The exclusive reaction of pion quasi-elastic knockout from nucleon <Emphasis Type="Italic">p(e,e′ π)B</Emphasis> to various states of the final baryon-spectator <Emphasis Type="Italic">B</Emphasis> and the quark models for the pion cloud of nucleon

The pion momentum distributions (MDs) in four channels of virtual decay p→B+π, B = N, Δ, N _1/2-(1535), N _1/2+(1440) are calculated in two models, the microscopic model of ³ P ₀ scalar q−q fluctuation with the pion as a composite q−q-system and the chiral semi-microscopic model of πq interaction with the pion as a structureless Goldstone boson. The results of the above models are similar for the baryon states B = N, Δ, N _1/2-(1535) but are rather different for the Roper resonance N _1/2+(1440) which corresponds to excitation of two oscillator quanta in the nucleon. The experimental investigation of pion MDs by means of the reaction of quasi-elastic knockout of pion by an electron of a few GeV energy p(e, e′ π)B may be very suitable for Jefferson Laboratory, Virginia (JLab).     

The Number of Open Paths in an Oriented <Emphasis Type="Italic">ρ</Emphasis>-Percolation Model

We study the asymptotic properties of the number of open paths of length n in an oriented ρ-percolation model. We show that this number is e ^{n α(ρ)(1+o(1))} as n→∞. The exponent α is deterministic, it can be expressed in terms of the free energy of a polymer model, and it can be explicitly computed in some range of the parameters. Moreover, in a restricted range of the parameters, we even show that the number of such paths is n ^−1/2 We ^{n α(ρ)}(1+o(1)) for some nondegenerate random variable W. We build on connections with the model of directed polymers in random environment, and we use techniques and results developed in this context.     

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).      

<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.     

Quantum measurement and pure dephasing

The prerequisite of quantum measurement is a transformation of an initially off-diagonal density matrix _ρmα;nβ describing an interacting measured object and measuring device into a diagonal density matrix _{ρmα;mαδmnδαβ} . The latter density matrix describes a proper mixture of states having definitem-values. On the other hand, the irreversible relaxation (towards the thermodynamic equilibrium) is also characterized by transformation of an initially off-diagonal matrix into a diagonal one. It has been shown that the process of irreversible relaxation can be used to perform quantum measurement, provided the duration Δt of the measurement is much larger thanT ₂, the phase relaxation time, and much smaller thanT ₁, the population relaxation time:T ₂ ≪ Δt ≪T ₁. Agedanken experiment describing this kind of measurement is provided. Aπ/2-pulse transforms an initials _z = −1/2 state into superposition ofs _z = ±1/2 states. The irreversible relaxation leads to the proper mixture ofs _z = 1/2 ands _z = −1/2 state. Results of the measurements are verified by the second electromagnetic pulse.     

Estimates of the number of quantal bound states in one and three dimensions

Using the relation between the number of bound states and the number of zeros of the radial eigen-functionψ(r), or equivalently, that ofφ(r)=rψ(r) in the range 0⩽r⩽∞, the upper bounds on the number of bound states generated by potentialV(r) in different angular momentum channels are obtained in three dimension. Using a similar procedure, the upper bound on the number of bound states in one dimension is also deduced. The analysis is restricted to a class of potentials for whichE=0 is the threshold. By taking a number of specific examples, it is demonstrated that both in one and three dimensions, the estimate of the upper bound obtained by this procedure is very close to or equal to the exact number of bound states. The correlation of the present method with the Levison’s theorem and WKB approximation is discussed.     

Dark Energy with Generalized Equation of State in Bianchi Type-I Cosmological Model

Dark energy with the usually used equation of state p=γρ, where γ=const<0 is hydrodynamically unstable. To overcome this drawback we consider the cosmology of a perfect fluid with a linear equation of state of a more general form p=α(ρ−ρ ₀), where the constants α and ρ ₀ are free parameters. The anisotropic Bianchi type-I cosmological model filled with dark energy has been considered. A generalized equation of state for the dark energy component of the universe has been used. The exact solutions to the corresponding Einstein field equations and the statefinder diagnostic pair i.e. {r,s} parameters have been obtained in three interesting cases (i) when ρ _Λ>0 and A>0 (ii) when ρ _Λ>0 and A<0 and (iii) when ρ _Λ<0 and A>0 at the singularities i.e. t→0 and t→±∞.     

Condensation of the Roots of Real Random Polynomials on the Real Axis

We introduce a family of real random polynomials of degree n whose coefficients a _k are symmetric independent Gaussian variables with variance , indexed by a real α≥0. We compute exactly the mean number of real roots 〈N _n 〉 for large n. As α is varied, one finds three different phases. First, for 0≤α<1, one finds that . For 1<α<2, there is an intermediate phase where 〈N _n 〉 grows algebraically with a continuously varying exponent, . And finally for α>2, one finds a third phase where 〈N _n 〉∼n. This family of real random polynomials thus exhibits a condensation of their roots on the real line in the sense that, for large n, a finite fraction of their roots 〈N _n 〉/n are real. This condensation occurs via a localization of the real roots around the values , 1≪k≤n.     

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.     

Effect of the velocity-dependent potentials on the energy eigenvalues of the Morse potential

We investigate the effect of the isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Morse potential for any quantum states. When the velocity-dependent term is used as a constant parameter, ρ(r) = ρ ₀, the energy eigenvalues can be obtained analytically by using the Pekeris approximation. When the velocity-dependent term is considered as an harmonic oscillator type, ρ(r) = ρ ₀ r ², we show how to obtain the energy eigenvalues of the Morse potential without any approximation for any n and ℓ quantum states by using numerical calculations. The calculations have been performed for different energy eigenvalues and different numerical values of ρ ₀, in order to show the contribution of the velocity-dependent potential on the energy eigenvalues of the Morse potential.     

Self-consistent treatment of the quark condensate and hadrons in nuclear matter

We calculate the contribution of pions to the $\bar qq$-expectation value κ(ρ) =<M|ˉq q|M> in symmetric nuclear matter. We employ exact pion propagator renormalized by nucleon-hole and isobar-hole excitations. Conventional straightforward calculation leads to the “pion condensation” at unrealistically small values of densities, causing even earlier restoration of chiral symmetry. This requires a self-consistent approach, consisting in using the models, which include direct dependence of in-medium mass values on κ(ρ), e.g. the Nambu–Jona-Lasinio–model. We show, that in the self-consistent approach the ρ-dependence of the condensate is described by a smooth curve. The “pion condensate” point is removed to much higher values of density. The chiral restoration does not take place at least while ρ < 2.8ρ₀ with ρ₀ being the saturation value. Validity of our approach is limited by possible accumulation of heavier baryons (delta isobars) in the ground state of nuclear matter. For the value of effective nucleon mass at the saturation density we found m ^*(ρ₀) = 0.6m, consistent with nowadays results of other authors. Received: 8 October 1998     

Convexity of internal energy of cubic crystal deformed to orthorhombic structure

A generalized set of strain variablesq _r ^N , has been defined to develop the expression for a generalized set of second order and third-order elastic moduliC _rs ^N andC _rst ^N for a cubic crystal deformed to orthorhombic structure. The HessainC _rs ^N δq_rδq_s andC _rst ^N δq_rδq_sδq_t (r=1, 2……6; summation convention) are calculated in the new variables and compared withG-strength andS-strength, for both positive and negative loading environment. The convexity of the internal energy relative to various choice of strain measure is examined considering up to third degree terms in the internal energy expression. The computational results forbcc iron is presented according to the new moduli. The stable ranges thus obtained for iron under hydrostatic compressive and tensile stresses is found to generate the classical stable range, green-stable range and stretch-stable range as the specific cases. However,bcc iron does not seem to follow any conventional stable ranges under hydrostatic compression, where the present generalized stable range is found satisfactory.     

Large-scale amplification of a magnetic field by turbulent helicity fluctuations

In this paper the procedure of large-scale averaging of the magnetic-field diffusion equation with the α-term curlα(r,t)B(r,t) is used to show that a nonuniform distribution of the turbulent helicity fluctuations (more precisely, the fluctuations of the coefficient α) with a zero average value gives rise to large-scale amplification of the initial magnetic field. A detailed study is carried out of the dependence of the resulting large-scale α effect on the characteristics of the correlator 〈〈α(r, t)α(r″,t″)〉〉 in a rotating medium with a nonuniform distribution of the angular velocity ω=ω(ρ,z) (ρ is the distance for the rotation axis z). The effect of helicity fluctuations and the diffusion coefficient on the turbulent diffusion process is also investigated. Zh. éksp. Teor. Fiz. 116, 85–104 (July 1999)     

Scales in nuclear matter: Chiral dynamics with pion nucleon form factors<Superscript>⋆</Superscript>

A systematic calculation of nuclear matter is performed which includes the long-range correlations between nucleons arising from one- and two-pion exchange. Three-body effects from 2π exchange with excitations of virtual Δ(1232)-isobars are also taken into account in our diagrammatic calculation of the energy per particle ˉ(k _f). In order to eliminate possible high-momentum components from the interactions we introduce at each pion-baryon vertex a form factor of monopole type. The empirical nuclear matter saturation point, ρ₀ ≃ 0.16fm^-3, ˉ₀ ≃ - 16MeV, is well reproduced with a monopole mass of Λ ≃ 4πf _π ≃ 1.16GeV. As in the recent approach based on the universal low-momentum NN potential V _low-k, the inclusion of three-body effects is crucial in order to achieve saturation of nuclear matter. We demonstrate that the dependence of the pion exchange contributions to ˉ(k _f) on the “resolution” scale Λ can be compensated over a wide range of Λ by counterterms with two “running” contact couplings. As a further application we study the in-medium chiral condensate 〈ˉq〉(ρ) beyond the linear density approximation. For ρ ⩽ 1.5ρ₀ we find small corrections from the derivative dˉ(k _f)/dm _π, which are stable against variations of the monopole regulator mass Λ.     

Polarons in axial transport in single-layer high-T<Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> superconductors

The temperatureT dependencies ρ(T) of normal state electric resistivitiesρ _c (axial) andρ _ab (in plane) of single-layer high-T _c superconductors show common trends: AsT is raised, the resistivity first drops steeply before it starts rising αT above an apparent semiconductor-to-metal crossoverT _cross . To analyze ρ(T) we plottT/ρ againstT at various dopingsx for bothρ _c andρ _ab .T/ρ is inversely proportional to the traversal time across a potential barrier as an ionic particle drifts in an electric field. We findT/ρ in good agreement with theT dependence of the quantum rate of migrating particles: AsT is raised, a zero-point rate at the lowestT is extended to a nearly flat plateau before a thermally activated branch sets in. We also find evidence for the admixture of 1- & 2-phonon absorptions below the Arrhenius range. These features shape the semiconductor-like branch below T _cross . AboveT _cross a metallic-like branch sets in, its αT character deriving from the field coupling of the migrating particle. Our analysis suggests that metal physics may not suffice if ionic features play a role in transport. We attribute our conclusions to the drift of strong-coupling polarons along Cu−O bonds. These “bond polarons” originate from carrier scattering by double-well potentials associated with the bonds. A bond polaron dissociates to a free hole as it passes onto a neighboring O-O link.     

On the phase boundaries of the integer quantum Hall effect. Part II

It has been shown that the observation of the transitions between the dielectric phase and the integer-quantum-Hall-effect phases with the quantized Hall conductivity σ _xy ^q ≥ 3e ²/h announced in a number of works is unjustified. In these works, the crossing points of the magnetic-field dependence of the diagonal resistivity ρ _xx at different temperatures T and ω_cτ = 1 have been misidentified as the critical points of the phase transitions. In fact, these crossing points are due to the sign change of the derivative dρ _xx /dT owing to the quantum corrections to the conductivity. Here, ω_c = eB/m is the cyclotron frequency, τ is the transport relaxation time, and m is the effective electron mass.     

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.     

Propagator of the Lattice Domain Wall Fermion and the Staggered Fermion

We calculate the propagator of the domain wall fermion (DWF) of the RBC/UKQCD collaboration with 2 + 1 dynamical flavors of 16³ × 32 × 16 lattice in Coulomb gauge, by applying the conjugate gradient method. We find that the fluctuation of the propagator is small when the momenta are taken along the diagonal of the 4-dimensional lattice. Restricting momenta in this momentum region, which is called the cylinder cut, we compare the mass function and the running coupling of the quark-gluon coupling α _s,g1(q) with those of the staggered fermion of the MILC collaboration in Landau gauge. In the case of DWF, the ambiguity of the phase of the wave function is adjusted such that the overlap of the solution of the conjugate gradient method and the plane wave at the source becomes real. The quark-gluon coupling α _s,g1(q) of the DWF in the region q > 1.3 GeV agrees with ghost-gluon coupling α _s (q) that we measured by using the configuration of the MILC collaboration, i.e., enhancement by a factor (1 + c/q ²) with c ≃ 2.8 GeV² on the pQCD result. In the case of staggered fermion, in contrast to the ghost-gluon coupling α _s (q) in Landau gauge which showed infrared suppression, the quark-gluon coupling α _s,g1(q) in the infrared region increases monotonically as q→ 0. Above 2 GeV, the quark-gluon coupling α _s,g1(q) of staggered fermion calculated by naive crossing becomes smaller than that of DWF, probably due to the complex phase of the propagator which is not connected with the low energy physics of the fermion taste. An erratum to this article can be found at     

Landauer resistance in the case of multichannel scattering

The Landauer resistance ρ _N ^L has been generalized to the case of multichannel scattering of a particle by the system of N nonoverlapping random potentials that are localized at the points x _i (i = 1, 2,..., N) and depend on x − x _i and y. It has been shown that, in this case, a new resistance ρ _N ^L appears, which is an exponential function of N. The recurrence equation for determining the Landauer resistance ρ _N ^L has been derived and its solution in the general case has been obtained.     

On the Truncation of Systems with Non-Summable Interactions

In this note we consider long-range q-states Potts models on Z ^d , d≥ 2. For various families of non-summable ferromagnetic pair potentials φ(x)≥ 0, we show that there exists, for all inverse temperature β > 0, an integer N such that the truncated model, in which all interactions between spins at distance larger than N are suppressed, has at least q distinct infinite-volume Gibbs states. This holds, in particular, for all potentials whose asymptotic behaviour is of the type φ(x)∼ ‖x‖^−α, 0≤α≤ d. These results are obtained using simple percolation arguments. Work supported by Swiss National Foundation for Science, Conselho Nacional de Desenvolvimento Cientìfico e Tecnològico, and Programa de Auxìlio para Recèm Doutores PRPq-UFMG.