104,284 research outputs found
Condensation of Eigen Microstate in Statistical Ensemble and Phase Transition
In a statistical ensemble with microstates, we introduce an
correlation matrix with the correlations between microstates as its elements.
Using eigenvectors of the correlation matrix, we can define eigen microstates
of the ensemble. The normalized eigenvalue by represents the weight factor
in the ensemble of the corresponding eigen microstate. In the limit , weight factors go to zero in the ensemble without localization of
microstate. The finite limit of weight factor when indicates a
condensation of the corresponding eigen microstate. This indicates a phase
transition with new phase characterized by the condensed eigen microstate. We
propose a finite-size scaling relation of weight factors near critical point,
which can be used to identify the phase transition and its universality class
of general complex systems. The condensation of eigen microstate and the
finite-size scaling relation of weight factors have been confirmed by the Monte
Carlo data of one-dimensional and two-dimensional Ising models.Comment: 9 pages, 16 figures, accepted for publication in Sci. China-Phys.
Mech. Astro
Event patterns extracted from anisotropic spectra of charged particles produced in Pb-Pb collisions at 2.76 TeV
Event patterns extracted from anisotropic spectra of charged particles
produced in lead-lead collisions at 2.76 TeV are investigated. We use an
inverse power-law resulted from the QCD calculus to describe the transverse
momentum spectrum in the hard scattering process, and a revised Erlang
distribution resulted from a multisource thermal model to describe the
transverse momentum spectrum and anisotropic flow in the soft excitation
process. The pseudorapidity distribution is described by a three-Gaussian
function which is a revision of the Landau hydrodynamic model. Thus, the event
patterns at the kinetic freeze-out are displayed by the scatter plots of the
considered particles in the three-dimensional velocity, momentum, and rapidity
spaces.Comment: 19 pages, 8 figures, The European Physical Journal A, accepte
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