Study of Kinetic Freeze-Out Parameters as a Function of Rapidity in pp Collisions at CERN SPS Energies.

We used the blast wave model with the Boltzmann-Gibbs statistics and analyzed the experimental data measured by the NA61/SHINE Collaboration in inelastic (INEL) proton-proton collisions at different rapidity slices at different center-of-mass energies. The particles used in this study were π+, π-, K+, K-, and p¯. We extracted the kinetic freeze-out temperature, transverse flow velocity, and kinetic freeze-out volume from the transverse momentum spectra of the particles. We observed that the kinetic freeze-out temperature is rapidity and energy dependent, while the transverse flow velocity does not depend on them. Furthermore, we observed that the kinetic freeze-out volume is energy dependent, but it remains constant with changing the rapidity. We also observed that all three parameters are mass dependent. In addition, with the increase of mass, the kinetic freeze-out temperature increases, and the transverse flow velocity, as well as kinetic freeze-out volume decrease.

Study of Dependence of Kinetic Freezeout Temperature on the Production Cross-Section of Particles in Various Centrality Intervals in Au-Au and Pb-Pb Collisions at High Energies.

Transverse momentum spectra of π+, p, Λ, Ξ or Ξ¯+, Ω or Ω¯+ and deuteron (d) in different centrality intervals in nucleus-nucleus collisions at the center of mass energy are analyzed by the blast wave model with Boltzmann Gibbs statistics. We extracted the kinetic freezeout temperature, transverse flow velocity and kinetic freezeout volume from the transverse momentum spectra of the particles. It is observed that the non-strange and strange (multi-strange) particles freezeout separately due to different reaction cross-sections. While the freezeout volume and transverse flow velocity are mass dependent, they decrease with the resting mass of the particles. The present work reveals the scenario of a double kinetic freezeout in nucleus-nucleus collisions. Furthermore, the kinetic freezeout temperature and freezeout volume are larger in central collisions than peripheral collisions. However, the transverse flow velocity remains almost unchanged from central to peripheral collisions.

Corrigendum: A Stronger Multi-observable Uncertainty Relation.

This corrects the article DOI: 10.1038/srep44764.

A Stronger Multi-observable Uncertainty Relation.

Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty relation. Here we present a variance-based sum uncertainty relation for N incompatible observables stronger than the simple generalization of an existing uncertainty relation for two observables. Further comparisons of our uncertainty relation with other related ones for spin- and spin-1 particles indicate that the obtained uncertainty relation gives a better lower bound.