Jayanta K. Bhattacharjee

General dynamic scaling theory of critical ultrasonic attenuation and dispersion

Abstract Because of the critical slowing down of the order parameter fluctuations, they do not follow the temperature oscillations produced adiabatically by a pressure wave. The resulting hysteresis leads to the observed dispersion and attenuation of ultrasound. The effect depends entirely upon the frequency dependent specific heat. We discuss here the mathematical features of this function, including it dynamic scaling properties.

Critical ultrasonic and hypersonic attenuation for the liquid-gas phase transition

Abstract Joining the dynamic scaling concept with the frequency dependent specific heat approach of Herzfeld, Rice, and Fixman enables us to set up a new theory of the critical point ultrasonic attenuation. The critical point attenuation per wavelength has the frequency independent universal value α c λ = 0.27 times a background correction. Thermodynamic data determine the background correction unambiguously and the resulting agreement of the theory with measured values α c λ is excellent.

Universality in the critical dynamics of fluids: ultrasonic attenuation

In contrast to the binary liquids, the order-parameter relaxation rates in the pure fluids are greatly affected by a large non-critical component. With the appropriate crossover correction to dynamic scaling, we restore universality and demonstrate that the ultrasonic data for both the one- and two-component fluids fall on the same scaling plot.

Homogeneous isotropic turbulence in randomly stirred fluids: Self‐consistent mode coupling and perturbation theory

The randomly stirred model of DeDominices and Martin [Phys. Rev. A 19, 419 (1979)] is considered in the framework of self‐consistent mode coupling theories of dynamic critical phenomena. It is found that the theory is finite when the forcing yields the Kolmogorov spectrum. Perturbation theory can now be set up for universal amplitudes and results agree with the renormalization group calculations of Yakhot and Orszag [Phys. Rev. Lett. 57, 1722 (1986); J. Sci. Comput. 1, 1 (1986)].

Equation-of-Motion Approach to the Critical Dynamics of Liquid Helium at the Lambda Point*

A complete treatment of dynamic scaling in liquid helium at the lambda point is developed straightforwardly from explicit application of the nonlinear mode-coupling equations of motion, without Langevin noise terms. Special attention is given to the ratio w of the order-parameter and entropy relaxation rates. Various estimates indicate w = O(0.1), which produces a characteristic double-humped fluctuation spectrum, amenable to experimental verification. Further details are a thorough study of the transient solutions as well as the presentation of a new expansion scheme similar to the ɛ expansion but of superior accuracy.

Effect of applied field on the spin correlations in a ferromagnetic superconductor

Abstract Oscillatory coaxial concentric cylindrical arrays of magnetization are set up around the vortices induced by an applied field in a ferromagnetic superconductor above its Curie point. Experimental detection of these arrays by neutron scattering is facilitated by their particular temperature, wave number, and angular dependence.

λ-point critical dynamics for the pedestrian: High temperature expansion

Abstract A “high-temperature” expansion in powers of |t| − 2 3 , where t is the reduced temperature is employed to calculate the thermal conductivity, second sound damping and the fluctuation spectrum near the lambda transition. The smallness of the dynamic critical region makes such an approach useful.

Self-consistent screening approximation, long range interactions and the critical exponent η

Abstract The self-consistent screening approximation of Bray is used in the presence of long range interactions to suggest that the critical exponent η might differ from its classical value of 2 - σ, under certain circumstances.

Analytic properties of the critical dynamics ε expansion

The e‐expansion technique for evaluating certain integrals in critical dynamics is studied in detail. The analytic properties in the complex e plane are exploited to get improved answers at the physical value of e. A different scheme—the ? expansion—is suggested. This has a simpler analytic structure and thus gives more reliable results.

To Scale or Not to Scale? — The Puzzle at the Lambda Point of Liquid 4He

Light scattering measures both static and dynamic properties of liquid 4He. Recent work reconciles the dynamic scaling theory with apparent experimental discrepancies. Some questions remain regarding the statics.