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arxiv: 2508.07830 · v2 · submitted 2025-08-11 · 🌀 gr-qc · hep-th· quant-ph

Memory Effects and Entanglement Dynamics of Finite time Acceleration

Nitesh K. Dubey , Sanved Kolekar This is my paper

Pith reviewed 2026-05-18 23:47 UTC · model grok-4.3

classification 🌀 gr-qc hep-thquant-ph
keywords Unruh-DeWitt detectorfinite-time accelerationmemory effectentanglement harvestingFisher informationRindler trajectorycomplete positivityBogoliubov transformations
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The pith

Finite-duration acceleration induces a memory effect in Unruh-DeWitt detectors that is quantified by Fisher information while allowing harvested entanglement to return smoothly to initial values.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper introduces a smooth trajectory in Minkowski spacetime where a detector accelerates uniformly only for a finite interval but remains inertial in the distant past and future. The construction allows direct comparison with the usual eternal Rindler case because the new path reduces to the standard Rindler trajectory in a controlled limit. The central result is that a single detector retains a memory of the finite acceleration interval, and this memory is captured quantitatively by the Fisher information. When two detectors follow combinations of these trajectories, the total correlation and the entanglement they harvest both recover their starting values smoothly once acceleration and deceleration end, whereas the transition rate does not. The memory imprint does not produce a measurable change in negativity or mutual information.

Core claim

We construct a smooth trajectory in Minkowski spacetime that is inertial in the asymptotic past and future but undergoes approximately uniform acceleration for a finite duration. In a suitable limit this trajectory reduces to the standard Rindler trajectory, reproducing the expected Bogoliubov transformations and results consistent with the thermal time hypothesis. Analysis of an Unruh-DeWitt detector on this path shows a memory effect due to the finite duration of acceleration, quantified by the Fisher information. For two detectors along various trajectory combinations, unlike the transition rate, both the total correlation and the entanglement harvested return smoothly to their initial值值值

What carries the argument

The smooth finite-time acceleration trajectory in Minkowski spacetime that approximates the Rindler trajectory for a controlled interval and permits comparison with eternal acceleration results.

If this is right

  • Complete positivity divisibility of the detector evolution depends on frequency, acceleration strength, and acceleration duration.
  • The memory effect appears in the detector response and is independently quantified by Fisher information.
  • Harvested entanglement and total correlations between detector pairs are restored after the finite acceleration ends.
  • Correlation measures exhibit the same behavior in accelerating and decelerating segments.
  • The sign of the flux of acceleration-induced radiation carries physical significance for the energy accounting.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The finite-time construction provides a controlled way to interpolate between inertial and accelerated regimes, which may help isolate transient effects in other quantum-field settings.
  • Absence of memory imprint on negativity while it appears in Fisher information suggests that different correlation quantifiers probe distinct aspects of the finite-duration dynamics.
  • The smooth return of entanglement after deceleration raises the possibility that information carried by field correlations is preserved across the entire inertial-to-accelerated-to-inertial sequence.

Load-bearing premise

The chosen smooth trajectory reduces in the appropriate limit to the standard Rindler trajectory while remaining inertial in the asymptotic past and future.

What would settle it

A calculation in which two Unruh-DeWitt detectors on these finite-acceleration trajectories fail to show harvested entanglement returning to its initial value after the acceleration phase would falsify the smooth-recovery claim.

Figures

Figures reproduced from arXiv: 2508.07830 by Nitesh K. Dubey, Sanved Kolekar.

Figure 1
Figure 1. Figure 1: The red curve represents the variable acceleration trajectory given by Eqs. ( [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The above plots show the Bogoluobov calculation results for the expectation value of number density observed [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The thick lines in the top panels of the plots above represent the transition rate of a UDW detector following [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The first plot of the top panel shows P0 for a UDW detector traveling along eternal Rindler trajectory Eqs. (6)- (7) while all other plots of P0 correspond to finite duration accelerated trajectory given in Eqs (3)-(4). In the second plot of the top panel, we show P1 for which P0 is everywhere positive because if P0 is negative, then no need to check P1. 15 [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The plots above show the Fisher information with respect to time, considered as the parameter [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The above plots show Fisher information considering [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Plots showing the mutual information and negativity obtained by the entanglement harvesting protocol [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Plots showing mutual information and negativity obtained from the entanglement harvesting protocol with [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Plots showing mutual information obtained from the entanglement harvesting protocol discussed in subsection [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The left panel shows the kink trajectory defined in Eq.( [PITH_FULL_IMAGE:figures/full_fig_p025_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The top panels of the above plots display the negativity obtained by two inertial detectors in front of a [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗
read the original abstract

We construct a smooth trajectory in Minkowski spacetime that is inertial in the asymptotic past and future but undergoes approximately uniform acceleration for a finite duration. In a suitable limit, this trajectory reduces to the standard Rindler trajectory, reproducing the expected Bogoliubov transformations and results consistent with the thermal time hypothesis. We analyze the behavior of an Unruh-DeWitt (UDW) detector following such a trajectory and explore the dependence of complete positivity (CP) divisibility on the detector's frequency, acceleration, and the duration of acceleration. Notably, we find that the detector exhibits a memory effect due to the finite duration of acceleration, which is also quantified by the Fisher information. We further examine two UDW detectors along various trajectory combinations and show that, unlike the transition rate, both the total correlation and the entanglement harvested return smoothly to their initial values after the acceleration/deceleration phase. These correlation measures behave similarly in both accelerating and decelerating segments. Interestingly, we do not observe any measurable effect of the memory effect on negativity or mutual information. We also discuss the physical significance of the sign of the flux of acceleration-induced radiation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript constructs a smooth trajectory in Minkowski spacetime that is inertial in the asymptotic past and future but undergoes approximately uniform acceleration for a finite duration. In a suitable limit this reduces to the standard Rindler trajectory, reproducing expected Bogoliubov transformations. The authors analyze a single Unruh-DeWitt detector along this trajectory, reporting a memory effect due to finite acceleration duration that is quantified by the Fisher information, and examining the dependence of complete positivity divisibility on detector frequency, acceleration parameter, and duration. For two detectors they show that, unlike the transition rate, both total correlation and harvested entanglement return smoothly to their initial values after the acceleration/deceleration phase, with similar behavior in accelerating and decelerating segments; they also discuss the physical significance of the sign of the flux of acceleration-induced radiation.

Significance. If the results are robust to the details of the smoothing procedure, the work provides a controlled setting for studying finite-time Unruh effects and non-Markovian detector dynamics. The contrast between the non-recovery of the transition rate and the smooth recovery of entanglement and total correlation is a potentially useful observation, and the use of Fisher information supplies a concrete quantifier of memory. The explicit reduction to the eternal Rindler case and the exploration of multiple trajectory combinations are strengths that allow direct comparison with known results.

major comments (2)
  1. [Trajectory construction] Trajectory construction section: the central claim that the memory effect and the smooth return of correlations/entanglement are generic features of finite-duration acceleration (rather than artifacts of the chosen smoothing) requires explicit checks that the long-time behavior of the Wightman function integrals is independent of the ramp-up/ramp-down profile. Different smoothing functions should be compared, or an argument given that residual correlations from the matching to asymptotic inertial segments vanish in the relevant limits.
  2. [Two-detector analysis] Two-detector analysis: the statement that total correlation and entanglement return smoothly (unlike the transition rate) must be shown to hold for the full range of trajectory combinations examined; the manuscript should clarify whether this recovery persists when the two detectors follow qualitatively different finite-acceleration profiles.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'we do not observe any measurable effect of the memory effect on negativity or mutual information' should be accompanied by quantitative bounds or a statement of the precision with which these quantities were evaluated.
  2. [Notation and equations] Notation: ensure the acceleration parameter a and the finite duration parameter are introduced with consistent symbols and units in all equations and figures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the major points below and will revise the manuscript to incorporate clarifications and additional arguments where appropriate.

read point-by-point responses

  1. Referee: [Trajectory construction] Trajectory construction section: the central claim that the memory effect and the smooth return of correlations/entanglement are generic features of finite-duration acceleration (rather than artifacts of the chosen smoothing) requires explicit checks that the long-time behavior of the Wightman function integrals is independent of the ramp-up/ramp-down profile. Different smoothing functions should be compared, or an argument given that residual correlations from the matching to asymptotic inertial segments vanish in the relevant limits.

    Authors: We agree that strengthening the genericity claim is valuable. In the revised manuscript we will add an analytic argument showing that the long-time asymptotics of the relevant Wightman integrals are controlled by the identical inertial segments at early and late times; the finite-duration acceleration phase contributes only transient terms that decay due to rapid phase oscillations for large time separations. We will also include a short numerical comparison with an alternative smoothing profile (a C^infty bump function) confirming that the Fisher information and the asymptotic values of the correlation measures remain unchanged within numerical precision. revision: yes

  2. Referee: [Two-detector analysis] Two-detector analysis: the statement that total correlation and entanglement return smoothly (unlike the transition rate) must be shown to hold for the full range of trajectory combinations examined; the manuscript should clarify whether this recovery persists when the two detectors follow qualitatively different finite-acceleration profiles.

    Authors: The manuscript already examines several combinations, including symmetric finite-acceleration trajectories, one detector accelerating while the other remains inertial, and trajectories with mismatched durations. The smooth recovery of total correlation and harvested entanglement is observed in all these cases. We will revise the text to state explicitly that the recovery persists for qualitatively different profiles and briefly explain that this follows from the structure of the two-point functions: the correlation measures integrate over the full history in a manner insensitive to the precise ramp details once the detectors return to inertial motion, in contrast to the irreversible excitation captured by the transition rate. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper defines an explicit smooth trajectory that is inertial at early and late times and approximates uniform acceleration over finite duration, with a controlled limit recovering the standard Rindler case and its Bogoliubov coefficients. All subsequent detector observables (transition rates, Fisher information, total correlations, negativity, mutual information) are obtained from direct integration of the Wightman function along this worldline using the standard Unruh-DeWitt coupling. These quantities are not fitted to data within the paper, nor are they renamed versions of the trajectory definition itself; the memory effect and the smooth return of correlations appear as computed outcomes that can be varied by changing the acceleration duration or profile. No load-bearing self-citation or uniqueness theorem from the same authors is invoked to force the results.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard Minkowski quantum field theory and the Unruh-DeWitt detector model without introducing new particles or forces; free parameters are the acceleration magnitude and finite duration, chosen to interpolate between inertial and Rindler regimes.

free parameters (2)
  • finite acceleration duration
    Duration of the approximately uniform acceleration phase is a tunable parameter of the constructed trajectory.
  • acceleration parameter a
    Magnitude of the uniform acceleration during the finite interval.
axioms (2)
  • domain assumption Existence of a smooth trajectory that is asymptotically inertial yet approximates Rindler motion for finite time
    Invoked to reproduce standard Bogoliubov transformations in the appropriate limit.
  • domain assumption Validity of the Unruh-DeWitt detector as a probe of field correlations
    Standard two-level system linearly coupled to a scalar field in Minkowski vacuum.

pith-pipeline@v0.9.0 · 5728 in / 1346 out tokens · 49559 ms · 2026-05-18T23:47:27.705737+00:00 · methodology

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