Application of the equipartition theorem to the thermal excitation of quartz tuning forks

TL;DR

This study verifies the equipartition theorem's applicability to quartz tuning forks across a temperature range from 140K to 300K by analyzing thermal amplitude measurements and discusses its relevance at liquid helium temperatures.

Contribution

The paper experimentally confirms the validity of the equipartition theorem for quartz tuning forks over a broad temperature range, including cryogenic temperatures.

Findings

Thermal amplitude measurements match theoretical predictions from the equipartition theorem.

The equipartition theorem remains valid for quartz tuning forks down to 140K.

Discussion on the theorem's applicability at liquid helium temperatures.

Abstract

The deflection signal of a thermally excited force sensor of an atomic force microscope can be analyzed to gain important information about the detector noise and about the validity of the equipartion theorem of thermodynamics. Here, we measured the temperature dependence of the thermal amplitude of a tuning fork and compared it to the expected values based on the equipartition theorem. In doing so, we prove the validity of these assumptions in the temperature range from 140K to 300K. Furthermore, the application of the equipartition theorem to quartz tuning forks at liquid helium temperatures is discussed.