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Bibliographic Details
Main Author: Singh, Navinder
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2509.07590
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author Singh, Navinder
author_facet Singh, Navinder
contents We present a calculation of the imaginary part of the polarizability of a Wigner crystal using the Fluctuation-Dissipation theorem. The oscillations of the localized electrons about their equilibrium positions are treated in the harmonic approximation and the electric dipole-moment -- dipole-moment correlator is computed by a normal mode expansion. The amplitudes and phases of the different normal modes are assumed to be statistically independent. In the first case, polarizability is computed in the high temperature limit, $k_B T>>\hbar Ω_W$ (here, $Ω_W$ is the Wigner frequency, analogous to the Debye frequency of the phonon case). In the second case, a general expression (valid both at high and low temperature limits) is obtained using a phenomenological damping model. The connection between our general expression and that of the Lorentz oscillator model is discussed. It turns out that the Wigner crystal would be transparent for applied frequencies greater than the Wigner frequency. A standard ellipsometry set-up can test the predictions of the theory.
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institution arXiv
publishDate 2025
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spellingShingle Polarizability of a Wigner crystal
Singh, Navinder
Strongly Correlated Electrons
Mesoscale and Nanoscale Physics
We present a calculation of the imaginary part of the polarizability of a Wigner crystal using the Fluctuation-Dissipation theorem. The oscillations of the localized electrons about their equilibrium positions are treated in the harmonic approximation and the electric dipole-moment -- dipole-moment correlator is computed by a normal mode expansion. The amplitudes and phases of the different normal modes are assumed to be statistically independent. In the first case, polarizability is computed in the high temperature limit, $k_B T>>\hbar Ω_W$ (here, $Ω_W$ is the Wigner frequency, analogous to the Debye frequency of the phonon case). In the second case, a general expression (valid both at high and low temperature limits) is obtained using a phenomenological damping model. The connection between our general expression and that of the Lorentz oscillator model is discussed. It turns out that the Wigner crystal would be transparent for applied frequencies greater than the Wigner frequency. A standard ellipsometry set-up can test the predictions of the theory.
title Polarizability of a Wigner crystal
topic Strongly Correlated Electrons
Mesoscale and Nanoscale Physics
url https://arxiv.org/abs/2509.07590