Dynamics of Critical Fluctuations. I
スポンサーリンク
概要
- 論文の詳細を見る
The dynamics of critical fluctuations is treated theoretically by extending the usual macroscopic dynamical variables to include all other dynamical variables that could exhibit the critical slowing-down. The equations of motion for these generalized macroscopic dynamical variables are derived with the help of Mori's general theory of Brownian motion, which involve the "first moment frequency matrix" Q_q and the microscopic damping for these new dynamical variables, where q is the wave vector characterizing macroscopic inhomogeneity. The latter involves only the dynamical variables that perform rapid random motions and is disregarded, or is disposed of by means of a dimensional argument. Then the dynamics of critical fluctuations is completely governed by Q_q which is expressed in terms of equaltime correlations of long wave-length fluctuations only and allows the analysis with the help of the Widom-Kadanoff static scaling laws. The theory is applied to the problem of anomalous spin relaxations in ferro and antiferromagnets in the paramagnetic region, and the inverse characteristic times near the transition points are found to behave asymptotically as k^<(5-η)/2>f(q/k) and k^<3/2>f(q/k), respectively, where k is the inverse correlation range of spin fluctuations and η the parameter measuring the deviation of spin pair correlation from the Ornstein-Zernike form. Finally a close analogy is pointed out between the present treatment of critical fluctuations and the theory of hydrodynamic turbulence.
- 理論物理学刊行会の論文
- 1968-05-25
著者
関連論文
- Dimensional Reduction in Phase-Separating Critical Fluids under Shear Flow : Condensed Matter and Statistical Physics
- Nonlinear Elastic Network Model of Swelling Gels
- Elastic Instability of Gels upon Swelling
- Two Topics in Dynamics of Ordering Processes in Complex Systems : Complex Dynamics in Nonlinear Systems
- Diffusive Phase Boundary of Gel Rods
- Renormalization Group Approach to the Interfacial Order Parameter Profile near the Critical Point
- Dynamics of Critical Fluctuations. II
- Spinodal Decomposition in Binary Critical Fluids
- Dynamics of Fluctuations in Unstable Systems. II : Evolution Equation of Long Wavelength Fluctuation Spectra
- Fluctuations in Nonequilibrium Steady States with Laminar Shear Flow : Classical Fluids near the Critical Point
- Critical Phenomena in Two-Dimensional Incompressible Flows
- Vertex Dynamics of Two-Dimensional Cellular Patterns
- Topological Defects and Non-Equilibrium
- Dynamics of Critical Fluctuations. I
- A Simple Model for the Formation of Heterogenous Structure
- Hopping Processes from Dynamical Density Functional Theory for a Deeply Supercooled Hard-Sphere Liquid
- On the Behavior of Thermal Conductivity near the Magnetic Transition Point
- Early Stage of Slow dynamics in Dynamical Density Functional Theory of a Hard-Sphere Liquid near the Glass Transition
- Anisotropic Spinodal Decomposition under Shear Flow : Condensed Matter and Statistical Physics
- Effect of the Gravitational Field on the Surface Roughening Transition
- Critical Phenomena under Non-Uniform External Force Fields
- Proton Dynamics and Ultrasonic Attenuation of KDP-Type Ferroelectrics
- Renormalization Group Theory of the Interfacial Roughening Transition
- Continuum Theory of Excitation Spectra of Topologically Disordered Systems
- The Mode-Coupling Approach to Sound Propagation in a Critical Fluid. II : Four Heat-Mode Contribution
- Kinetic Drumhead Model of Interface. I
- Defect-Phase Dynamics for Dissipative Media with Potential
- Kinetic Drumhead Models of Interface. II
- Estimate of Error Terms in the Dynamical Theory of Critical Fluctuations
- An Entropy Concept in Statistical Mechanics
- Critical Phenomena of Classical Fluids under Flow. I : Mean Field Approximation
- Time-Dependent Ising Model with Long Range Interaction
- Application of Extended Mode-Coupling Theory to Long-Time Behavior of Correlation Functions
- The Mode-Coupling Approach to Sound Propagation in a Critical Fluid. I : Correction Due to Hydrodynamic Interactions
- A Theorist's View on Supercooled Liquids and Glass Transitions
- AVALANCHE PHENOMENA IN TWO-DIMENSIONAL FOAM SYSTEMS(Session III : Complex Fluids, The 1st Tohwa University International Meeting on Statistical Physics Theories, Experiments and Computer Simulations)
- Dynamics of Fluctuations in Unstable Systems. I
- Theory of Early Stage Spinodal Decomposition in Fluids Near the Critical Point. I
- Spin Pair Correlation in the Heisenberg Ferromagnet
- Renormalization Group Equations in Critical Dynamics. III : Scaling Far from Equilibrium
- Nonlinear Effects in the Shear Viscosity of Critical Mixtures
- Theory of Early Stage Spinodal Decomposition in Fluids near the Critical Point. II