Paper
Spontaneous Decoherence from Imaginary-Order Spectral Deformations
Authors
Sridhar Tayur
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 for a positive self-adjoint Hamiltonian . The deformation modifies dynamical phases through the factor , 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 . 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 . 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 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.