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Decoherence, Perturbations and Symmetry in Lindblad Dynamics

A. Y. Klimenko

TL;DR

This work extends the perturbative Dyson framework and discrete-symmetry constraints from unitary quantum dynamics to a dephasing Lindblad description, incorporating stochastic realism with dual temporal conditioning. By deriving and applying a dephasing master equation, it connects decoherence to diffractive processes in $pp$ and $p\bar{p}$ collisions, and demonstrates that a CPT-invariant decoherence model with a universal factor $\varepsilon \approx 0.89$ substantially improves SD and DD cross-section descriptions across multiple experiments. The approach yields testable CPT- and CP-symmetric predictions for diffractive channels and provides a quantitative framework to extract and interpret decoherence effects from high-energy scattering data. The findings have potential implications for understanding the thermodynamic arrow of time in open quantum systems and for constraining non-unitary contributions in strong-interaction phenomena.

Abstract

We extend a perturbative Dyson-type treatment and discrete-symmetry constraints from the Schrödinger and von Neumann equations to a dephasing Lindblad framework. This work develops further the odd-symmetric formulation -- based on stochastic realism and dual temporal boundary conditions -- from general dynamical considerations to specific tools of quantum mechanics. Applying the resulting scaling relations to published single- and double-diffractive data in $pp$ and $p\bar{p}$ collisions (ISR, UA4, UA5, CDF, D0, ALICE, and E710), we show that single-diffraction cross sections are well described by a three-parameter fit with a relative RMS deviation of $\sim 4\%$, substantially improving upon conventional approximations that neglect decoherence. The extracted decoherence factor is consistently $φ\approx 0.89$, in agreement across SD, DD, and E710-based (direct) estimates, and is naturally interpreted as $φ=1$ for CP-invariant dephasing but $φ<1$ for CPT-invariant dephasing, favouring the latter.

Decoherence, Perturbations and Symmetry in Lindblad Dynamics

TL;DR

This work extends the perturbative Dyson framework and discrete-symmetry constraints from unitary quantum dynamics to a dephasing Lindblad description, incorporating stochastic realism with dual temporal conditioning. By deriving and applying a dephasing master equation, it connects decoherence to diffractive processes in and collisions, and demonstrates that a CPT-invariant decoherence model with a universal factor substantially improves SD and DD cross-section descriptions across multiple experiments. The approach yields testable CPT- and CP-symmetric predictions for diffractive channels and provides a quantitative framework to extract and interpret decoherence effects from high-energy scattering data. The findings have potential implications for understanding the thermodynamic arrow of time in open quantum systems and for constraining non-unitary contributions in strong-interaction phenomena.

Abstract

We extend a perturbative Dyson-type treatment and discrete-symmetry constraints from the Schrödinger and von Neumann equations to a dephasing Lindblad framework. This work develops further the odd-symmetric formulation -- based on stochastic realism and dual temporal boundary conditions -- from general dynamical considerations to specific tools of quantum mechanics. Applying the resulting scaling relations to published single- and double-diffractive data in and collisions (ISR, UA4, UA5, CDF, D0, ALICE, and E710), we show that single-diffraction cross sections are well described by a three-parameter fit with a relative RMS deviation of , substantially improving upon conventional approximations that neglect decoherence. The extracted decoherence factor is consistently , in agreement across SD, DD, and E710-based (direct) estimates, and is naturally interpreted as for CP-invariant dephasing but for CPT-invariant dephasing, favouring the latter.
Paper Structure (19 sections, 1 theorem, 101 equations, 3 figures)

This paper contains 19 sections, 1 theorem, 101 equations, 3 figures.

Table of Contents

  1. Modelling of decoherence and stochastic realism
  2. The dephasing Lindblad equation
  3. Note on bath dephasing
  4. A minimal model for diffractive dissociation: Lindblad--Dyson formulation
  5. Symmetries and the arrow of time in reduced quantum dynamics
  6. Diffractive dissociations and decoherence
  7. Interaction diagram and interference with decoherence
  8. Effect on diffractive dissociation reactions
  9. Experimental cross-sections for SD collisions
  10. Compiled data and experimental notes
  11. Approximating SD cross sections
  12. Experimental cross sections for DD collisions
  13. Discussion
  14. Conclusion
  15. The dephasing Lindblad equation preserving energy
  16. ...and 4 more sections

Key Result

Proposition A.1

In the dephasing Lindblad equation (L1) with Hermitian $H$ and $L_{j}$ and ${ \if@compatibility \mathchar"010D {} \mathchar"010D } _{j}>0$, conservation of the energy expectation holds for any density matrix ${ \if@compatibility \mathchar"011A {} \mathchar"011A }$ if and only if $[H,L_{j

Figures (3)

  • Figure 1: Interaction diagrams for proton (antiproton) single diffraction (SD, left) and double diffraction (DD, right) via Pomeron $\mathbb{P}$ exchange, often sketched as two-gluon colour-singlet. The central inset sketches the QCD-motivated ladder picture of the Pomeron, and its split at the triple-$\mathbb{P}$ vertex.
  • Figure 2: SD cross-section $2{ \if@compatibility \mathchar"011B {} \mathchar"011B } _{\mathrm{SD}}$ vs $\sqrt{(s)}$. Experimental data are from ISR, UA4, UA5, CDF, E710, D0 and ALICE collaborations. Approximations: -- -- -- SDF1 (colour) or SDC1 (black), $\cdot$$\cdot$$\cdot$$\cdot$$\cdot$$\cdot \ $ SDF2 (colour) or SDC4 (black), $\cdot$ -- $\cdot$ -- $\cdot$ -- SDCln.
  • Figure 3: DD cross-section ${ \if@compatibility \mathchar"011B {} \mathchar"011B } _{\mathrm{DD}}$ vs $\sqrt{(s)}$. Experimental data are from UA5, CDF and ALICE collaborations. Approximations: -- -- -- DDF1 (colour) or DDC1 (black), $\cdot$$\cdot$$\cdot$$\cdot$$\cdot$$\cdot \ $ DDF2

Theorems & Definitions (1)

  • Proposition A.1