Violation of FluctuationDissipation Theorem Results in Robustness of Fluctuation Against Localization
© The Physical Society of Japan
This article is on
Robustness of Equilibrium OffDiagonal Current Fluctuation against Localization of Electron States in Macroscopic TwoDimensional Systems
(JPSJ Editors' Choice)
J. Phys. Soc. Jpn. 91, 024004 (2022).
We study equilibrium current fluctuations in systems without timereversal symmetry, violating the fluctuationdissipation theorem. Notably, the offdiagonal fluctuation is insensitive to system imperfections in contrast to other fluctuations and conductivity.
The fluctuationdissipation theorem (FDT) claims that the current fluctuation in a macroscopic equilibrium system is equal to the product of the temperature and electrical conductivity. This “theorem” was proved for classical systems for all components of fluctuations including offdiagonal fluctuations, namely crosstime correlations between currents flowing in different directions.
However, the validity of the FDT in quantum systems was questioned, because disturbances by quantum measurement often play a crucial role, which was ignored in the proof of the FDT for classical systems. Recently, this longstanding question was formally solved, and the FDT was shown to be violated even when the fluctuation is measured in a way that simulates the classical ideal measurement as closely as possible. However, this formal solution neither gave concrete systems that exhibit the FDT violation nor estimated the magnitude of violation.
We propose a twodimensional electron system in a magnetic field as a real physical system in which the FDT is violated. We clarify the conditions for large violations and show that the magnitude of violation is macroscopically large. In fact, the FDT for the offdiagonal component is significantly violated in a strong magnetic field at low temperatures, whereas the FDT for the diagonal component holds for any values of the parameters. In the standard setup used in the quantum Hall effect experiments, the offdiagonal current fluctuation is several tens of times larger than the product of temperature and Hall conductivity (offdiagonal conductivity).
Such a large violation implies novel properties of offdiagonal current fluctuations that are yet to be studied. Localized states of electrons contribute to the offdiagonal current fluctuation to the same extent as extended states, and hence, the offdiagonal fluctuation is insensitive to system imperfections. This is in sharp contrast to the Hall conductivity that is very sensitive to the imperfections because only extended states contribute. Moreover, as an application of this finding, we propose a new method for estimating the electron number density by measuring the offdiagonal fluctuation. Because fluctuations are a cause of error and noise, our results are expected to provide fundamental design guidelines for applications.
(Written by K. Kubo, K. Asano, and A. Shimizu)
Robustness of Equilibrium OffDiagonal Current Fluctuation against Localization of Electron States in Macroscopic TwoDimensional Systems
(JPSJ Editors' Choice)
J. Phys. Soc. Jpn. 91, 024004 (2022).
Share this topic
Fields
Related Articles

A Neural Thermometer for Predicting Phase Transitions of Unknown Systems
Measurement, instrumentation, and techniques
Statistical physics and thermodynamics
2024911
A novel convolutional neural network predicts phase transition temperatures from spin configurations without prior information about order parameters, paving the way for the discovery of new materials in condensed matter physics.

Discovery of LightInduced Mirror Symmetry Breaking
Dielectric, optical, and other properties in condensed matter
Electronic transport in condensed matter
202492
The authors discovered the lightinduced mirror symmetry breaking, paving the way for controlling mirror symmetries via light and for realizing various phenomena utilizing the mirror symmetry breaking.

Discovery of Unconventional PressureInduced Superconductivity in CrAs
Superconductivity
Electronic transport in condensed matter
2024813
A new study has discovered pressureinduced superconductivity in the helimagnet CrAs, originating in the vicinity of the helimagnetic ordering, representing the first example of superconductivity in Crbased magnetic systems.

Antiferromagnetism Induces Dissipationless Transverse Conductivity
Electronic transport in condensed matter
Magnetic properties in condensed matter
Electronic structure and electrical properties of surfaces and nanostructures
2024724
An investigation using highquality NbMnP crystals demonstrates that the anomalous Hall conductivity arising from antiferromagnetism is dissipationless, as expected from the intrinsic mechanism.

Solving a Stochastic Differential Equation is Solving a MeanField Quantum Spin System
Statistical physics and thermodynamics
Mathematical methods, classical and quantum physics, relativity, gravitation, numerical simulation, computational modeling
Magnetic properties in condensed matter
2024516
The replica method maps matrixvalued geometric Brownian motion to a meanfield quantum spin system. This correspondence makes it possible to obtain an exact solution for matrixvalued geometric Brownian motion.