Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2605.20141

Relativistic saturation of Coulomb-induced electron decoherence: from eikonal phase noise to Bethe--Salpeter kinetic theory

Yury A. Budkov
View original source ↗Read source document ↗Export metadata ↓

Abstract

We develop a microscopic theory of the mutual coherence and small-angle scattering of relativistic electron matter waves propagating through a Coulomb-fluctuating medium. Starting from the Dirac equation, we derive a relativistic paraxial wave equation and then obtain, rather than assume, the Bethe--Salpeter and Wigner--Boltzmann kinetic equations for the disorder-averaged two-point coherence. The Coulomb environment enters through the eikonal phase-coupling factor $A_{\rm rel}=1/(\hbar v)$, which saturates at $1/(\hbar c)$ for ultra-relativistic particles. This saturation is the central physical result: increasing the beam voltage suppresses Coulomb phase noise only up to a finite relativistic floor. We first formulate the eikonal approximation, in which the transmitted electron wave accumulates a random longitudinal phase. For a one-component Coulomb medium the electrostatic potential correlator retains a Coulomb tail, producing a logarithmic phase structure function and an algebraic decay of the transverse mutual coherence. We then go beyond the eikonal construction by deriving the Bethe--Salpeter equation for the Cooperon-like two-point coherence propagator directly from the paraxial wave equation. After a longitudinal Markov projection this equation reduces, after a Wigner transform, to a kinetic equation with a Coulomb small-angle scattering kernel. The coordinate-space solution of the same Bethe--Salpeter equation recovers the eikonal mutual coherence function, while the Wigner form additionally describes angular diffusion and transverse broadening caused by multiple small-angle scattering. The resulting theory separates three effects which are often conflated in charged-particle wave propagation: attenuation of the coherent amplitude, decay of mutual coherence, and conservative redistribution of intensity in transverse phase space.

Explore related subjects

cond-mat.dis-nn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yury A. Budkov. 2026-07-06. Relativistic saturation of Coulomb-induced electron decoherence: from eikonal phase noise to Bethe--Salpeter kinetic theory. https://arxiv.org/abs/2605.20141

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The critical slowing down in training diffusion models

Computational sampling has been central to the sciences since the mid-20th century. While machine-learning-based approaches have recently enabled major advances, their behavior remains poorly understood, with limited theoretical control over when and why they succeed. Here we provide such insight for diffusion models---a class of generative schemes highly effective in practice---by analyzing their application to the $O(n)$ model of statistical field theory in the Gaussian limit $n \to \infty$. In this analytically tractable setting, we show that training a score model with a one-layer network architecture matching the exact solution exhibits a form of critical slowing down in parameter learning. This slowing down also impacts the generation process, indicating that the well-known difficulties of sampling near criticality persist even for learned generative models. To overcome this bottleneck, we consider the power of architectural depth. We find that using a two-layer architecture drastically reduces the critical slowing down, with the training time scaling logarithmically rather than quadratically with system size. Using a Fourier implementation of the architecture, we further show that this acceleration in training time can be achieved without drastically increasing operational complexity. Taken together, these results demonstrate that diffusion models can overcome the critical slowing down through appropriate architectural design, and establish a controlled framework for understanding and improving learned sampling methods in statistical physics and beyond.

cond-mat.dis-nn↗
arXiv2026

Switching diffusivity selects Pareto tail exponent in random growth with redistribution

Random multiplicative growth with redistribution generates stationary Pareto wealth tails in the Bouchaud-Mézard model, but assumes a fixed multiplicative noise intensity. This is restrictive for physical and financial growth processes, where volatility (diffusivity) is often fluctuating. We replace the constant noise intensity by a switching diffusivity and ask how these fluctuations select the Pareto stationary tail. For a geometric Brownian motion with switching diffusivity, the long-time Gaussian limit holds when the redraw law has finite mean and variance. The asymptotic variance retains a contribution from diffusivity persistence. With redistribution and a general redraw law, the stationary large-wealth problem is characterized by a spectral condition for admissible algebraic modes. For a two-state diffusivity, an exact tail analysis gives a Pareto exponent interpolating between the high-diffusivity slow-refresh limit and the mean-diffusivity fast-refresh Bouchaud-Mézard limit.

cond-mat.dis-nn↗
arXiv2026

Signatures of Nonergodicity in Sparse Random Matrices

The prevalence of sparsity in the Fock space graph of interacting many-body systems motivates an investigation into the spectral statistics of sparse random matrices with on-site disorder. We numerically determine the delocalization-localization transition in the ground state as a function of the sparsity. The short-range energy correlation in the bulk indicates that the Anderson transition at infinite temperature occurs at the critical percolation limit of the sparse graph. By analytically deriving the energy moments and calculating the shifted kurtosis, we show that the critical sparsity threshold matches the Anderson transition. Furthermore, long-range energy correlations in the bulk spectrum reveal a Thouless energy scale, suggesting a broad nonergodic regime within the delocalized phase.

cond-mat.dis-nn↗