Enhancement of Critical Slowing Down in Chiral Phase Transition -- Langevin Dynamics Approach --

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.

Style file is changed, references are added, 42 pages, 14 figures, Nucl. Phys. A in press

References in corpus (39)

• QCD Phenomenology based on a Chiral Effective Lagrangian
• Signatures of the Tricritical Point in QCD
• Event-by-Event Fluctuations in Heavy Ion Collisions and the QCD Critical Point
• The QCD phase diagram for small densities from imaginary chemical potential
• Lattice determination of the critical point of QCD at finite T and μ
• The QCD thermal phase transition in the presence of a small chemical potential
• Finite density QCD via imaginary chemical potential
• A new method to study lattice QCD at finite temperature and chemical potential
• Elliptic flow at SPS and RHIC: from kinetic transport to hydrodynamics
• Universality, the QCD critical/tricritical point and the quark number susceptibility
• Chiral Phase Transition within Effective Models with Constituent Quarks
• The QCD Phase Diagram for Three Degenerate Flavors and Small Baryon Density
• Strong Dissipative Behavior in Quantum Field Theory
• Microphysical Approach to Nonequilibrium Dynamics of Quantum Fields
• Chiral and Color-superconducting Phase Transitions with Vector Interaction in a Simple Model
• Chiral and Color-superconducting Phase Transitions with Vector Interaction in a Simple Model (Addenda)
• Coarse graining and decoherence in quantum field theory
• Classical Fields Near Thermal Equilibrium
• From Reversible Quantum Microdynamics to Irreversible Quantum Transport
• Scalar density fluctuation at critical end point in NJL model
• Pion Propagation near the QCD Chiral Phase Transition
• Dynamical renormalization group approach to relaxation in quantum field theory
• Real-time pion propagation in finite-temperature QCD
• Hydrodynamics Near a Chiral Critical Point
• Stochastic interpretation of Kadanoff-Baym equations and their relation to Langevin processes
• Dynamical renormalization group resummation of finite temperature infrared divergences
• Precursor of Color Superconductivity in Hot Quark Matter
• Forming Disoriented Chiral Condensates through Fluctuations
• Stochastic treatment of Disoriented Chiral Condensates within a Langevin description
• Pair Production in the Quantum Boltzmann Equation
• Derivation of Transport Equations using the Time-Dependent Projection Operator Method
• Coarse Grainings and Irreversibility in Quantum Field Theory
• Relaxing Near the Critical Point
• A New Expansion of the Heisenberg Equation of Motion with Projection Operator
• Dynamics near the critical point: the hot renormalization group in quantum field theory
• Hydrodynamic scaling from the dynamics of relativistic quantum field theory
• Generalized Bloch equations for a strongly driven tunneling system
• Renormalization by Projection: On the Equivalence of the Bloch-Feshbach Formalism and Wilson's Renormalization
• Projection Operator Approach to Langevin Equations in ${\varphi }^4$ Theory

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• Microscopic Derivation of Causal Diffusion Equation using Projection Operator Method
• A Lagrangian formulation of relativistic Israel-Stewart hydrodynamics
• Shock propagation and stability in causal dissipative hydrodynamics
• Shear viscosity, Bulk viscosity and Relaxation Times of Causal Dissipative Relativistic Fluid-Dynamics at Finite Temperature and Chemical Potential
• Domain Growth in Chiral Phase Transitions
• Phenomenological approach to the critical dynamics of the QCD phase transition revisited
• Dynamic aspect of the chiral phase transition in the mode coupling theory
• Generalized nonlinear Langevin equation from quantum nonlinear projection operator
• Domain Growth in Chiral Phase Transitions: Inertial Dynamics
• Chiral symmetry breaking and pion condensation in the early universe
• Overdamping Phenomena near the Critical Point in O($N$) Model
• Dynamics and Stability of Chiral Fluid
• Dynamic nature at the QCD Critical End Point
• Transport coefficients of chiral fluid dynamics using low-energy effective models