Spontaneous Decoherence from Logarithmic Spectral Phase Deformations

TL;DR

This paper introduces a mechanism of spontaneous decoherence caused by logarithmic spectral phase deformations of the Hamiltonian, which suppresses interference without losing quantum coherence, motivated by clock imperfections and quantum gravity considerations.

Contribution

It proposes a novel spectral deformation of the Hamiltonian leading to decoherence through phase suppression, maintaining unitarity and the core structure of quantum mechanics.

Findings

Oscillatory contributions decay as 1/|β| for large |β|.

Decoherence occurs without norm loss or collapse, via interference suppression.

Experimental constraints suggest |β| is less than about 10^{-5}.

Abstract

We examine a mechanism of spontaneous decoherence in which the generator of quantum dynamics is deformed to a logarithmically modified self-adjoint operator \begin{equation*} F_\beta(H) = H + \beta H \log \frac{H}{E_*} \end{equation*} for a positive self-adjoint Hamiltonian $H$ and a fixed reference scale $E_* > 0$. Dynamical phases acquire energy-dependent factors $\exp[-it\beta E \log(E/E_*)]$, whose rapid variation across the spectrum suppresses interference between distinct energies through a non-stationary-phase mechanism. Stationary-phase analysis shows that oscillatory contributions to amplitudes decay at least as $\mathcal{O}(1/|\beta|)$ when $|\beta|$ is large. Since $F_\beta(H)$ is self-adjoint for every real $\beta$, the evolution operator $U_\beta(t) = \exp[-itF_\beta(H)]$ is unitary. The kinematical structure of quantum mechanics -- Hilbert-space inner products, projection operators, the Born rule -- remains unchanged. Decoherence arises as suppression of interference terms in coarse-grained observables and decoherence functionals, not as norm loss or stochastic collapse. Physical motivation for logarithmic spectral deformations comes from clock imperfections, renormalization-group and effective-action corrections introducing $\log E$ terms, and semiclassical gravity analyses with complex actions generating spectral factors involving $\log(E/E_{\text{P}})$. The mechanism is illustrated with two-level systems, quartic oscillators, FRW minisuperspace models, and Schwarzschild-interior-type Hamiltonians. Current superconducting-qubit coherence times constrain $|\beta| \lesssim 10^{-5}$; trapped ions, NV centers, and cold atoms could strengthen this to $|\beta| \lesssim 10^{-8}$.