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arxiv: 2603.23137 · v3 · submitted 2026-03-24 · ❄️ cond-mat.mtrl-sci · cond-mat.other

Open Quantum System Theory of Muon Spin Relaxation in Materials

Elvis F. Arguelles , Osamu Sugino This is my paper

Pith reviewed 2026-05-15 00:55 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.other
keywords muon spin relaxationnon-Markovian dynamicsopen quantum systemsmuSR spectroscopyLi0.73CoO2Kubo-Toyabe relaxationSchwinger-Keldysh formalismmemory kernel
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The pith

A non-Markovian open quantum system theory derives a stochastic muon spin equation with a phenomenological memory kernel, enabling global fits to ZF and weak LF μSR spectra beyond the strong-collision limit.

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

The paper formulates muon spin relaxation as an open quantum system where the implanted muon couples to a temporally correlated local magnetic environment. Using a Schwinger-Keldysh influence functional, it produces an equation of motion whose fluctuation kernel is set by the local-field correlation tensor and whose retarded torque is supplied by a fitted backaction kernel. In suitable limits the description recovers standard Kubo-Toyabe relaxation. When applied to Li0.73CoO2 the model decomposes the observed relaxation into a quenched static width and a lithium-driven dynamical component whose fluctuation rates track activated behavior across an intermediate temperature window.

Core claim

The central claim is that a Schwinger-Keldysh-derived stochastic equation for the muon spin, with fluctuation kernel fixed by the local-field correlation tensor and retarded memory supplied by an effective phenomenological backaction kernel, reduces to Kubo-Toyabe descriptions in the appropriate limits and permits quantitative, global analysis of zero-field and weak longitudinal-field μSR spectra, supporting a decomposition of the relaxation in Li0.73CoO2 into quenched and Li-driven dynamical parts whose rates are consistent with activated behavior.

What carries the argument

Schwinger-Keldysh influence-functional formulation that yields a stochastic equation of motion for the muon spin, with the fluctuation kernel fixed by the local-field correlation tensor and the retarded memory torque supplied by a phenomenological backaction kernel.

If this is right

  • Quantitative global fitting of ZF and weak LF μSR spectra becomes possible without invoking the strong-collision approximation.
  • The relaxation in Li0.73CoO2 separates cleanly into a temperature-independent quenched width and a Li-driven dynamical component.
  • The extracted fluctuation rates follow activated temperature dependence over the intermediate-temperature window.
  • The memory parameter produces observable effects precisely in the crossover regime between quasi-static and fast-fluctuation limits.

Where Pith is reading between the lines

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

  • The same stochastic-equation structure could be applied to other muon-implanted compounds whose local-field correlations are known from independent measurements.
  • Future work could replace the phenomenological backaction kernel with an explicit microscopic expression derived from the host lattice's spin dynamics.
  • The framework naturally extends to time-dependent external fields or to higher-order correlation functions beyond the two-time tensor used here.

Load-bearing premise

The functional form and temperature dependence of the effective phenomenological backaction kernel are chosen to fit the spectra rather than derived from the microscopic dynamics of the material.

What would settle it

A first-principles microscopic calculation of the retarded backaction kernel for Li0.73CoO2 that produces a temperature dependence incompatible with the fitted memory parameter would falsify the phenomenological choice.

Figures

Figures reproduced from arXiv: 2603.23137 by Elvis F. Arguelles, Osamu Sugino.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic representation of the muon spin relaxation as an open quantum system. By [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Muon polarization [PITH_FULL_IMAGE:figures/full_fig_p024_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Effect of the backaction (retarded-torque) strength Λ (in units of [PITH_FULL_IMAGE:figures/full_fig_p028_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Sensitivity of the spin-SDE polarization to the retarded-torque strength Λ (in units of [PITH_FULL_IMAGE:figures/full_fig_p030_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Spin SDE description of [PITH_FULL_IMAGE:figures/full_fig_p032_5.png] view at source ↗
read the original abstract

We present a non-Markovian theory of muon spin relaxation that treats the implanted muon as an open quantum spin coupled to a temporally correlated local magnetic environment. Using a Schwinger-Keldysh influence-functional formulation, we derive a stochastic equation of motion for the muon spin, in which the fluctuation kernel is fixed by the local-field correlation tensor, while the retarded memory torque is introduced through an effective phenomenological backaction kernel. In the appropriate limits, the theory reduces to standard Kubo-Toyabe descriptions. This enables quantitative, global analysis of zero-field (ZF) and weak longitudinal-field (LF) $\mu$SR spectra beyond the strong-collision approximation. Applied to $\mathrm{Li}_{0.73}\mathrm{CoO}_2$, the model supports a decomposition into a quenched width and a Li-driven dynamical component within the adopted parametrization, and yields fluctuation rates approximately consistent with activated behavior over the intermediate-temperature window. The fitted memory parameter is most visible in the crossover between quasi-static and fast-fluctuation limits.

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 / 1 minor

Summary. The manuscript develops a non-Markovian open-quantum-system theory of muon spin relaxation using a Schwinger-Keldysh influence-functional approach. It derives a stochastic equation of motion for the muon spin in which the fluctuation kernel is fixed by the local-field correlation tensor while the retarded memory torque is supplied by an effective phenomenological backaction kernel; the theory reduces to standard Kubo-Toyabe forms in appropriate limits and is applied to global fits of zero-field and weak longitudinal-field μSR spectra in Li0.73CoO2, yielding a decomposition into a quenched width plus a Li-driven dynamical component whose fluctuation rates are reported as consistent with activated behavior.

Significance. If the central decomposition can be shown to be robust under variation of the kernel, the framework would provide a useful extension of μSR analysis beyond the strong-collision approximation, enabling quantitative global fitting of ZF/LF data in materials with temporally correlated local fields. The explicit reduction to Kubo-Toyabe limits and the ability to treat both quenched and dynamical contributions within a single stochastic equation are clear strengths.

major comments (2)
  1. [Abstract and derivation of stochastic equation of motion] Abstract and the section deriving the stochastic equation of motion: the retarded memory torque is introduced through an effective phenomenological backaction kernel whose functional form and temperature dependence are chosen to fit the spectra rather than derived from the microscopic Hamiltonian. This choice is load-bearing for the central claim of a robust decomposition into quenched and dynamical components, because alternative kernels consistent with the same correlation tensor could shift the extracted fluctuation rates or the apparent crossover between quasi-static and fast-fluctuation regimes.
  2. [Application to Li0.73CoO2] Application to Li0.73CoO2 and the fitting procedure: the memory parameter and fluctuation rates are determined by fitting to the same ZF/LF spectra that are subsequently interpreted, so the reported consistency with activated behavior is a post-fit observation rather than an independent test. No sensitivity analysis to the kernel form is presented, undermining the assertion that the framework enables quantitative analysis beyond strong-collision approximations.
minor comments (1)
  1. [Theory section] The notation for the backaction kernel and its relation to the influence functional could be clarified with an explicit equation reference to avoid ambiguity when comparing to standard Kubo-Toyabe expressions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful review and valuable comments on our manuscript. We address each of the major comments below and have made revisions to the manuscript to strengthen the presentation and address the concerns raised.

read point-by-point responses

  1. Referee: Abstract and the section deriving the stochastic equation of motion: the retarded memory torque is introduced through an effective phenomenological backaction kernel whose functional form and temperature dependence are chosen to fit the spectra rather than derived from the microscopic Hamiltonian. This choice is load-bearing for the central claim of a robust decomposition into quenched and dynamical components, because alternative kernels consistent with the same correlation tensor could shift the extracted fluctuation rates or the apparent crossover between quasi-static and fast-fluctuation regimes.

    Authors: We acknowledge that the backaction kernel is phenomenological, as explicitly stated in the manuscript, since a fully microscopic derivation would require detailed knowledge of the underlying spin dynamics in the material, which is beyond the scope of the present work. The fluctuation kernel is determined by the local-field correlation tensor, providing a link to the microscopic environment. To address the robustness of the decomposition, we will add a sensitivity analysis in the revised manuscript by considering an alternative form for the memory kernel (e.g., a simple exponential decay) and showing that the extracted quenched width and dynamical fluctuation rates remain consistent within uncertainties, although the precise crossover temperature may shift slightly. This addition will be included in the section discussing the application to Li0.73CoO2. revision: yes

  2. Referee: Application to Li0.73CoO2 and the fitting procedure: the memory parameter and fluctuation rates are determined by fitting to the same ZF/LF spectra that are subsequently interpreted, so the reported consistency with activated behavior is a post-fit observation rather than an independent test. No sensitivity analysis to the kernel form is presented, undermining the assertion that the framework enables quantitative analysis beyond strong-collision approximations.

    Authors: We agree that the reported consistency with activated behavior is indeed a post-fit observation rather than an a priori prediction. This is inherent to the fitting procedure used to extract the parameters. We will revise the manuscript to explicitly note this and to include the sensitivity analysis mentioned above, which will demonstrate that the framework provides a useful extension beyond the strong-collision approximation by allowing for non-Markovian effects within a single stochastic equation. The main conclusions regarding the decomposition into quenched and dynamical components hold under the variations tested. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper derives the stochastic equation of motion from a Schwinger-Keldysh influence-functional formulation, with the fluctuation kernel fixed by the local-field correlation tensor (an independent microscopic input) and the retarded memory torque introduced explicitly as a phenomenological backaction kernel whose form is chosen to fit data. This reduces to standard Kubo-Toyabe limits in appropriate regimes without reference to the Li0.73CoO2 spectra. The application fits the memory parameter to the ZF/LF spectra and observes that the extracted fluctuation rates are approximately consistent with activated behavior as a post-fit check. No load-bearing step equates any claimed result to its inputs by construction, renames a known pattern, or relies on a self-citation chain; the phenomenological status is stated openly, and the framework remains self-contained against external benchmarks such as the strong-collision approximation.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the Schwinger-Keldysh contour for the muon-environment coupling and on the assumption that a single phenomenological memory kernel suffices to capture back-action across the temperature range studied.

free parameters (2)
  • memory parameter
    Effective phenomenological backaction kernel introduced to account for retarded torque; its value is fitted to spectra.
  • fluctuation rates
    Extracted from the local-field correlation tensor and adjusted to match temperature-dependent data.
axioms (2)
  • standard math Schwinger-Keldysh contour formalism for open quantum systems
    Invoked to derive the influence functional and stochastic equation of motion.
  • domain assumption Local magnetic environment can be represented by a temporally correlated classical field
    Underlies the fluctuation kernel construction.

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