Method for validating a first principles theory of the lambda transition in liquid helium 4

This paper explains how a first principles theory for critical fluctuations consisting of isothermal fourth sound waves in bulk liquid He II can be tested experimentally. The first principles theory is able to predict the detailed behavior of isothermal fourth sound wave signals very near the lambda transition. Experimental detection of the predicted signals would validate this theory to a high degree of confidence and thereby provide a new paradigm for understanding the physical mechanism responsible for critical properties in liquid helium 4. Theoretical and experimental results that support the predictions of this theory are presented. The method of detection rests on formulas derived here for the time-dependent density-density correlation function and associated pressure fluctuations in superfluid He II that is in thermodynamic equilibrium near the lambda transition temperature. Plots of predicted signals are presented and experimental apparatus that uses an electron-tunneling sensor that can detect the pressure fluctuations is described. Some implications of how validation of this first principles theory would impact general understanding of critical fluctuations and lambda transitions are discussed.