Edwards Localization

arXiv:2511.11771v2 Announce Type: replace-cross Abstract: We study the localization problem in quantum stochastic mechanics. We start from the Edwards model for a particle in a bath of scattering centers and prove static localization of the ground state wavefunction of the particle in a one dimensional square well coupled to Dirac delta like scattering centers in arbitrary but fixed positions. We see how the localization increases for increasing coupling $g$ and increasing number of scattering centers at constant density. Then we choose the scattering centers positions as pseudo random numbers with a uniform probability distribution and observe an increase in the localization of the average of the ground state over the many positions realizations. We discuss how this averaging procedure is consistent with a picture of a particle in a Bose-Einstein condensate of of non interacting boson scattering centers interacting with the particle with Dirac delta functions pair potential. We then study the dynamics of the ground state wave function. We conclude with a discussion of the affine quantization version of the Lax model which reduces to a system of contiguous square wells with walls in arbitrary positions independently of the coupling constant $g$.

Abstract:We study the localization problem in quantum stochastic mechanics. We start from the Edwards model for a particle in a bath of scattering centers and prove static localization of the ground state wavefunction of the particle in a one dimensional square well coupled to Dirac delta like scattering centers in arbitrary but fixed positions. We see how the localization increases for increasing coupling $g$ and increasing number of scattering centers at constant density. Then we choose the scattering centers positions as pseudo random numbers with a uniform probability distribution and observe an increase in the localization of the average of the ground state over the many positions realizations. We discuss how this averaging procedure is consistent with a picture of a particle in a Bose-Einstein condensate of of non interacting boson scattering centers interacting with the particle with Dirac delta functions pair potential. We then study the dynamics of the ground state wave function. We conclude with a discussion of the affine quantization version of the Lax model which reduces to a system of contiguous square wells with walls in arbitrary positions independently of the coupling constant $g$.

Materials Science (cond-mat.mtrl-sci); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Computational Physics (physics.comp-ph); Quantum Physics (quant-ph)

arXiv:2511.11771 [cond-mat.mtrl-sci]

(or arXiv:2511.11771v2 [cond-mat.mtrl-sci] for this version)

Eur. Phys. J. B 99, 89 (2026)

https://doi.org/10.1140/epjb/s10051-026-01195-2 DOI(s) linking to related resources

From: Riccardo Fantoni Dr. [view email] [v1] Fri, 14 Nov 2025 09:34:42 UTC (90 KB) [v2] Sun, 19 Jul 2026 12:46:30 UTC (52 KB)

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Edwards Localization

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