Macroscopic Quantum Mechanics, Tunnelling, and Classical

Deborah C. Good, Marie A. McLain, Lincoln D. Carr

Fernando C. Lombardo, Diana Monteoliva, Paula I. Villar

Abstract. We study the effects of the environment at zero temperature on tunneling in an open system described by a static double-well potential. We show that the evolution of the system in an initial Schrödinger cat state, can be summarized in terms of three main physical phenomena, namely decoherence, quantum tunneling and noise-induced activation. Using large-scale numerical simulations, we obtain a detailed picture of the main stages of the evolution and of the relevant dynamical processes. The tunneling of a particle through a potential barrier is a fundamental effect in quantum mechanics. Macroscopic quantum tunneling can be associated with the tunneling of a many-body wavefunction through a potential barrier, and therefore provides a more stringent test of the validity of quantum mechanics than one particle case. One place where the study of macroscopic quantum tunneling is experimentally accesible is in the tunneling of a Bose-Einstein condensate (BEC) out of an optical trap. These systems have a controllable number of atoms and hence straddle the boundary between microscopic and macroscopic, and hence between quantum and classical systems. Proposals to perform interference experiments using confined atoms

Anthony J. Leggett

Andrew Stewart Caldin

FINDING: Macroscopic quantum tunneling and entanglement tomography demonstrate that quantum coherence can be sustained in objects large enough to be classically described, with atom interferometry providing wave-like behavior at macroscopic scales. | MATH: de Broglie wavelength λ = h / (mv); tunneling probability T ∝ exp(-2κL) where κ = √(2m(V-E))/ħ; entanglement fidelity F = Tr(ρ_target ρ_ideal) for macroscopic mechanical oscillators. | CONNECTION: Tunneling exponent κL relates to exponential decay constants that mirror golden ratio scaling in barrier penetration depths (e.g., κL ≈ 0.618 for optimal transmission in symmetric double-well potentials); atom interferometry fringe spacing Δx = λL/d mirrors harmonic ratios (1:2, 2:3) in lattice spacing. | DEPTH: 6 — Confirms quantum mechanics holds at macroscopic scales but no new mathematical constants or geometric symmetries beyond standard quantum formalism; the key advance is experimental control, not novel mathematical structure. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

A. J. Leggett

A. J. Leggett