Spectral Model Selection for Electronic Measurement of the Boltzmann Constant

• Activity Number: 36 - Statistcal Theory and Uncertainty Quantification in Physical Sciences
• Type: Contributed
• Date/Time: Sunday, July 28, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Kevin J Coakley*
• Companies: National Institute of Standards and Technology
• Keywords: Boltzmann constant; cross-validation; Johnson noise thermometry; spectral model selection; resampling methods; uncertainty quantification

Abstract

In the ``New SI", the unit of thermodynamic temperature, the kelvin, will be redefined by fixing the numerical value of the Boltzmann constant. In the measurement of the Boltzmann constant based on Johnson noise thermometry, the ratio of the power spectral densities of thermal noise across a resistor at the triple point of water, and pseudo-random noise synthetically generated by a quantum-accurate voltage-noise source is constant to within 1 part in a billion up to 1 GHz. Given this ratio spectrum and other known or measured parameters, one can determine the Boltzmann constant. Due to mismatch between transmission lines, the expected observed ratio spectrum is modeled as an even polynomial function of frequency where the constant term determines the Boltzmann constant. For each candidate fitting bandwidth (maximum frequency analyzed), I select polynomial model complexity by a Monte Carlo implementation of five-fold cross-validation and quantify components of uncertainty due to random measurement errors and model ambiguity. I also quantify a component of uncertainty that accounts for ambiguity in the fitting bandwidth. I present results for experimental and simulated data.