Fibonacci Lattice Condensates as FCCL Simulators: Born Rule Measurement and Golden-Ratio Revivals in Bose-Einstein Condensates
Year: 2026
Type: preprint
Abstract: We show that a Bose-Einstein condensate (BEC) loaded into a Fibonacci-modulated optical lattice constitutes a direct experimental implementation of the Fibonacci Cascade Conformal Layer (FCCL). The FCCL Born rule ๐(๐) = ๐^{โ2๐}/โ5 manifests as the timeof-flight momentum distribution after ballistic expansion: peaks at momenta ๐_๐ = ๐๐โ carry amplitudes decaying as ๐โ๐/5^{1/4}, with consecutive peak ratios exactly equal to ๐. Three additional predictions follow from the FCCL cascade structure: (i) quantum revival times spaced by the golden ratio, ๐ก_๐ = ๐กโ๐^๐; (ii) critical temperatures for successive subbands scaling as ๐_๐(๐)/๐_๐(0) = ๐^{โ๐/3}, with ๐_๐(3)/๐_๐(0) = 1/๐ exactly; (iii) a spectral bandwidth exactly equal to 2๐ฝโ (independent of the ratio ๐ฝโ/๐ฝโ), from the Fibonacci identity ๐ โ1 + ๐โ2 = 1. These predictions are accessible with current cold-atom technology and constitute the first direct laboratory test of the FCCL Born rule that does not require a particle collider.
Author: Leroy, Rรฉmi
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7211871345
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