Universal Description of Decoherence in Scale-Invariant Environments

TL;DR

This paper demonstrates that decoherence in scale-invariant environments is universally characterized by an unparticle bath, with fixed exponents determined solely by the environment's scaling dimension, leading to broad physical implications.

Contribution

It proves that under certain symmetries, decoherence always takes the form of an unparticle bath, unifying diverse physical phenomena through a scale-invariant framework.

Findings

Decoherence exponents are fixed by the scaling dimension d_U.

Validated framework with data from the unitary Fermi gas, finding d_U=7/4.

Predicts a decoherence phase transition at d_U=5/2.

Abstract

When a quantum system couples to a scale-invariant environment, what form must its decoherence take? We prove that the answer is unique: under locality, Lorentz invariance, unitarity, and continuous scale invariance, the effect of any such environment is mathematically equivalent to that of an \emph{unparticle bath} -- a scale-invariant continuum of states -- characterized entirely by the scaling dimension $d_{\mathcal{U}}$ of the coupled operator. This is not a modelling choice but a consequence of conformal symmetry. All decoherence and dissipation exponents are fixed by $d_{\mathcal{U}}$ through exact consistency relations, providing falsifiable predictions independent of microscopic details. We validate the framework using multi-channel transport data from the unitary Fermi gas, where two genuinely independent observables yield a consistent $d_{\mathcal{U}} = 7/4$. We further show that quantum Ising criticality, inflationary cosmology, and high-energy astrophysical neutrinos -- spanning more than 25 orders of magnitude in energy -- are unified as specific realizations of the same structure. A decoherence phase transition at $d_{\mathcal{U}} = 5/2$, where quantum coherence is \emph{protected} rather thandestroyed at long times, is a qualitative prediction inaccessible to any memoryless dynamical description.