Characterizing chaotic melodies in automatic music composition

In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests. (c) 2010 American Institute of Physics. [doi: 10.1063/1.3487516]

Measurement of transverse single-spin asymmetries for J/psi production in polarized p plus p collisions at root s=200 GeV

We report the first measurement of transverse single-spin asymmetries in J/psi production from transversely polarized p + p collisions at root s = 200 GeV with data taken by the PHENIX experiment in 2006 and 2008. The measurement was performed over the rapidity ranges 1.2 < vertical bar y vertical bar < 2.2 and vertical bar y vertical bar < 0.35 for transverse momenta up to 6 GeV/c. J/psi production at the Relativistic Heavy Ion Collider is dominated by processes involving initial-state gluons, and transverse single-spin asymmetries of the J/psi can provide access to gluon dynamics within the nucleon. Such asymmetries may also shed light on the long-standing question in QCD of the J/psi production mechanism. Asymmetries were obtained as a function of J/psi transverse momentum and Feynman-x, with a value of -0.086 +/- 0.026(stat) +/- 0.003(syst) in the forward region. This result suggests possible nonzero trigluon correlation functions in transversely polarized protons and, if well defined in this reaction, a nonzero gluon Sivers distribution function.

Transverse momentum dependence of J/psi polarization at midrapidity in p plus p collisions at root s=200 GeV

We report the measurement of the transverse momentum dependence of inclusive J/psi polarization in p + p collisions at root s = 200 GeV performed by the PHENIX Experiment at the Relativistic Heavy Ion Collider. The J/psi polarization is studied in the helicity, Gottfried-Jackson, and Collins-Soper frames for p(T) < 5 GeV/c and vertical bar y vertical bar < 0.35. The polarization in the helicity and Gottfried-Jackson frames is consistent with zero for all transverse momenta, with a slight (1.8 sigma) trend towards longitudinal polarization for transverse momenta above 2 GeV/c. No conclusion is allowed due to the limited acceptance in the Collins-Soper frame and the uncertainties of the current data. The results are compared to observations for other collision systems and center of mass energies and to different quarkonia production models.

Transition in Yield and Azimuthal Shape Modification in Dihadron Correlations in Relativistic Heavy Ion Collisions

Hard-scattered parton probes produced in collisions of large nuclei indicate large partonic energy loss, possibly with collective produced-medium response to the lost energy. We present measurements of pi(0) trigger particles at transverse momenta p(T)(t) = 4-12 GeV/c and associated charged hadrons (p(T)(a) = 0.5-7 GeV/c) vs relative azimuthal angle Delta phi in Au + Au and p + p collisions at root s(NN) = 200 GeV. The Au + Au distribution at low p(T)(a), whose shape has been interpreted as a medium effect, is modified for p(T)(t) < 7 GeV/c. At higher p(T)(t), the data are consistent with unmodified or very weakly modified shapes, even for the lowest measured p(T)(a), which quantitatively challenges some medium response models. The associated yield of hadrons opposing the trigger particle in Au + Au relative to p + p (I(AA)) is suppressed at high p(T) (I(AA) approximate to 0.35-0.5), but less than for inclusive suppression (R(AA) approximate to 0.2).

Detailed measurement of the e(+)e(-) pair continuum in p plus p and Au plus Au collisions at root s(NN)=200 GeV and implications for direct photon production

PHENIX has measured the e(+)e(-) pair continuum in root s(NN) = 200 GeV Au+Au and p+p collisions over a wide range of mass and transverse momenta. The e(+)e(-) yield is compared to the expectations from hadronic sources, based on PHENIX measurements. In the intermediate-mass region, between the masses of the phi and the J/psi meson, the yield is consistent with expectations from correlated c (c) over bar production, although other mechanisms are not ruled out. In the low-mass region, below the phi, the p+p inclusive mass spectrum is well described by known contributions from light meson decays. In contrast, the Au+Au minimum bias inclusive mass spectrum in this region shows an enhancement by a factor of 4.7 +/- 0.4(stat) +/- 1.5(syst) +/- 0.9(model). At low mass (m(ee) < 0.3 GeV/c(2)) and high p(T) (1 < p(T) < 5 GeV/c) an enhanced e(+)e(-) pair yield is observed that is consistent with production of virtual direct photons. This excess is used to infer the yield of real direct photons. In central Au+Au collisions, the excess of the direct photon yield over the p+p is exponential in p(T), with inverse slope T = 221 +/- 19(stat) +/- 19(syst) MeV. Hydrodynamical models with initial temperatures ranging from T(init) similar or equal to 300-600 MeV at times of 0.6-0.15 fm/c after the collision are in qualitative agreement with the direct photon data in Au+Au. For low p(T) < 1 GeV/c the low-mass region shows a further significant enhancement that increases with centrality and has an inverse slope of T similar or equal to 100 MeV. Theoretical models underpredict the low-mass, low-p(T) enhancement.

Inclusive cross section and double helicity asymmetry for pi(0) production in p plus p collisions at root s=62.4 GeV

The PHENIX experiment presents results from the RHIC 2006 run with polarized p + p collisions at root s = 62.4 GeV, for inclusive pi(0) production at midrapidity. Unpolarized cross section results are measured for transverse momenta p(T) = 0.5 to 7 GeV/c. Next-to-leading order perturbative quantum chromodynamics calculations are compared with the data, and while the calculations are consistent with the measurements, next-to-leading logarithmic corrections improve the agreement. Double helicity asymmetries A(LL) are presented for p(T) = 1 to 4 GeV/c and probe the higher range of Bjorken x of the gluon (x(g)) with better statistical precision than our previous measurements at root s = 200 GeV. These measurements are sensitive to the gluon polarization in the proton for 0.06 < x(g) < 0.4.

CMB in a box: Causal structure and the Fourier-Bessel expansion

This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light cone of the observer. This foretold manifestation of causality in position (real) space happens order by order in a series expansion in powers of the visibility gamma = e(-mu), where mu is the optical depth to Thomson scattering. We show that the contributions of order gamma(N) to the cosmic microwave background (CMB) anisotropies are regulated by spacetime window functions which have support only inside the past light cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. The viability of the Fourier-Bessel series for treating the CMB is a consequence of the fact that the visibility function becomes exponentially small at redshifts z >> 10(3), effectively cutting off the past light cone and introducing a finite radius inside which initial conditions can affect physical observables measured at our position (x) over right arrow = 0 and time t(0). Hence, for each multipole l there is a discrete tower of momenta k(il) (not a continuum) which can affect physical observables, with the smallest momenta being k(1l) similar to l. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation-no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies.

Position-dependent noncommutativity in quantum mechanics

The model of the position-dependent noncommutativity in quantum mechanics is proposed. We start with given commutation relations between the operators of coordinates [(x) over cap (i), (x) over cap (j)] = omega(ij) ((x) over cap), and construct the complete algebra of commutation relations, including the operators of momenta. The constructed algebra is a deformation of a standard Heisenberg algebra and obeys the Jacobi identity. The key point of our construction is a proposed first-order Lagrangian, which after quantization reproduces the desired commutation relations. Also we study the possibility to localize the noncommutativity.

Hard thermal loops in static external fields

We examine, in the imaginary-time formalism, the high temperature behavior of n-point thermal loops in static Yang-Mills and gravitational fields. We show that in this regime, any hard thermal loop gives the same leading contribution as the one obtained by evaluating the loop integral at zero external energies and momenta.

Hydro-kinetic approach to relativistic heavy ion collisions

We develop a combined hydro-kinetic approach which incorporates a hydrodynamical expansion of the systems formed in A + A collisions and their dynamical decoupling described by escape probabilities. The method corresponds to a generalized relaxation time (tau(rel)) approximation for the Boltzmann equation applied to inhomogeneous expanding systems; at small tau(rel) it also allows one to catch the viscous effects in hadronic component-hadron-resonance gas. We demonstrate how the approximation of sudden freeze-out can be obtained within this dynamical picture of continuous emission and find that hypersurfaces, corresponding to a sharp freeze-out limit, are momentum dependent. The pion m(T) spectra are computed in the developed hydro-kinetic model, and compared with those obtained from ideal hydrodynamics with the Cooper-Frye isothermal prescription. Our results indicate that there does not exist a universal freeze-out temperature for pions with different momenta, and support an earlier decoupling of higher p(T) particles. By performing numerical simulations for various initial conditions and equations of state we identify several characteristic features of the bulk QCD matter evolution preferred in view of the current analysis of heavy ion collisions at RHIC energies.

Comparison of (120)Sn((6)He, (6)He)(120)Sn and (120)Sn(alpha,alpha)(120)Sn elastic scattering and signatures of the (6)He neutron halo in the optical potential

Cross sections of (120)Sn(alpha,alpha)(120)Sn elastic scattering have been extracted from the alpha-particle-beam contamination of a recent (120)Sn((6)He,(6)He)(120)Sn experiment. Both reactions are analyzed using systematic double-folding potentials in the real part and smoothly varying Woods-Saxon potentials in the imaginary part. The potential extracted from the (120)Sn((6)He,(6)He)(120)Sn data may be used as the basis for the construction of a simple global (6)He optical potential. The comparison of the (6)He and alpha data shows that the halo nature of the (6)He nucleus leads to a clear signature in the reflexion coefficients eta(L) : The relevant angular momenta L with eta(L) >> 0 and eta(L) << 1 are shifted to larger L with a broader distribution. This signature is not present in the alpha-scattering data and can thus be used as a new criterion for the definition of a halo nucleus.

Azimuthal di-hadron correlations in d plus Au and Au plus Au collisions at root s(NN)=200 GeV measured at the STAR detector

Yields, correlation shapes, and mean transverse momenta p(T) of charged particles associated with intermediate-to high-p(T) trigger particles (2.5 < p(T) < 10 GeV/c) in d + Au and Au + Au collisions at root s(NN) = 200 GeV are presented. For associated particles at higher p(T) greater than or similar to 2.5 GeV/c, narrow correlation peaks are seen in d + Au and Au + Au, indicating that the main production mechanism is jet fragmentation. At lower associated particle pT < 2 GeV/c, a large enhancement of the near- (Delta phi similar to 0) and away-side (Delta phi similar to pi) associated yields is found, together with a strong broadening of the away-side azimuthal distributions in Au + Au collisions compared to d + Au measurements, suggesting that other particle production mechanisms play a role. This is further supported by the observed significant softening of the away-side associated particle yield distribution at Delta phi similar to pi in central Au + Au collisions.

Spectra of identified high-p(T) pi(+/-) and p((p)over-bar ) in Cu + Cu collisions at root s(NN)=200 GeV

We report new results on identified (anti) proton and charged pion spectra at large transverse momenta (3 < p(T) < 10 GeV/c) from Cu + Cu collisions at root s(NN) = 200 GeV using the STAR detector at the Relativistic Heavy Ion Collider (RHIC). This study explores the system size dependence of two novel features observed at RHIC with heavy ions: the hadron suppression at high-p(T) and the anomalous baryon to meson enhancement at intermediate transverse momenta. Both phenomena could be attributed to the creation of a new form of QCD matter. The results presented here bridge the system size gap between the available pp and Au + Au data, and allow for a detailed exploration of the onset of the novel features. Comparative analysis of all available 200 GeV data indicates that the system size is a major factor determining both the magnitude of the hadron spectra suppression at large transverse momenta and the relative baryon to meson enhancement.

Charged and strange hadron elliptic flow in Cu plus Cu collisions at root s(NN)=62.4 and 200 GeV

We present the results of an elliptic flow, v(2), analysis of Cu + Cu collisions recorded with the solenoidal tracker detector (STAR) at the BNL Relativistic Heavy Ion Collider at root s(NN) = 62.4 and 200 GeV. Elliptic flow as a function of transverse momentum, v(2)(p(T)), is reported for different collision centralities for charged hadrons h(+/-) and strangeness-ontaining hadrons K(S)(0), Lambda, Xi, and phi in the midrapidity region vertical bar eta vertical bar < 1.0. Significant reduction in systematic uncertainty of the measurement due to nonflow effects has been achieved by correlating particles at midrapidity, vertical bar eta vertical bar < 1.0, with those at forward rapidity, 2.5 < vertical bar eta vertical bar < 4.0. We also present azimuthal correlations in p + p collisions at root s = 200 GeV to help in estimating nonflow effects. To study the system-size dependence of elliptic flow, we present a detailed comparison with previously published results from Au + Au collisions at root s(NN) = 200 GeV. We observe that v(2)(p(T)) of strange hadrons has similar scaling properties as were first observed in Au + Au collisions, that is, (i) at low transverse momenta, p(T) < 2 GeV/c, v(2) scales with transverse kinetic energy, m(T) - m, and (ii) at intermediate p(T), 2 < p(T) < 4 GeV/c, it scales with the number of constituent quarks, n(q.) We have found that ideal hydrodynamic calculations fail to reproduce the centrality dependence of v(2)(p(T)) for K(S)(0) and Lambda. Eccentricity scaled v(2) values, v(2)/epsilon, are larger in more central collisions, suggesting stronger collective flow develops in more central collisions. The comparison with Au + Au collisions, which go further in density, shows that v(2)/epsilon depends on the system size, that is, the number of participants N(part). This indicates that the ideal hydrodynamic limit is not reached in Cu + Cu collisions, presumably because the assumption of thermalization is not attained.

Longitudinal spin transfer to Lambda and Lambda hyperons in polarized proton-proton collisions at s=200 GeV

The longitudinal spin transfer, D(LL), from high energy polarized protons to Lambda and Lambda hyperons has been measured for the first time in proton-proton collisions at s=200 GeV with the STAR detector at the Relativistic Heavy Ion Collider. The measurements cover pseudorapidity, eta, in the range |eta|< 1.2 and transverse momenta, p(T), up to 4 GeV/c. The longitudinal spin transfer is found to be D(LL)=-0.03 +/- 0.13(stat)+/- 0.04(syst) for inclusive Lambda and D(LL)=-0.12 +/- 0.08(stat)+/- 0.03(syst) for inclusive Lambda hyperons with <>=0.5 and << p(T)>>=3.7 GeV/c. The dependence on eta and p(T) is presented.