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Main Author: Isobe, Hiroki
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2603.29390
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author Isobe, Hiroki
author_facet Isobe, Hiroki
contents The quantum Hall effect realizes a quantized Hall resistance $R_{xy} = h/(νe^2)$ whereas the longitudinal resistance vanishes. The quantized value consists of the fundamental physical quantities, the elementary charge $e$ and the Planck constant $h$, along with an integer or fractional constant $ν$. High precision measurements of $R_{xy}$ allude to a linear relation between the applied current $I$ and the Hall voltage $V_\mathrm{H}$. Here, we argue that a nonlinear relation between $I$ and $V_\mathrm{H}$ could arise when the electric field is spatially inhomogeneous. We first discuss that the linear $I$-$V_\mathrm{H}$ relation holds with Galilean invariance. Then we consider a hydrodynamic description of a quantum Hall liquid to deal with an axially symmetric electric field. It reveals a nonlinear electronic response arising from the centrifugal force exerted on a curved flow and the density gradient invoked by vorticity.
format Preprint
id arxiv_https___arxiv_org_abs_2603_29390
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Nonlinear hydrodynamic response of a quantum Hall system
Isobe, Hiroki
Mesoscale and Nanoscale Physics
Strongly Correlated Electrons
Fluid Dynamics
Quantum Physics
The quantum Hall effect realizes a quantized Hall resistance $R_{xy} = h/(νe^2)$ whereas the longitudinal resistance vanishes. The quantized value consists of the fundamental physical quantities, the elementary charge $e$ and the Planck constant $h$, along with an integer or fractional constant $ν$. High precision measurements of $R_{xy}$ allude to a linear relation between the applied current $I$ and the Hall voltage $V_\mathrm{H}$. Here, we argue that a nonlinear relation between $I$ and $V_\mathrm{H}$ could arise when the electric field is spatially inhomogeneous. We first discuss that the linear $I$-$V_\mathrm{H}$ relation holds with Galilean invariance. Then we consider a hydrodynamic description of a quantum Hall liquid to deal with an axially symmetric electric field. It reveals a nonlinear electronic response arising from the centrifugal force exerted on a curved flow and the density gradient invoked by vorticity.
title Nonlinear hydrodynamic response of a quantum Hall system
topic Mesoscale and Nanoscale Physics
Strongly Correlated Electrons
Fluid Dynamics
Quantum Physics
url https://arxiv.org/abs/2603.29390