2017/04/04 by Keun-Young Kim, Chao Niu, Kim, Keun-Young +1 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Dark Matter and Cosmic Phenomena #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.str-el #hep-th
paper · pdf · doi:10.48550/arxiv.1704.00947
24 pages, 6 figures, v2 minor edits and references added
openalex publication_date 2017/04/04 · arxiv created 2017/04/23 · arxiv updated 2017/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study diffusion and butterfly velocity (vB) in two holographic models, linear axion and axion-dilaton model, with a momentum relaxation parameter (β) at finite density or chemical potential (μ). Axion-dilaton model is particularly interesting since it shows linear-T-resistivity, which may have something to do with the universal bound of diffusion. At finite density, there are two diffusion constants D_± describing the coupled diffusion of charge and energy. By computing D_± exactly, we find that in the incoherent regime (β/T ≫ 1, β/μ≫ 1) D+ is identified with the charge diffusion constant (Dc) and D- is identified with the energy diffusion constant (De). In the coherent regime, at very small density, D_± are `maximally' mixed in the sense that D+(D-) is identified with De(Dc), which is opposite to the case in the incoherent regime. In the incoherent regime De ∼ C- ℏ vB2 / kB T where C- = 1/2 or 1 so it is universal independently of β and μ. However, Dc ∼ C+ ℏ vB2 / kB T where C+ = 1 or β2/16π2 T2 so, in general, C+ may not saturate to the lower bound in the incoherent regime, which suggests that the characteristic velocity for charge diffusion may not be the butterfly velocity. We find that the finite density does not affect the diffusion property at zero density in the incoherent regime.