Low-temperature transport in metals with strong dipole fluctuations
Determine how electron–electron interactions with energy scales U much smaller than ħω_g, together with significant dipole fluctuations characterized by the geometric length ℓ_g, modify electron dynamics near the Fermi surface; quantify these effects in transport and quantum oscillations, derive the mechanism of spectral-weight transfer to zero frequency, and identify how quantum geometry accelerates charge carriers.
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That said, many fundamental questions remain open, and the full implications of quantum geometry in solid state physics are in its infancy. A key open challenge is understanding how interactions combined with significant dipole fluctuations affect the dynamics of electrons around the Fermi surface in metals. Can these effects be quantified through electronic transport at the Fermi surface, such as in its quantum oscillations? How can interactions with energies substantially smaller than the geometric energy U \ll \hbar\omega_g lead to the transfer of spectral weight to zero frequencies, enhancing charge transport, both in metals and correlated condensates? What is the mechanism by which geometry "speeds up" charge carriers in quantum matter?