Properties of condensed matter from fundamental physical constants

Abstract

Fundamental physical constants play a profound role in physics. For example, they govern nuclear reactions, formation of stars, nuclear synthesis and stability of biologically vital elements. These are high-energy processes discussed in particle physics, astronomy and cosmology. More recently, it was realised that fundamental physical constants extend their governing reach to low-energy processes and properties operating in condensed matter systems, often in an unexpected way. These properties are those we experience daily and can routinely measure, including viscosity, thermal conductivity, elasticity and sound. Here, we review this work. We start with the lower bound on liquid viscosity, its origin and show how to relate the bound to fundamental physical constants. The lower bound of kinematic viscosity represents the global minimum on the phase diagram. We show how this result answers the long-standing question considered by Purcell and Weisskopf, namely why viscosity never falls below a certain value. An accompanying insight is that water viscosity and water-based life are well attuned to fundamental constants including the Planck constant. We then discuss viscosity minima in liquid He above and below the λ-point. We subsequently consider a very different property, thermal diffusivity, and show that it has the same minimum fixed by fundamental physical constants as viscosity. We also discuss bounds related to elastic properties, elastic moduli and their analogues in low-dimensional systems, and show how these bounds are related to the upper bound for the speed of sound. We conclude with listing ways in which the discussion of fundamental constants and bounds advance physical theories.

Keywords:

• fundamental physical constants
• fine-tuning in the Universe
• liquid theory
• viscosity
• quantum liquids
• thermal conductivity
• elastic properties
• speed of sound

Acknowledgments

I am grateful to the EPSRC for support, to V. V. Brazhkin, B. Carr, L. Noirez, G. Volovik and U. Windberger for discussions and to V. V. Brazhkin for contributing to Section 5.2 in 2021.

Disclosure statement

No potential conflict of interest was reported by the author.