Enhancement of critical slowing down in chiral phase transition—Langevin dynamics approach

2004/04/30 by T. Koide, M. Maruyama, Masahiro Maruyama · 1 citation
Chemistry · Materials Science · Mathematics · Physics and Astronomy · #Brownian dynamics #Brownian motion #Chemistry #Condensed matter physics #Critical phenomena #Critical point (mathematics) #Langevin dynamics #Langevin equation #Material Dynamics and Properties #Mathematics #Oscillation (cell signaling) #Phase (matter) #Phase diagram #Phase transition #Physics #Quantum many-body systems #Quantum mechanics #Relaxation (psychology) #Statistical physics #Theoretical and Computational Physics #Thermalisation #Thermodynamics #Tricritical point #cond-mat.stat-mech #hep-ph #nucl-th

paper · pdf · doi:10.1016/j.nuclphysa.2004.06.013

published as Nucl.Phys. A742 (2004) 95-129 · Style file is changed, references are added, 42 pages, 14 figures, Nucl. Phys. A in press

arxiv created 2004/06/21 · openalex publication_date 2004/07/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We derive the linear Langevin equation that describes the behavior of the fluctuations of the order parameter of the chiral phase transition above the critical temperature by applying the projection operator method to the Nambu-Jona-Lasinio model at finite temperature and density. The Langevin equation relaxes exhibiting oscillation, reveals thermalization and converges to the equilibrium state consistent with the mean-field approximation as time goes on. With the help of this Langevin equation, we further investigate the relaxation of the critical fluctuations. The relaxation time of the critical fluctuations increases at speed as the temperature approaches toward the critical temperature because of the critical slowing down. The critical slowing down is enhanced as the chemical potential increases because of the Pauli blocking. Furthermore, we find another enhancement of the critical slowing down around the tricritical point.

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