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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.09236 |
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| _version_ | 1866915693928120320 |
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| author | Tayur, Sridhar |
| author_facet | Tayur, Sridhar |
| contents | 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_β(H) = H + βH \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 $\exp[-itβE \log(E/E_*)]$, 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 $\mathcal{O}(1/|β|)$ when $|β|$ is large.
Since $F_β(H)$ is self-adjoint for every real $β$, the evolution operator $U_β(t) = \exp[-itF_β(H)]$ 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 $|β| \lesssim 10^{-5}$; trapped ions, NV centers, and cold atoms could strengthen this to $|β| \lesssim 10^{-8}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_09236 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spontaneous Decoherence from Logarithmic Spectral Phase Deformations Tayur, Sridhar Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics 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_β(H) = H + βH \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 $\exp[-itβE \log(E/E_*)]$, 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 $\mathcal{O}(1/|β|)$ when $|β|$ is large. Since $F_β(H)$ is self-adjoint for every real $β$, the evolution operator $U_β(t) = \exp[-itF_β(H)]$ 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 $|β| \lesssim 10^{-5}$; trapped ions, NV centers, and cold atoms could strengthen this to $|β| \lesssim 10^{-8}$. |
| title | Spontaneous Decoherence from Logarithmic Spectral Phase Deformations |
| topic | Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2512.09236 |