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Exact Non-Perturbative Description of Quantum Proton Transfer in Open Biomolecular Systems via Lie-Algebraic Observable-Dependent Renormalization

Isamu Ohnishi

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.2139/ssrn.6545738

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Excited state proton transfer is an ubiquitous phenomenon in biology and chemistry, spanning from the ultrafast reactions of photobases and acids to light-driven, enzymatic catalysis and photosynthesis. However, the simulation of such dynamics involves multiple challenges, since high-dimensional, out-of-equilibrium vibronic states play a crucial role, while a fully quantum description of the proton's dissipative, real-space dynamics is also required. In this work, we extend the powerful matrix product state approach to open quantum systems (TEDOPA) to study these demanding dynamics, and also more general nonadiabatic processes that can appear in complex photochemistry subject to strong laser driving. As an illustration, we initially consider an open model of a four-level electronic system interacting with hundreds of intramolecular vibrations that drive ultrafast excited state proton transfer, as well as an explicit photonic environment that allows us to directly monitor the resulting dual fluorescence in this system. We then demonstrate how to include a continuous "reaction coordinate" of the proton transfer that allows numerically exact simulations that can be understood, visualized and interpreted in the familiar language of diabatic and adiabatic dynamics on potential surfaces, while also retaining an exact quantum treatment of dissipation and driving effects that could be used to study diverse problems in ultrafast photochemistry.

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COMPUTATIONAL MODELING OF TEMPORAL DECOHERENCE IN QUANTUM INFORMATION SYSTEMS USING LIE-ALGEBRAIC RENORMALIZATION

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We present a rigorous Lie‑algebraic realization of the temporal interpretation of quantum decoherence recently proposed by Lemeshko et al. (2026). By promoting the temporal drift δτ(t) to an observable‑dependent generator Xtime inside the dynamical Lie algebra g = Lie{ iH, Lk, L†k, Oi } we perform systematic Lie closure to extract the maximal Lie‑observable‑dependent symmetry (Lie‑ODS) subalgebra whose adjoint action leaves the entire Krylov tower of phase‑synchronization observables { Re(ac), Im(ac), a†cac } invariant. Embedding this construction into the hierarchical Lie‑observable‑dependent renormalization (LA‑ODR) flow yields a universal fixed‑point Lindbladian L˜* of remarkably small and constant dimension d* = 4–9, independent of the ultraviolet cutoff. The resulting model exactly reproduces the exponential phase‑damping law ρij(t) = ρij(0) · exp(−Γτ · t) of the original temporal picture, with the decoherence rate γ ≡ Γτ emerging as a universal fixed‑point parameter. Non‑Markovian memory effects and 1/f noise appear naturally as residual temporal correlations between successive RG scales, while complete positivity and trace preservation are rigorously maintained at every coarse‑graining step. When augmented with variational quantum minimal models (VQMM), the framework enables NISQ photonic devices to self‑optimize their own temporal synchronization in real time, achieving Bloch‑vector errors below 3.2 × 10⁻⁴. The surviving Lie‑ODS subalgebra supplies a precise open‑system analogue of Noether’s theorem for temporal symmetries and opens a direct route to topological diagnostics via cyclic multi‑information measures. This work closes the long‑standing interpretive gap between phenomenological temporal pictures and exact effective theories in the thermodynamic limit. It unifies the temporal desynchronization ansatz with the same LA‑ODR machinery previously applied to quantum frequency combs and exciton‑polariton condensation, revealing the remarkable universality of observable‑dependent renormalization. The resulting fixed‑point Lindbladian is computationally trivial yet physically complete, offering powerful new tools for noise analysis, phase stability, and quantum information processing in complex open systems. Future extensions include spatially inhomogeneous drifts, dynamical fermions, and holographic analogues of quantum gravity in open quantum systems.

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Non-perturbative Description of Quantum Systems

И. Д. Феранчук, Alexey Ivanov, Van-Hoang Le +1 more

Lecture notes in physics•Dec 19, 2014•36 citations
Excited state proton transfer is an ubiquitous phenomenon in biology and chemistry, spanning from the ultrafast reactions of photobases and acids to light-driven, enzymatic catalysis and photosynthesis. However, the simulation of such dynamics involves multiple challenges, since high-dimensional, out-of-equilibrium vibronic states play a crucial role, while a fully quantum description of the proton's dissipative, real-space dynamics is also required. In this work, we extend the powerful matrix product state approach to open quantum systems (TEDOPA) to study these demanding dynamics, and also more general nonadiabatic processes that can appear in complex photochemistry subject to strong laser driving. As an illustration, we initially consider an open model of a four-level electronic system interacting with hundreds of intramolecular vibrations that drive ultrafast excited state proton transfer, as well as an explicit photonic environment that allows us to directly monitor the resulting dual fluorescence in this system. We then demonstrate how to include a continuous "reaction coordinate" of the proton transfer that allows numerically exact simulations that can be understood, visualized and interpreted in the familiar language of diabatic and adiabatic dynamics on potential surfaces, while also retaining an exact quantum treatment of dissipation and driving effects that could be used to study diverse problems in ultrafast photochemistry.
We present a rigorous Lie‑algebraic realization of the temporal interpretation of quantum decoherence recently proposed by Lemeshko et al. (2026). By promoting the temporal drift δτ(t) to an observable‑dependent generator Xtime inside the dynamical Lie algebra g = Lie{ iH, Lk, L†k, Oi } we perform systematic Lie closure to extract the maximal Lie‑observable‑dependent symmetry (Lie‑ODS) subalgebra whose adjoint action leaves the entire Krylov tower of phase‑synchronization observables { Re(ac), Im(ac), a†cac } invariant. Embedding this construction into the hierarchical Lie‑observable‑dependent renormalization (LA‑ODR) flow yields a universal fixed‑point Lindbladian L˜* of remarkably small and constant dimension d* = 4–9, independent of the ultraviolet cutoff. The resulting model exactly reproduces the exponential phase‑damping law ρij(t) = ρij(0) · exp(−Γτ · t) of the original temporal picture, with the decoherence rate γ ≡ Γτ emerging as a universal fixed‑point parameter. Non‑Markovian memory effects and 1/f noise appear naturally as residual temporal correlations between successive RG scales, while complete positivity and trace preservation are rigorously maintained at every coarse‑graining step. When augmented with variational quantum minimal models (VQMM), the framework enables NISQ photonic devices to self‑optimize their own temporal synchronization in real time, achieving Bloch‑vector errors below 3.2 × 10⁻⁴. The surviving Lie‑ODS subalgebra supplies a precise open‑system analogue of Noether’s theorem for temporal symmetries and opens a direct route to topological diagnostics via cyclic multi‑information measures. This work closes the long‑standing interpretive gap between phenomenological temporal pictures and exact effective theories in the thermodynamic limit. It unifies the temporal desynchronization ansatz with the same LA‑ODR machinery previously applied to quantum frequency combs and exciton‑polariton condensation, revealing the remarkable universality of observable‑dependent renormalization. The resulting fixed‑point Lindbladian is computationally trivial yet physically complete, offering powerful new tools for noise analysis, phase stability, and quantum information processing in complex open systems. Future extensions include spatially inhomogeneous drifts, dynamical fermions, and holographic analogues of quantum gravity in open quantum systems.