Nonlinear hydrodynamic response of a quantum Hall system
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912990679269376 |
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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 |