Velocity matrix transport - #332
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Phonon group velocities were obtained by central differences of the SORTED eigenvalues at k +/- h. Wherever branches cross or are degenerate the sorted index swaps character, so the difference quotient connects two different branches. Inside a degenerate multiplet the eigenvectors are an arbitrary basis, so per-mode velocities are not defined there at all; the velocity matrix was additionally symmetrized element-wise over the little group of k, which is a no-op only for the diagonal of a non-degenerate mode and suppresses the velocities of degenerate ones. Both effects are large in supercells, where zone folding manufactures degeneracies, but also affect primitive cells with symmetry-enforced degenerate branches. Test: Si (Stillinger-Weber cubic IFCs), primitive cell (2M)^3 mesh vs a diagonal 2x supercell M^3 mesh, which sample identical absolute q points. Before: 470.435 vs 322.883 W/m/K (tetrahedron), with a symmetry-forbidden kappa_xy = 4.74 in the supercell. After: identical to relative 1e-15 at M = 3..6 with Gaussian smearing, kappa_xy ~ 1e-13. Default formulation (RTA and PRINTVEL): - velocity matrix without element-wise symmetrization, with the nonanalytic contribution and its sublattice-phase connection term (calc_nonanalytic_k_* fold the sublattice phase into D_na, so its finite difference needs + i 2pi (t_j - t_i) D_na to match Allen's displacement-aware convention); NONANALYTIC = 3 uses fc2_without_dipole for the velocity matrix as eval_k_ewald does for the eigenproblem - Peierls weights as degenerate-block traces Tr(P V^a P V^b P), coherent term over cross-block pairs only; boundary speed as the block mean - blocks: subdivide the damping-averaging groups with an anchored 1e-6 cm^-1 numerical tolerance; the worst splitting/linewidth ratio among merged blocks is reported since the band-like limit overestimates their weight by 1 + (dw/Gamma)^2 - band-path PRINTVEL differentiates with the segment direction (kvec_na) used by its eigenproblem Cost: the full velocity matrix (nk ns^2 x 3 complex) is built only when KAPPA_COHERENT = 1. Otherwise each k point is contracted on the fly to a per-branch block diad (nk ns x 9 doubles). Eigenvector projections are O(ns^3) matrix products; MPI gathers are chunked below INT_MAX/2. Result files carry /kappa attribute "formulation" from checkpoint creation on; accumulating mixed formulations in one file is refused at open. ALAMODE_LEGACY_VELOCITY=1 restores the previous behaviour for comparison. Legacy mode preserves the historical formulation within floating-point roundoff; bitwise identity is not guaranteed because the Eigen projection changes summation order, and result-file bytes differ in any case because of the new /kappa "formulation" attribute. Not changed: adaptive smearing (ISMEAR = 2) and the IBTE solver keep finite-difference velocities and remain cell dependent; tetrahedron linewidths remain cell dependent (sorted-branch interpolation). Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Rename damping_groups -> freq_groups and reword the comments in degeneracy_utils.h: the groups being subdivided are frequency-degeneracy groups (the ones the damping is averaged over), and no damping value is consulted when forming transport blocks. Comment and identifier change only. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
…mulation The formulation check refused any restart whose file carried a different transport formulation. That was over-conservative: the stored three-phonon linewidths do not depend on the velocity formulation (boundary and isotope terms are added at run time, adaptive widths use finite differences in both formulations), and a plain restart recomputes every kappa slice from them. Restarting a file written by an older version therefore reuses its gammas and yields the recomputed kappa with the new stamp; the reverse (legacy over a corrected file) likewise recomputes legacy kappa. Mixing is now refused only where an old kappa value would actually survive unrecomputed: a temperature-resolved file holding valid rows for temperatures this run does not cover. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Theory page: group velocity from the velocity matrix (convention, non-analytic connection term, no element-wise symmetrization, legacy finite-difference path), degenerate-multiplet block traces in the Peierls term and their exclusion from the coherent term, the frequency-only block criterion and its reported error measure, the block boundary speed, and the cell-independence remark with the paths that remain cell dependent. Add Simoncelli, Marzari and Mauri, PRX 12, 041011 (2022). Input page: RESTART now documents the formulation stamp and restart compatibility; KAPPA_COHERENT documents the storage cost of the full velocity matrix. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Introduce D-tilde for the dynamical matrix whose phase carries the full interatomic separation, state its unitary relation to D, and write the velocity matrix in terms of D-tilde and its eigenvectors, so that the convention question reduces to which matrix is differentiated. Remove the description of the element-wise symmetrization from the theory page; it is an implementation detail documented in the source. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
…is a convention Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
In the page's normalization the factor reduces to 1/(Gamma_j + Gamma_j'), not 1/[2(Gamma_j + Gamma_j')]; the latter belongs to the code's convention with a compensating prefactor. Make the equality with the Peierls weight c v v tau explicit. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
… for cumulative kappa
The Peierls kappa of anphon is now assembled from the degenerate-block
velocity diad W^{mu nu}_{qj} = sum_{j' in B(j)} V^mu_{jj'} V^nu_{j'j}
(block trace), whereas analyzer.py rebuilt kappa from the stored
finite-difference velocities v^mu v^nu, so its cumulative and
boundary-limited kappa did not reproduce kappa_peierls of the run
(Si 8^3: 435.480 vs 445.110 W/mK).
anphon: write W per irreducible-point copy and branch as
/scattering/3ph/velocity_diad (shape {nequiv,ns,3,3}, or
{nt,nequiv,ns,3,3} in the temperature-resolved layout, unit (m/s)^2)
whenever the velocity-matrix formulation is active; legacy runs leave
the dataset out. A restart over a file from an older version creates it.
analyzer.py: read velocity_diad (and the /kappa formulation stamp) and
use W in place of v^mu v^nu in --calc kappa/cumulative/cumulative2 and
the boundary-scattering models, with sqrt(tr W) as the mode speed for
mean free paths; fall back to the finite-difference velocities on files
that lack the dataset, warning when the file's kappa was nevertheless
stamped with the velocity-matrix formulation.
Checks (Si, 8^3, Gaussian, KAPPA_COHERENT=1): default run writes
velocity_diad (512,6,3,3), analyzer --calc kappa and the large-L limit of
--calc cumulative/cumulative2 give 445.110 = kappa_peierls; legacy run
(ALAMODE_LEGACY_VELOCITY) keeps 435.480 on both sides; default restart
over the legacy file yields 445.110 and adds the dataset; the
temperature-resolved layout writes the (nt,...) slices.
Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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