arXiv:2603.09115 · Physics Letters A

Emergence of Classical Dynamics from a Random Matrix Schrödinger Model

Alexey A. Kryukov

quant-phSubmitted Mar 10, 2026• Announced Mar 11, 2026• 0 citations• Revised Jun 17, 2026 (v2)

Abstract

The Newtonian motion of a macroscopic particle is derived from the linear Schrödinger equation with a Hamiltonian consisting of the free-particle term and a random Hamiltonian drawn from the Gaussian Unitary Ensemble. The random term models interaction with the environment. We show that the parameters governing the resulting state-space random walk, together with the treatment of experimentally indistinguishable states as equivalence classes, explain the contrasting behavior of microscopic and macroscopic systems. The analysis extends previous work deriving the Born rule for microscopic particles when the free-particle term is negligible.

Journal reference: Physics Letters A, Volume 589, 2026, 131791
DOI: 10.1016/j.physleta.2026.131791

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