Related papers: Spontaneous Decoherence from Imaginary-Order Spectral Deformations

Spontaneous Decoherence from Imaginary-Order Spectral Deformations

URL: http://arxiv.org/abs/2512.09236v3
Date: Tue, 16 Dec 2025 12:35:33 GMT
Title: Spontaneous Decoherence from Imaginary-Order Spectral Deformations
Authors: Sridhar Tayur,
Abstract summary: A mechanism of spontaneous decoherence is examined in which the generator of quantum dynamics is replaced by the imaginary-order.<n>The deformation modifies dynamical phases through the factor $Ei=eilog E$, whose rapid oscillation suppresses interference between distinct energies.<n>A detailed related-work analysis contrasts the present mechanism with Milburn-type intrinsic decoherence, Disi-Penrose gravitational collapse, GRW/CSL models, clock-induced decoherence, and energy-conserving collapse models.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: A mechanism of spontaneous decoherence is examined in which the generator of quantum dynamics is replaced by the imaginary-order (which is fundamentally different from real-order fractional calculus) spectral deformation $H^{1+iβ}$ for a positive self-adjoint Hamiltonian $H$. The deformation modifies dynamical phases through the factor $E^{iβ}=e^{iβ\log E}$, whose rapid oscillation suppresses interference between distinct energies. A non-stationary-phase analysis yields quantitative estimates: oscillatory contributions to amplitudes or decoherence functionals decay at least as $\mathcal{O}(1/|β|)$. The kinematical structure of quantum mechanics -- the Hilbert-space inner product, projection operators, and the Born rule -- remains unchanged; the modification is entirely dynamical and acts only through spectral phases. Physical motivations for the deformation arise from clock imperfections, renormalization-group and effective-action corrections that introduce logarithmic spectral terms, and semiclassical gravity analyses in which complex actions produce spectral factors of the form $E^{iβ}$. The mechanism is illustrated in examples relevant to quantum-gravity-inspired quantum mechanics. A detailed related-work analysis contrasts the present mechanism with Milburn-type intrinsic decoherence, Diósi-Penrose gravitational collapse, GRW/CSL models, clock-induced decoherence, and energy-conserving collapse models, as well as environmental frameworks such as Lindblad master equations, Caldeira-Leggett baths, and non-Hermitian Hamiltonian deformations. This positions $H^{1+iβ}$ dynamics as a compact, testable, and genuinely novel phenomenological encapsulation of logarithmic spectral corrections arising in quantum-gravity-motivated effective theories, while remaining fully compatible with standard quantum kinematics.

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