Planckian dissipation: definitions and inference

Scope

A Planckian-scale claim compares a defined relaxation rate with $k_BT/\hbar$. It must identify the observable, residual subtraction and uncertainty. Charge transport, optical response, single-particle decay and quantum scrambling need not share one lifetime. An approximate coefficient near unity is an empirical observation within a model, not a universal theorem obtained from a straight resistivity curve. R1

The evidence has several levels: measured conductivity, an extracted rate, a cross-material scaling relation, and a proposed bound. Moving between them adds assumptions. Bruin's transport comparison, Legros's cuprate analysis, angular magnetoresistance and frequency-resolved film measurements test different parts of this chain. A useful comparison retains each experiment's conditions instead of pooling every quoted coefficient. R2 R3 R4 R6

Mathematical assumptions

Write $\gamma_{\mathrm{tr}}=\gamma_0+\alpha_{\mathrm{inel}}k_BT/\hbar$. Then $\alpha_{\mathrm{tot}}=\hbar\gamma_{\mathrm{tr}}/(k_BT)=\alpha_{\mathrm{inel}}+\hbar\gamma_0/(k_BT)$. A constant residual rate makes the total ratio temperature dependent even when the inelastic slope is fixed. Twenty-seven independent synthetic parameter checks verify this algebra; they do not justify additive scattering in a material. R1

With temperature-independent density and mass in a single-band Drude model, $\rho=m^\ast\gamma_{\mathrm{tr}}/(ne^2)$ gives $\alpha_{\mathrm{inel}}=(\hbar ne^2/k_Bm^\ast)d\rho/dT$. A two-dimensional, spin-degenerate parabolic band instead uses sheet slope $A_1^\square$, areal density $n_{2D}$ and $T_F=\pi\hbar^2n_{2D}/(m^\ast k_B)$, yielding $A_1^\square T_F=\alpha_{\mathrm{inel}}h/(2e^2)$. The geometric conversion and mass estimate are essential inputs, not outputs of a resistivity slope. Noncircular or multiple Fermi surfaces require additional analysis. R3

An independent angular-scattering illustration makes the lifetime distinction explicit. On a circular Fermi line, define an elastic event kernel $W(\theta)=\gamma[1+a\cos\theta]/(2\pi)$ with $|a|\leq1$. The event rate is $\int_0^{2\pi}W\,d\theta=\gamma$, whereas current relaxation weights changes of direction: $\int_0^{2\pi}W(1-\cos\theta)\,d\theta=\gamma(1-a/2)$. Fifteen numerical quadratures verify both integrals. Forward-weighted events therefore relax current less efficiently in this specified model. The event rate is explicitly defined; it is not silently identified with a spectral half-width. This elastic Boltzmann example proves neither a quantum bound nor a superconducting mechanism. R1

For a fitted Drude denominator $\Gamma-i\nu$, both variables use cycles per second. The corresponding decay rate is $\gamma=2\pi\Gamma$, so $\Gamma=\alpha k_BT/h$ and $\gamma=\alpha k_BT/\hbar$ have the same dimensionless coefficient after conversion. Mixing the conventions without converting the fitted width changes the apparent coefficient by $2\pi$. Parallel channels add conductivities, further limiting inference from total resistance. R4

Experimental criteria

Bruin and colleagues report linear resistivity in Sr3Ru2O7 at 7.9 T and use independently characterized Fermi-surface inputs to estimate scattering. The retrieved opening page describes a 1.5–400 K transport study and a field-induced nematic region below 1.2 K near that field. Those boundaries matter: the available page does not justify extending the measured law through the intervening phase or verify every cross-material fit. The remaining article pages and supplementary tables are outside this check. R2

Legros's author manuscript compares sheet-resistance slopes with Fermi-temperature estimates. Its electron-doped comparison gives $\alpha=1.0\pm0.3$; the hole-doped estimates require more approximate geometry and specific-heat masses, with temperature-dependent mass an explicit complication in Nd-LSCO. The displayed $\alpha=1$ prediction is a tested assumption, not an independent lifetime measurement. This article uses selected author-version passages; a complete comparison with the final publication remains open. R3

Grissonnanche's final Nd-LSCO analysis separates an isotropic temperature-dependent component from anisotropic elastic scattering and reports $\alpha=1.2\pm0.4$. The band-energy scale is constrained by specific heat, and the quoted uncertainty includes fitting and sample-geometry contributions. Measurements at 45 T include superconducting angular sectors at the lower temperatures; those sectors are excluded. Neither a large applied field nor the isotropic inelastic term makes every datum normal-state or the total scattering isotropic. R6

Romero's author manuscript fits two FeTe1−xSex films over 20–40 K using a narrow Drude contribution plus a broad background. It reports cycle-frequency coefficients 3.02 for $x=0.45$ and 2.42 for $x=0.35$, with widths below 0.2 THz unresolved in its spectral window. These are author-version fit values, not newly reproduced final-paper estimates. The published abstract confirms a parallel-channel interpretation; complete version comparison and fitting covariance remain open. A linear narrow-channel width can coexist with nonlinear total resistivity. R4

Limits and disputes

The conditional chaos result $\lambda_L\leq2\pi k_BT/\hbar$ bounds exponential growth of a suitable regularized out-of-time-order correlator. Its argument requires thermal-strip analyticity and boundedness, controlled factorization errors and separated dissipation and scrambling scales. This is not a measured charge-transport rate; identifying the exponent with one requires another, model-specific argument. The theorem alone neither fixes a transport coefficient to one nor verifies a material's inferred mass. R5 R1

Complete scientific acceptance remains open. Selected primary passages, figures and independent model checks do not constitute raw-data reproduction. Distinguish published results from the author's interpretation of universality; preserve unresolved frequency coverage, final-version and calibration limits. Spectral weight entering a condensate also does not identify the pairing mediator. R2 R3 R4

Discovery implications

Compare rates only after aligning channel definitions, sample conditions and frequency units. Test whether alternative band weights or a temperature-dependent mass can explain the same measured curve. Then seek independent optical or angle-dependent constraints. A connection between normal-state relaxation and superconductivity is a research hypothesis to test; faster scattering does not, by itself, predict a higher transition temperature. R3 R4 R6

Related topics

Strange metals, Linear-T resistivity, and Iron-based superconductors.

Material cases

Values describe individual reports, not a ranking. Unknown means the checked source did not supply the field at this review scope.