https://doi.org/10.1140/epjb/s10051-026-01195-2
Research – Statistical and Nonlinear Physics
Edwards localization
Dipartimento di Fisica, Università di Trieste, strada Costiera 11, Grignano, 34151, Trieste, Italy
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Received:
9
December
2025
Accepted:
28
May
2026
Published online:
1
July
2026
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 position 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.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjb/s10051-026-01195-2.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
