Understanding the proton spin “puzzle” with a new “minimal” quark model

We investigate the spin structure of the nucleon in an extended Jaffe-Lipkin quark model. In addition to the conventional 3q structure, different (3q)(Q ) admixtures in the nucleon wave function are also taken into account. The contributions to the nucleon spin from various components of the nucleon wave function are discussed. The effect due to the Melosh-Wigner rotation is also studied. It is shown that the Jaffe-Lipkin term is only important when antiquarks are negatively polarized. We arrive at a new “minimal” quark model, which is close to the naive quark model, in order to understand the proton spin “puzzle”. Received: 4 November 2000 / Accepted: 23 October 2001     

Properties of the ground state in a spin—2 transverse Ising model with the presence of a srystal field

The properties of the ground state in the spin-2 transverse Ising model with the presence of a crystal of a crystal field are studied by using the effective-field theory with correlations,The longitudinal and transverse magnetizations,the phase diagram and the internal energy in the ground state are given numerically for a honeycomb lattice(z=3).     

Knot invariants associated with a particularN→∞ continuous limit of the Baxter-Bazhanov model

First we briefly recall the definition of the three-dimensional Baxter-Bazhanov lattice model. The spins of this model are elements ofZ _N and theR-matrix is associated to the algebraU _q sl(n) ifq is a primitiveNth root of unity. Then we construct a particularN limit of the model, in which it is meaningful to interpret the spins as elements ofR and which gives the free Gaussian boson model. Finally, we study special limits of the rapidity variables in which we obtain braid group representations and we show that forn odd the associated knot invariants are given by the inverse of products of Alexander polynomials, evaluated at certain roots of unity.     

Justification of the “symmetric damping” model of the dynamical Casimir effect in a cavity with a semiconductor mirror*

A “microscopic” justification of the “symmetric damping” model of a quantum oscillator with time-dependent frequency and time-dependent damping is given. This model is used to predict the results of experiments on simulating the dynamical Casimir effect in a cavity with a photo-excited semiconductor mirror. It is shown that the most general bilinear time-dependent coupling of a selected oscillator (field mode) to a bath of harmonic oscillators results in two equal friction coefficients for the both quadratures, provided all the coupling coefficients are proportional to a single arbitrary function of time whose duration is much shorter than the periods of all oscillators. The choice of coupling in the rotating wave approximation form leads to the “minimum noise” model of the quantum damped oscillator, introduced earlier in a pure phenomenological way.     

Localization in the ground-state of the one dimensionalX−Y model with a random transverse field

We consider the ground-state of the quantum spin model in one-dimension, where {h _i, iZ} are independent identically distributed random variables. By means of a Jordan-Wigner transformation the model is mapped into a free Fermi gas in the presence of a random external potential. We then use exponential localization of the one particle states to prove exponential decay for the spin-spin correlation functions.Partially supported by the NSF under grants DMS8702301 and INT8703059Partially supported by the CNPq under grant 303795-77FA     

Inequivalent quantizations of the rational Calogero model with a Coulomb type interaction

We consider the inequivalent quantizations of a N-body rational Calogero model with a Coulomb type interaction. It is shown that for a certain range of the coupling constants, this system admits a one-parameter family of self-adjoint extensions. We analyze both the bound and scattering state sectors and find novel solutions of this model. We also find the ladder operators for this system, with which the previously found solutions can be constructed.     

Exact results for the Barabási model of human dynamics

Human activity patterns display a bursty dynamics with interevent times following a heavy tailed distribution. This behavior has been recently shown to be rooted in the fact that humans assign their active tasks different priorities, a process that can be modeled as a priority queueing system [A.-L. Barabási, Nature (London) 435, 207 (2005)]. In this Letter we obtain exact results for the Barabási model with two tasks, calculating the priority and waiting time distribution of active tasks. We demonstrate that the model has a singular behavior in the extremal dynamics limit, when the highest priority task is selected first. We find that independently of the selection protocol, the average waiting time is smaller or equal to the number of active tasks, and discuss the asymptotic behavior of the waiting time distribution. These results have important implications for understanding complex systems with extremal dynamics.     

Directed transport of modulated structures in the Frenkel–Kontorova model with a pulsating coupling

We study the directed transport of commensurate and incommensurate modulated phases of the Frenkel–Kontorova model by (parametric driving) periodic pulsed variation of the nearest-neighbor coupling in the dissipative limit of the dynamics. We obtain that a directed current flow appears as the amplitude of the pulsating coupling C increases above a threshold coupling C_th. This threshold coupling depends on the average interspacing ω between the oscillators displaying singularities as the system becomes commensurable with the underlying lattice. By making use of the discommensuration theory of modulated phases we obtain that the dependence of the directed current on ω is a piecewise linear function with integer slope. Numerical results confirm these predictions.     

Spectroscopic factors of resonance states with the Gamow shell model

We provide an investigation of the spectroscopic factor of resonance states in A=5-8 nuclei, utilizing the Gamow shell model(GSM). Within the GSM, the configuration mixing is taken into account exactly with the shell model framework, and the continuum coupling is addressed via the complex-energy Berggren ensemble, which treats bound, resonance, and non-resonant continuum single-particle states on an equal footing. As a result, both the configuration mixing and continuum coupling are meticulously...     

Experimental test of the Preisach–Arrhenius model with temperature

The magnetic aftereffect was measured for a magnetic particle tape over a temperature range of 10–380 K. Data were obtained for the saturation magnetization, the coercive field, and the remanent coercive field as a function of temperature. Switching field distributions and other Preisach parameters were also determined as a function of temperature. Based on these data, the Preisach–Arrhenius (PA) model predicts that the decay rate, S, should decrease monotonically as the temperature is reduced. It was found that, for the material studied, S is nearly proportional to temperature, T, for T between about 150 and 380 K, in good agreement with the PA model, but that there is considerable deviation for T<150 K and a temperature range exists over which S increases with decreasing temperature. A modification of the PA model is required to explain this low-temperature behavior is briefly noted.     

Experimental identification of the lateral human–structure interaction mechanism and assessment of the inverted-pendulum biomechanical model

Within the context of crowd-induced lateral bridge vibration, human–structure interaction (HSI) is a widely studied phenomenon. Central to this study is the self-excited component of the ground reaction force (GRF). This force harmonic, induced by a walking pedestrian, resonates with lateral deck motion, irrespective of the pedestrian?s pacing frequency. Its presence can lead to positive feedback between pedestrian GRFs and structural motion. Characterisation of the self-excited force as equivalent structural mass and damping has greatly improved the understanding of HSI and its role in developing lateral dynamic instability. However, despite this evolving understanding, a key question has remained unanswered; what are the features of a pedestrian?s balance response to base motion that gives rise to the self-excited force? The majority of the literature has focussed on the effects of HSI with the underlying mechanism receiving comparatively little attention. This paper presents data from experimental testing in which 10 subjects walked individually on a laterally oscillating treadmill. Lateral deck motion as well as the GRFs imposed by the subject was recorded. Three-dimensional motion capture equipment was used to track the position of visual markers mounted on the subject. Thus whole body response to base motion was captured in addition to the GRFs generated. The data presented herein supports the authors’ previous findings that the self-excited force is a frequency sideband harmonic resulting from amplitude modulation of the lateral GRF. The gait behaviour responsible for this amplitude modulation is a periodic modulation of stride width in response to a sinusoidally varying inertia force induced by deck motion. In a separate analysis the validity of the passive inverted pendulum model, stabilised by active control of support placement was confirmed. This was established through comparison of simulated and observed frontal plane CoM motion. Despite the relative simplicity of this biomechanical model, remarkable agreement was observed.     

Comparison of the ratios of the yields of cumulative K + and K − mesons with the predictions of the model of a collective sea of quark-antiquark pairs in nuclei

The results obtained by simulating, within the flucton model, the production and secondary interactions of cumulative K ⁺ and K ^? mesons in nuclei indicate that the ratios of their yields are in acceptable agreement with the predictions of the model of a collective sea of quark-antiquark pairs in nuclei. The calculations were performed with allowance for the kaon-hadronization length according to the model of bremsstrahlung-gluon emission and the parton model.     

On the nature of the phase transition triggered by vortex-like defects in the 2D Ginzburg–Landau model

The two-dimensional lattice Ginzburg–Landau Hamiltonian is simulated numerically for different values of the coherence length ξ in units of the lattice spacing a, a parameter which controls amplitude fluctuations. The phase diagram on the plane T–ξ is measured. Amplitude fluctuations change dramatically the nature of the phase transition: for values of ξ/a≃1, instead of the smooth Kosterlitz–Thouless transition there is a first-order transition with a discontinuity in the vortex density v and a sharper drop in the helicity modulus Γ. Both observables v and Γ are analyzed in detail at the crossover region between first and second order which occurs for intermediate values of ξ/a.     

Entanglement dynamics of a double two-photon Jaynes-Cummings model with Kerr-like medium

In this paper, the entanglement dynamics of a double two-photon Jaynes--Cummings model with Kerr-like medium is investigated. It is shown that initial entanglement has an interesting subsequent time evolution, including the so-called entanglement sudden death effect. It is also shown analytically that the Kerr-like medium can repress entanglement sudden death and enhance the degree of atom--atom entanglement. A more interesting fact is that the Kerr effect is more obvious when each of the two cavities with have the Kerr-like medium than only one of them with the Kerr-like medium.     

Products of distributions and collision of a δ-wave with a δ′-wave in a turbulent model

We study the possibility of collision of a δ-wave with a stationary δ′-wave in a model ruled by equation f (t)u _t+[u²?β(x?γ(t))u]_x = 0, where f, β and γ are given real functions and u = u(x, t) is the state variable. We adopt a solution concept which is a consistent extension of the classical solution concept. This concept is defined in the setting of a distributional product, which is not constructed by approximation processes. By a convenient choice of f, β and γ, we are able to distinguish three distinct dynamics for that collision, to which correspond phenomena of solitonic behaviour, scattering, and merging. Also, as a particular case, taking f = 2 and β = 0 we prove that the referred collision is impossible to arise in the setting of the inviscid Burgers equation. To show how this framework can be applied to other physical models, we included several results already obtained.     

Relaxation processes and mobility of electrons in a semiconductor quantum well with the modified Pöschl-teller confining potential

Relaxation processes and mobility of electrons in a semiconductor quantum well are studied. The modified Pöschl-Teller potential is used as a confining potential. Scattering rates due to impurity ions, acoustic and piezoacoustic phonons are calculated taking into account the screening of scattering potentials by charge carriers. It is shown that when degenerate electrons are scattered by acoustic phonons, the dependence of scattering rate on electron wave number ν_ac(k) is almost linear. At small k, the acoustic phonon piezoelectric scattering rate of degenerate electrons increases with k, and then it decreases slightly when k > 8 × 10⁷ m⁻¹. The ionized impurity scattering rate of degenerate electrons does not depend on temperature, is directly proportional to the electron density, and decreases with increasing k. Dependences of electron mobility on surface ion density and temperature are studied. It is shown that in the case of non-degenerate or slightly degenerate electron gas, a maximum appears in the temperature dependence of the mobility, and the screening effect is negligible. The screening significantly increases the mobility of electrons in the case of high degeneration. Obtained results are applied to GaAs-based quantum wells.