244,686 research outputs found
Witnessing a Poincar\'e recurrence with Mathematica
The often elusive Poincar\'e recurrence can be witnessed in a completely
separable system. For such systems, the problem of recurrence reduces to the
classic mathematical problem of simultaneous Diophantine approximation of
multiple numbers. The latter problem then can be somewhat satisfactorily solved
by using the famous Lenstra-Lenstra-Lov\'{a}sz (LLL) algorithm, which is
implemented in the Mathematica built-in function \verb"LatticeReduce". The
procedure is illustrated with a harmonic chain. The incredibly large recurrence
times are obtained exactly. They follow the expected scaling law very well.Comment: 8 pages, 5 figure
Hadron-quark phase transition in asymmetric matter with dynamical quark masses
The two-Equation of State (EoS) model is used to describe the hadron-quark
phase transition in asymmetric matter formed at high density in heavy-ion
collisions. For the quark phase, the three-flavor Nambu--Jona-Lasinio (NJL)
effective theory is used to investigate the influence of dynamical quark mass
effects on the phase transition. At variance to the MIT-Bag results, with fixed
current quark masses, the main important effect of the chiral dynamics is the
appearance of an End-Point for the coexistence zone. We show that a first order
hadron-quark phase transition may take place in the region T=(50-80)MeV and
\rho_B=(2-4)\rho_0, which is possible to be probed in the new planned
facilities, such as FAIR at GSI-Darmstadt and NICA at JINR-Dubna. From isospin
properties of the mixed phase somepossible signals are suggested. The
importance of chiral symmetry and dynamical quark mass on the hadron-quark
phase transition is stressed. The difficulty of an exact location of
Critical-End-Point comes from its appearance in a region of competition between
chiral symmetry breaking and confinement, where our knowledge of effective QCD
theories is still rather uncertain.Comment: 13 pages, 16 figures (revtex
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