written as ε ⁻² with ε≪1. Three critical speeds can be identified. At \varOmega = \varOmega_c1 ~ |loge|\varOmega=\varOmega_{\mathrm{c_{1}}}\sim |\log\varepsilon| vortices start to appear and for |loge| << \varOmega < \varOmega_c2 ~ e^-1|\log\varepsilon|\ll\varOmega< \varOmega_{\mathrm{c_{2}}}\sim \varepsilon^{-1} the vorticity is uniformly distributed over the disc. For \varOmega 3 \varOmega _c2\varOmega\geq\varOmega _{\mathrm{c_{2}}} the centrifugal forces create a hole around the center with strongly depleted density. For Ω≪ε ⁻²|log ε|⁻¹ vorticity is still uniformly distributed in an annulus containing the bulk of the density, but at \varOmega = \varOmega_c3 ~ e^-2|loge|^-1\varOmega=\varOmega_{\mathrm {c_{3}}}\sim\varepsilon ^{-2}|\log\varepsilon |^{-1} there is a transition to a giant vortex state where the vorticity disappears from the bulk. The energy is then well approximated by a trial function that is an eigenfunction of angular momentum but one of our results is that the true minimizers break rotational symmetry in the whole parameter range, including the giant vortex phase.     

Nanoparticle Charging in a Twin Hewitt Charger

A new unipolar charger for aerosol nanoparticles has been developed. In this twin Hewitt charger two corona discharge zones are connected by a charging zone where the nanoparticle aerosol flows. Ions move into the charging zone alternating from each corona discharging zone by means of a square-wave voltage. The operation parameters of the device have been experimentally investigated at standard conditions with the goal to optimize the extrinsic charging efficiency in N₂ carrier gas. It has been found that there exists an optimal length of the charging channel for each gas flow rate through the charger which minimizes losses of charged particles and at the same time having a sufficient large n _iont-product. Extrinsic charging efficiencies of some 30% for particles with a diameter of 10 nm are obtained.     

<Emphasis Type="Italic">CP</Emphasis> violation due to multi-Froggatt–Nielsen fields

We study how to incorporate CP violation in the Froggatt–Nielsen (FN) mechanism. To this end, we introduce non-renormalizable interactions with a flavor democratic structure to the fermion mass generation sector. It is found that at least two iso-singlet scalar fields with a discrete symmetry imposed are necessary to generate CP violation due to the appearance of the relative phase between their vacuum expectation values. In the simplest model, the ratios of quark masses and the Cabibbo–Kobayashi–Maskawa (CKM) matrix including the CP violating phase are determined by the CKM element |V_us| and the ratio of two vacuum expectation values of FN fields, R=|R|e^iα (a magnitude and a phase). It is demonstrated how the angles φ_i (i=1,...,3) of the unitarity triangle and the CKM off-diagonal elements |V_ub| and |V_cb| are predicted as a function of |V_us|, |R| and α. Although the predicted value of the CP violating phase does not agree with the experimental data within the simplest model, the basic idea of our scenario would be promising if one wants to construct a more realistic model of flavor and CP violation. PACS 11.30.Er; 12.60.-i     

Two-particle dispersion in model two-dimensional velocity fields

We consider two-particle dispersion in a velocity field, where the relative two-point velocity scales according to v ²(r) ∝r ^α and the corresponding correlation time scales as τ(r) ∝r ^β, and fix α = 2/3, as typical for turbulent flows. We show that two generic types of dispersion behavior arize: For α/2 + β < 1 the correlations in relative velocities decouple and the diffusion approximation holds. In the opposite case, α/2 + β > 1, the relative motion is strongly correlated. The case of Kolmogorov flows corresponds to a marginal, nongeneric situation. In this case, depending on the particular parameters of the flow, the dispersion behavior can be rather diffusive or rather ballistic. Received 13 March 2001     

EPR of a non-Kramers iron ion in KTaO3

The EPR spectrum of the non-Kramers iron ion Fe⁴⁺ (S=2) in a KTaO₃:Fe crystal appearing after illumination of the sample in the visible has been detected and studied. Because of the large initial splitting (|D|=4.15 cm⁻¹), only transitions within the |±1〈 and |±2〈 doublets are seen experimentally. Superhyperfine structure in the spectrum of a non-Kramers ion in perovskites has been detected for the first time. A structure is proposed for the center responsible for the new EPR spectrum, which represents a complex of a Fe₄₊ ion substituting for Ta with an oxygen vacancy at the nearest anion site. Fiz. Tverd. Tela (St. Petersburg) 41, 1424–1427 (August 1999)     

Study of the semileptonic decays B→<Emphasis Type="Italic">π</Emphasis>, D→<Emphasis Type="Italic">π</Emphasis> and D→K

The semileptonic decay B→π is studied starting from a simple quark model that takes into into account the effect of the B^*-resonance. A novel, multiply subtracted, Omnès dispersion relation has been implemented to extend the predictions of the quark model to all q² values accessible in the physical decay. By comparison to the experimental data, we extract | V _ub| = (3.4±0.2(exp.)±0.7(theory))0^-3. As a further test of the model, we have also studied D→π and D→K decays for which we get good agreement with experiment.     

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

Quark momentum-space charge distribution in deuteron and neutron/proton structure functions ratio

The electromagnetic polarizabilities of the nucleon are shown to be essentially composed of the nonresonant α _p(E ₀₊) = + 3.2, α _n(E ₀₊) = + 4.1, the t-channel α ^t _{p, n} = - β ^t _{p, n} = + 7.6 and the resonant β _{p, n}(P ₃₃(1232)) = + 8.3 contributions (in units of 10^-4fm^3). The remaining deviations from the experimental data Δα _p = 1.2±0.6, Δβ _p = 1.2±0.6, Δα _n = 0.8±1.7 and Δβ _n = 2.0±1.8 are contributed by a larger number of resonant and nonresonant processes with cancellations between the contributions. This result confirms that dominant contributions to the electric and magnetic polarizabilities may be represented in terms of two-photon coupling to the σ-meson having the predicted mass m _σ = 666MeV and two-photon width Γ _γγ = 2.6keV.     

Electromagnetic moments of short lived β emitters 21F, 23Mg, 27Si and 39Ca

The β-NMR spectra of ²¹F, ²³Mg, ²⁷Si and ³⁹Ca which were produced in heavy ion collisions and implanted in various crystals have been observed. The magnetic moments of ²¹F and ²⁷Si were determined to be |μ(²¹F)| = 3.9194 ± 0.0012 μ_N and |μ(²⁷Si)| = 0.8653 ± 0.0003 μ_N, respectively. The electric quadrupole coupling constants were determined for the first time to be |eqQ(²¹F in MgF₂)/h|= 9.94 ± 0.09 MHz, |eqQ(²³Mg in MgF₂)/h|= 1.96 ± 0.06 MHz, |eqQ(²⁷Si in Al₂O₃)/h|= 1.90 ± 0.12 MHz, |eqQ(³⁹Ca in CaCO₃)/h|= 0.60 ± 0.04 MHz. From the present eqQ/h, the Q moments were deduced as |Q(²¹F)|= 110 ± 22 mb, |Q(²³Mg)|= 114 ± 3 mb, |Q(²⁷Si)|= 60 ± 13 mb and |Q(³⁹Ca)|= 36± 7 mb. The present data were compared with the theoretical values obtained by the OXBASH shell model code. This revised version was published online in August 2006 with corrections to the Cover Date.