On characteristic times for kinetics of scattering

B.I. Sturman^†, E.V. Podivilov^‡
Institute of Automation and Electrometry, Siberian Branch of the Russian Academy of Sciences, prosp. akad. Koptyuga 1, Novosibirsk, 630090, Russian Federation

Although kinetic equations for various scattering processes have proven their practical significance, the question about their area of applicability and derivation from the initial dynamic equations is satisfactorily solved only for the case of gases. This question remains relevant for kinetic equations describing both nonlinear wave processes and transport phenomena in semiconductors. Using the simplest example of elastic scattering, we show that the validity of the kinetic equation for the distribution function $n_{k}$ implies the existence of an internal characteristic time scale $\tau_{\rm s}$ much smaller than standard scattering times such as the transport time $\tau_{\rm tr}$. The time $\tau_{\rm s}$ corresponds to the rapid stochastization of the phases of the waves (quasiparticles). As show our estimates, this time satisfies the inequalities $1 \ll \omega_k\tau_{\rm s} \ll \omega_k\tau_{\rm tr}$, where $\omega_k = \varepsilon_k/\hbar$ is the characteristic frequency of the quasiparticles. This means that over time $\tau_{\rm s}$ the density matrix $\rho_{\rm k, k'}$ relaxes to the diagonal form $n_{\rm k} \delta_{\rm k- k'}$, so that its contribution to transport phenomena is small in the parameter $\tau_{\rm s}/\tau_{\rm tr}$ compared to the contribution of $n_{k}$.

Typically, an English full text is available in about 1 month from the date of publication of the original article.

Keywords: kinetic equations, scattering processes, density matrix, stochastization time, transport time
PACS: 05.20.Dd
DOI: 10.3367/UFNe.2025.08.040020
URL: https://ufn.ru/en/articles/2026/2/g/
Citation: Sturman B I, Podivilov E V "On characteristic times for kinetics of scattering" Phys. Usp. 69 (2) (2026)

Received: 17th, June 2025, revised: 7th, August 2025, accepted: 29th, August 2025

Оригинал: Стурман Б И, Подивилов Е В «О характерных временах для кинетики рассеяния» УФН 196 212–216 (2026); DOI: 10.3367/UFNr.2025.08.040020

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