Determination of very slow μ+ hop rates in Cu by LLF-μSRhop rates in Cu by LLF-μSR

Muon spin relaxation in low (weak) longitudinal magnetic field (LLF-μSR) provides a means of independently determining the static dipolar width Δ characterizing the μ⁺ lattice site and the correlation time τ_c for μ⁺ hopping, in a manner that is nearly model-independent for τ_c and especially accurate in the near-static limit (τ_c>τ_μ). The advantages of this method are illustrated by its application to muon hopping in Cu near the τ_c maximum around 50 K.     

Effects of Self-Correlation Time and Cross-Correlation Time of Additive and Multiplicative Colored Noises for Dynamical Properties of a Bistable System

Considering a bistable system driven by additive and multiplicative colored noises with colored cross-correlation, we obtain the analytic expressions of the stationary probability distribution P _st(x), the linear relaxation time T _c , and the correlated function C(s). The effects of the noise intensity, the self-correlation time and the cross-correlation time for the bistable system are discussed. The noise intensity D speeds up relaxation of the system from unstable points, which when D < Q, the effects are the most obvious; when D > Q, the effects are damped. The self-correlation time τ₁ and τ₂ make the stationary probability distribution of the dynamical variable x be shaper and speed up the fluctuation decay of the dynamical variable x. On the contrary, the cross-correlation time τ₃ makes the stationary probability distribution of the dynamical variable x be flatter and slows down the fluctuation decay of the dynamical variable x. The effect of the self-correlation time is more projecting than the effect of the cross-correlation time. PACS number: 05.40.−a, 02.50.−r, 05.10.Gg.     

Asymptotics of Determinants of Bessel Operators

 For aL ^∞ (ℝ₊)∩L ¹ (ℝ₊) the truncated Bessel operator B _τ (a) is the integral operator acting on L ² [0,τ] with the kernel

Intercepts of the momentum correlation functions in the $ \mu$ -Bose gas model and their asymptotics

The so-called μ-deformed oscillator (or μ-oscillator) introduced by A. Jannussis, though it possesses rather exotic properties with respect to other better known deformed oscillator models, also has a good potential for diverse physical applications. In this paper, the corresponding μ-Bose gas model based on μ-oscillators is developed. Within this model, the intercepts l⁽²⁾ \lambda^{{(2)}}_{}(K) and l⁽³⁾ \lambda^{{(3)}}_{}(K) of two- and three-particle momentum correlation functions are calculated with the goal of possible application for modeling the non-Bose-type behavior of the intercepts of two- and three-pion correlations, observed in the experiments on relativistic heavy-ion collisions. In the derivation of intercepts, a fixed order of approximation in the deformation parameter μ is assumed. For the asymptotics of the intercepts l⁽²⁾ \lambda^{{(2)}}_{}(K) and l⁽³⁾ \lambda^{{(3)}}_{}(K) , we derive exact analytical formulas. The results for l⁽²⁾ \lambda^{{(2)}}_{}(K) are compared with experimental data, and with earlier known results drawn using other deformed Bose gas models.     

B→K1?+?? decays in a family non-universal Z′ model

The implications of the family non-universal Z′ model in the B→K ₁(1270,1400)ℓ ⁺ ℓ ⁻(ℓ=e ,μ ,τ) decays are explored, where the mass eigenstates K ₁(1270, 1400) are the mixtures of ¹ P ₁ and ³ P ₁ states with the mixing angle θ. In this work, considering the Z′ boson and setting the mixing angle θ=(−34±13)^○, we analyze the branching ratio, the dilepton invariant mass spectrum, the normalized forward–backward asymmetry and lepton polarization asymmetries of each decay mode. We find that all observables of B→K ₁(1270)μ ⁺ μ ⁻ are sensitive to the Z′ contribution. Moreover, the observables of B→K ₁(1400)μ ⁺ μ ⁻ have a relatively strong θ-dependence; thus, the Z′ contribution will be buried by the uncertainty of the mixing angle θ. Furthermore, the zero crossing position in the FBA spectrum of B→K ₁(1270)μ ⁺ μ ⁻ at low dilepton mass will move to the positive direction with Z′ contribution. For the tau modes, the effects of Z′ are not remarkable due to the small phase space. These results could be tested in the running LHC-b experiment and Super-B factory.     

Bound states of the muon-antimuon system: Lifetimes and hyperfine splitting

We examine the properties of an atomic system consisting of a muon and antimuon. Expressions are derived for the probability of decay and the hyperfine splitting of the lower levels with allowance for the leading radiative corrections, which are of relative order α. The results for the lifetimes and the ground-state energy are τ(1³ S ₁)=1.7907(8)×10⁻¹² s, τ(1¹ S ₀)=0.59547(33)×10⁻¹² s, and E _hfs (1s)=4.23284(35)×10⁷ MHz. The relative probabilities for the various decay channels are calculated; in particular, for the 1 ³ S ₁ level it is found that Γ (μμ→eeγ)/Γ(μμ→ee)≈15%. Finally, possible applications are discussed. Zh. éksp. Teor. Fiz. 113, 409–431 (February 1998)     

Periodic Orbits Contribution to the 2-Point Correlation Form Factor for Pseudo-Integrable Systems

Using heuristic arguments based on the trace formulas we relate the 2-point correlation form factor, K ₂(τ), at small values of τ with sums over classical periodic orbits for typical examples of pseudo-integrable systems. The later sums have been explicitly calculated for the following models: (i) plane billiards in the form of right triangles with one angle π/n and (ii) rectangular billiards with the Aharonov-Bohm flux line. In the first model, using the properties of the Veech structure, it is shown that K ₂(0)=(n+ε(n))/(3(n−2)), where ε(n)= 0 for odd n, ε(n)= 2 for even n not divisible by 3, and ε(n)=6 for even n divisible by 3. For completeness we also recall informally the main features of the Veech construction. In the second model the answer depends on arithmetical properties of ratios of flux line coordinates to the corresponding sides of the rectangle. When these ratios are non-commensurable irrational numbers, K ₂(0)=1−3 , where is the fractional part of the flux through the rectangle when and it is symmetric with respect to the line when . The comparison of these results with numerical calculations of the form factor is discussed in detail. The above values of K ₂(0) differ from all known examples of spectral statistics, thus confirming analytically the peculiarities of statistical properties of the energy levels in pseudo-integrable systems. Received: 10 January 2000 / Accepted: 18 May 2001     

Monte Carlo simulations of the <Emphasis Type="Italic">μ</Emphasis>CF processes kinetics in deuterium gas

The kinetics of muon-catalyzed-fusion processes (μCF) in pure D₂ gas have been studied by means of Monte Carlo simulations for various target temperatures and densities. In particular, the role of resonant and non-resonant ddμ formation in μCF has been investigated. It has been shown that non-resonant formation can be directly observed at very short times in the neutron time spectra from μCF for low-density D₂ targets. The time spectra of neutrons from the low-temperature ortho-D₂ and para-D₂ gas targets have been calculated. These spectra display a strong ortho-para effect, which agrees with experimental results for the dilute-gas D₂ targets.     

Dielectric losses in statistical mixtures

The specific features of the dielectric spectra of statistical mixtures in the form of heterogeneous systems with spherical particles chaotically arranged in the space have been investigated. The distribution function of relaxation times f(τ) has been restored. It has been established that the relaxation times are continuously distributed within a wide interval [τ₁, τ₂]. Different methods for broadening the relaxation time distribution interval and approximating the relaxation time distribution function f(τ) have been analyzed. It has been demonstrated that f(τ) is a nonmonotonic function with two maxima at the boundaries and a minimum in the vicinity of the midpoint of the interval [τ₁, τ₂]. These features of the relaxation time distribution function are responsible for the large difference between the average relaxation frequencies of the permittivity and the dielectric loss (electrical conductivity).     

Photoproduction of baryons decaying into Nπ and Nη

A combined analysis of photoproduction data on γp↦ πN, ηN was performed including the data on KΛ and KΣ. The data are interpreted in an isobar model with s-channel baryon resonances and π, ρ (ω), K, and K ^* exchange in the t-channel. Three baryon resonances have a substantial coupling to ηN, the well-known N(1535)S ₁₁, N(1720)P ₁₃, and N(2070)D ₁₅. The inclusion of data with open strangeness reveals evidence for further new resonances, N(1840)P ₁₁, N(1875)D ₁₃ and, with weaker evidence, for N(2170)D ₁₃.     

Lepton polarization asymmetry and forward–backward asymmetry in exclusive B→K<Subscript>1</Subscript>τ<Superscript>+</Superscript>τ<Superscript>-</Superscript> decay in universal extra dimension scenario

Decay rate, forward–backward asymmetry and polarization asymmetries of the final state leptons in B→K₁τ⁺τ^-, where K₁ is the axial vector meson, are calculated in the standard model and in the universal extra dimension (UED) model. The sensitivity of the observables to the compactification radius R, the only unknown parameter in the UED model, is studied. Finally, the helicity fractions of the final state K₁ are calculated and their dependence on the compactification radius is discussed. This analysis of the helicity fraction is briefly extended to B→K^*ℓ⁺ℓ^- (ℓ=e,μ) and compared with the other approaches existing in the literature.     

Electron mobility in compensated VPE GaAs films

Electron Hall mobilities were measured on a series of intentionally compensated vapor phase epitaxy (VPE) GaAs layers. Using Sn and Zn as dopants, compensation ratiosK=(N_D+N_A)/(N_D-N_A) as high as 50 were obtained. Already for samples with the lowestK values the 300 K mobilities are higher than the 77 K values. In the range 20<T<100 [K] the data may be represented by μ∼T ^α with α increasing from 0.6 to 1.1 with compensation. The experimental μ values are smaller than those predicted from current models in all cases. It appears that scattering at ionized impurities is the dominant process also at temperatures well above 77 K, and that this scattering process is quantitatively underestimated in current models.     

Dynamics of liquid silane

Neutron scattering of cold neutrons from liquid silane at 137° K and 98°K is explained on the basis of a simple model. The rotational diffusion constant,D _r, and the delay time,τ ₀, after which rotational diffusion may be said to occur are derived on the basis of this model. At 137° K we getD _r=0.22×10¹³ sec⁻¹ andτ ₀=0.68×10⁻¹³ sec. At 98°KD _r (=0.06×10¹³ sec⁻¹) is down by a factor of more than three butτ ₀=(0.54×10⁻¹³ sec) shows only a small change. By comparison with data on liquid CH₄ it is concluded that the law of corresponding states is not applicable for describing rotational dynamics of CH₄ and SiH₄. Rotational motions in SiH₄ are more hindered than in CH₄ at the same reduced temperature.     

Probing grand unification with fermion masses,neutrino oscillations and proton decay

It is noted that a set of facts points to the relevance in four dimensions of conventional supersymmetric unification based on minimally a string-unifiedG(224) symmetry, or maximallySO(10). These include: (i) the observed family structure, (ii) quantization of electric charge, (iii) meeting of the three gauge couplings, (iv) neutrino oscillations (in particular the value of δm ²(νμ−δ _τ), suggested by SuperK), (v) the intricate pattern of the masses and mixings of the fermions, including the smallness ofV _cb and the largeness ofθ _μνμτ ^osc , and (vi) the need for B-L as a generator to implement baryogenesis (via leptogenesis). A concrete proposal is presented within a predictiveSO(10)/G(224) framework that successfully describes the masses and mixings of all fermions, including the neutrinos — with eight predictions, all in agreement with observation. Within this framework, a systematic study of proton decay is carried out, which (a) pays special attention to its dependence on the fermion masses, (b) limits the threshold corrections so as to preserve natural coupling unification, and (c) uses recently improved values of the matrix element and renormalization effects. Allowing for both minimal supersymmetric standard model (MSSM) and its proposed variant, the so-called extended supersymmetric standard model (ESSM), as effective low-energy the ories, the study shows that a conservative upper limit on the proton lifetime is about (l–2)× 10³⁴ years, with ·⁻K⁺ being the dominant decay mode, and quite possibly μ⁺ K ⁰ ande ⁺π⁰ being prominent. This in turn strongly suggests that an improvement in the current sensitivity by a factor of five to ten ought to reveal proton decay. For comparison, some alternatives to the conventional approach to unification pursued here are mentioned at the end. Invited paper presented at the International Summer School held at ICTP, Trieste (June, 2001) and at WHEPP-7 Conference, Allahabad, India (January, 2002). This is an updated version of the paper presented at the Erice School (September, 2000), hep-ph/0106082.     

Fluctuations of Power Injection in Randomly Driven Granular Gases

We investigate the large deviation function π_∞(w) for the fluctuations of the power W(t) = wt, integrated over a time t, injected by a homogeneous random driving into a granular gas, in the infinite time limit. Our analytical study starts from a generalized Liouville equation and exploits a Molecular Chaos-like assumption. We obtain an equation for the generating function of the cumulants μ(λ) which appears as a generalization of the inelastic Boltzmann equation and has a clear physical interpretation. Reasonable assumptions are used to obtain μ(λ) in a closed analytical form. A Legendre transform is sufficient to get the large deviation function π_∞(w). Our main result, apart from an estimate of all the cumulants of W(t) at large times t, is that π_∞ has no negative branch. This immediately results in the inapplicability of the Gallavotti-Cohen Fluctuation Relation (GCFR), that in previous studies had been suggested to be valid for injected power in driven granular gases. We also present numerical results, in order to discuss the finite time behavior of the fluctuations of W (t) . We discover that their probability density function converges extremely slowly to its asymptotic scaling form: the third cumulant saturates after a characteristic time τ larger than ∼50 mean free times and the higher order cumulants evolve even slower. The asymptotic value is in good agreement with our theory. Remarkably, a numerical check of the GCFR is feasible only at small times (at most τ/10), since negative events disappear at larger times. At such small times this check leads to the misleading conclusion that GCFR is satisfied for π_∞(w). We offer an explanation for this remarkable apparent verification. In the inelastic Maxwell model, where a better statistics can be achieved, we are able to numerically observe the “failure” of GCFR.     

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)     

The Effects of Time Delay on Stochastic Resonance in a Bistable System with Correlated Noises

The effects of time delay on stochastic resonance (SR) in a bistable system with time delay, correlated noises and periodic signal are studied by using the theory of signal-to-noise ratio (SNR). The expression of the SNR is derived under the adiabatic limit and the small delay time approximation. It is found that: (i) For the case of no correlations between multiplicative and additive noise, the delay time τ can enhance the SNR as a function of the multiplicative noise intensity α and it can restrain the SNR as a function of the additive noise intensity D; (ii) For the case of correlations between multiplicative and additive noise, τ can induce a minimum and maximum in curve of the SNR as a function of α, and can intensively restrain the SNR as a function of the D and there is a critical value of delay tim τ _c =0.1 in the height of the SNR peak with change of τ, i.e., when τ takes value blow τ _c , the τ boosts up the SNR as a function of the strength λ of correlations between multiplicative and additive noise, however, when τ takes value above τ _c , the τ restrains that.     

1H NMR relaxation investigation of herbicides interacting with photosystem II preparations fromSpinacia oleracea L.

The interaction of three common herbicides, paraquat, acifluorfen and alachlor, with spinach chloroplast photosystem II (PS II) was investigated by measuring¹H nuclear magnetic resonance spin-lattice relaxation rates, transient nuclear Overhauser effect (NOE) and NOE spectroscopy (NOESY) spectra. Binding to PS II was detected by (i) the enhancement of single-selective relaxation rates and (ii) the decrease in the optimal mixing time providing maximal cross-peak intensity in NOESY spectra. Titration of relaxation enhancements was used to calculate the dissociation constants (K _d) from the bound state for paraquat (K _d = 292 ± 71 μM⁻¹) and acifluorfen (K _d = 311 ± 58 μM⁻¹). A similarK _d was apparent for alachlor. Double-selective relaxation rates allowed the isolation of dipolar relaxation terms between selected proton pairs wherefrom dynamic features of the bound state were evaluated. In all cases the motional correlation time of bound herbicide (τ_c = 0.1−0.4 ns at 300 K) was found two orders of magnitude slower than in the free-solution state. In the case of alachlor the E and Z isomers were observed to bind differently to PS II and a change in conformation could be hypothesized.