Associate Professor KOBAYASHI, Kensuke; Professor ONO, Teruo “ Beyond Linear Response: Experimental Test of Fluctuation Theorem in Quantum Regime ” (Published in “Physical Review Letters”, 26 February 2010)

Associate Professor KOBAYASHI, Kensuke;
ONO, Teruo

(Laboratory of Nanospintronics, Division of Materials Chemistry)


Beyond Linear Response: Experimental Test of Fluctuation Theorem in Quantum Regime


Published in Physical Review Letters”, 26 February 2010

Associate Professor KOBAYASHI, Kensuke(left)
Professor ONO, Teruo (right)

“Nonequilibrium Fluctuation Relations in a Quantum Coherent Conductor” by Shuji Nakamura1, Yoshiaki Yamauchi1, Masayuki Hashisaka1, Kensaku Chida1, Kensuke Kobayashi1, Teruo Ono1, Renaud Leturcq2, Klaus Ensslin3, Keiji Saito4, Yasuhiro Utsumi5, and Arthur C. Gossard6

1Institute for Chemical Research, Kyoto University
2Institute of Electronics, Microelectronics and Nanotechnology, IEMN-CNRS, France
3Solid State Physics Laboratory, ETH Zürich, Switzerland
4Graduate School of Science, University of Tokyo, Japan
5Institute for Solid State Physics, University of Tokyo, Japan
6Materials Department, University of California, Santa Barbara, USA

The linear-response theory, which is one of the triumphs in physics, was proposed in 1950’s. Triggered by Einstein’s work on the Brownian motion followed by the Johnson-Nyquist relation in an electrical circuit, the fluctuation-dissipation relation has been developed into the linear-response theory, which successfully relates a macroscopic irreversible process with underlying microscopic reversible equation of motion. The theory is now well-established as a standard tool to quantitatively predict the response of a variety of physical systems, and constitutes a reliable foundation in a wide range of physics, especially in statistical physics and condensed-matter physics. However, the linear-response theory is only justified very close to the equilibrium, and its application to a wider range of natural phenomena in physics, chemistry and biology is limited, although it is often the case that the most fascinating phenomena, such as life activity, occur far from equilibrium. Therefore, an intensive attempt to expand the theory to non-equilibrium regimehas been conducted for about half a century.

In 1990’s, several exact relations that are validated even far from equilibrium were discovered. Among them, the fluctuation theorem (FT) is a microscopic expansion of the macroscopic second law of thermodynamics. While there is an experimental demonstration of its validity in a classical regime by using colloidal particles, the validity of FT in the quantum regime was left to be addressed.
Here, we show that FT indeed yields a non-trivial result in the quantum transport. We have experimentally demonstrated the presence of higher-order correlations (in applied bias voltage) between the current and the current noise in a mesoscopic electron interferometer, which corresponds to the next order correlation following to the Johnson-Nyqusit relation.

Figure: The atomic force microscope image of the mesoscopic electron interferometer, where our experimental test of FT was performed. The measurement setup is schematically shown.

In addition, we prove that the new relation is valid even in the presence of the electron-electron interactions, where the Onsager-Casmir relation is broken as a signature of the non-linearity and the non-equilibrium. Our results qualitatively validate the predictions based on FT, being the first experimental evidence of FT in the non-equilibrium quantum regime.
The present achievement will open up a new way to further explore non-equilibrium statistical mechanics.
This work is partially supported by KAKENHI, Yamada Science Foundation, SCAT, Matsuo Science Foundation.

Published in Physical Review Letters 104, 080602 (2010)