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Sufficiently large nonreciprocity allows colored noise to trigger multiple exceptional points that set the adiabatic tunneling probability in Landau-Zener systems.

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2026-06-30 00:54 UTC pith:73YHHBEK

load-bearing objection For large nonreciprocity, colored noise appears to trigger extra exceptional points that fix the adiabatic tunneling probability, but the numerical extraction of those points may be sensitive to solver details. the 1 major comments →

arxiv 2605.25008 v1 pith:73YHHBEK submitted 2026-05-24 quant-ph

Nonreciprocal Landau-Zener Tunneling in the Presence of Heat-Bath-Induced Colored Noise

Yi Cao , Jie Liu This is my paper
classification quant-ph
keywords nonreciprocal Landau-Zener tunnelingcolored noiseexceptional pointstunneling probabilitynon-Hermitian quantum systemsadiabatic tunnelingheat-bath noise
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper examines how heat-bath-induced colored noise influences nonreciprocal Landau-Zener tunneling. It shows through numerical calculations that noise causes fluctuations in energy levels and, when nonreciprocity parameters are large enough, induces multiple exceptional points. These points modify the tunneling probabilities, generally increasing them in nonadiabatic regimes and breaking reciprocity in the adiabatic limit. For large nonreciprocity, the adiabatic probability becomes independent of noise details and is fixed by the exceptional points. The work also provides exact expressions without noise and approximations in the white-noise limit.

Core claim

In the presence of colored noise, nonreciprocal Landau-Zener tunneling exhibits stochastic fluctuations in instantaneous energy levels. For large enough nonreciprocity parameters, the noise triggers the emergence of multiple exceptional points. The tunneling probability is enhanced by noise in nonadiabatic sweeping and loses reciprocity in the adiabatic limit, but for large nonreciprocity the adiabatic probability is determined solely by these exceptional points and insensitive to noise amplitude or correlation time.

What carries the argument

The nonreciprocity parameter in the Hamiltonian, which controls the asymmetry in the tunneling process and enables noise-induced multiple exceptional points in the complex energy spectrum.

Load-bearing premise

The numerical identification of exceptional points from the stochastic energy levels accurately reflects the true effect of the colored noise without introducing artifacts from the simulation method.

What would settle it

Measuring the adiabatic tunneling probability for varying noise correlation times at large nonreciprocity and finding dependence on those times, or failing to observe additional exceptional points as nonreciprocity increases, would falsify the claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Colored noise enhances the nonadiabatic tunneling probability compared to the noiseless case.
  • In the adiabatic limit, colored noise breaks the reciprocity of the tunneling probability.
  • For large nonreciprocity parameters, the adiabatic tunneling probability is insensitive to noise and solely determined by the locations of exceptional points.
  • The phase diagram of tunneling probability versus sweep rate and nonreciprocity parameter shifts with noise amplitude and correlation time.

Where Pith is reading between the lines

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

  • The interaction suggests a way to use nonreciprocity to stabilize tunneling probabilities against noise variations in quantum systems.
  • Exceptional points may serve as robust features in non-Hermitian dynamics under stochastic driving.
  • Similar effects could appear in other driven non-Hermitian quantum models with asymmetric couplings.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 2 minor

Summary. The manuscript studies nonreciprocal Landau-Zener tunneling in the presence of heat-bath-induced colored noise. Numerical simulations of the instantaneous eigenvalues of the stochastic non-Hermitian Hamiltonian reveal energy-level fluctuations and, for sufficiently large nonreciprocity parameters, the noise-induced appearance of multiple exceptional points. These features modify the tunneling probability, with colored noise generally enhancing nonadiabatic tunneling while breaking reciprocity in the adiabatic limit; for large nonreciprocity the adiabatic probability becomes insensitive to noise and is controlled by the exceptional points. Phase diagrams are presented as functions of sweep rate and nonreciprocity for varying noise amplitude and correlation time. Analytically, an exact expression for the noise-free case and an approximate solution in the white-noise limit are derived using Weber functions and the Wiener-Hermite expansion.

Significance. If the numerical identification of noise-triggered exceptional points is robust, the work provides a concrete link between colored noise, nonreciprocity, and exceptional-point physics in open quantum systems, extending beyond the white-noise and noise-free limits that are treated analytically. The use of standard special functions and the Wiener-Hermite method supplies reproducible analytic benchmarks, while the phase diagrams offer testable predictions for parameter regimes where noise effects saturate.

major comments (1)
  1. [numerical calculations of the instantaneous energy levels] Numerical calculations of instantaneous energy levels: the central claim that sufficiently large nonreciprocity parameters allow colored noise to trigger multiple exceptional points (whose locations then control the adiabatic tunneling probability) rests on stochastic eigenvalue trajectories. The manuscript does not specify the coalescence criterion (e.g., minimum eigenvalue separation or winding-number test), the integrator time step, the number of noise realizations, or the interpolation scheme used to locate crossings. Without these controls it is impossible to exclude the possibility that reported multiple EPs are discretization or ensemble artifacts, directly undermining the asserted causal relation between noise, nonreciprocity, and the phase diagram.
minor comments (2)
  1. [abstract] The abstract states that the adiabatic tunneling probability becomes “insensitive to noise and determined by exceptional points” for large nonreciprocity; a brief quantitative statement of the residual noise dependence (e.g., scaling with correlation time) would strengthen this claim.
  2. [analytic derivation] The Wiener-Hermite expansion is invoked for the white-noise limit; the truncation order and convergence criterion should be stated explicitly so that readers can reproduce the approximate tunneling probability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the major comment below.

read point-by-point responses

  1. Referee: Numerical calculations of instantaneous energy levels: the central claim that sufficiently large nonreciprocity parameters allow colored noise to trigger multiple exceptional points (whose locations then control the adiabatic tunneling probability) rests on stochastic eigenvalue trajectories. The manuscript does not specify the coalescence criterion (e.g., minimum eigenvalue separation or winding-number test), the integrator time step, the number of noise realizations, or the interpolation scheme used to locate crossings. Without these controls it is impossible to exclude the possibility that reported multiple EPs are discretization or ensemble artifacts, directly undermining the asserted causal relation between noise, nonreciprocity, and the phase diagram.

    Authors: We acknowledge that the manuscript does not provide the requested details on the numerical procedure for identifying exceptional points. This omission makes it difficult to fully assess the robustness of the results against potential artifacts. In the revised manuscript, we will add a dedicated subsection or paragraph detailing the coalescence criterion (using a combination of eigenvalue separation threshold and winding number analysis), the specific integrator time step employed, the number of noise realizations used for the ensemble, and the interpolation scheme for locating crossings in the eigenvalue trajectories. These additions will enable verification that the multiple exceptional points are physically meaningful rather than numerical artifacts, thereby supporting the claimed connection to the phase diagram. revision: yes

Circularity Check

0 steps flagged

No circularity: derivations rely on standard analytic methods and independent numerics

full rationale

The paper's analytic results consist of an exact no-noise tunneling probability expressed via Weber functions and a white-noise approximation obtained through the Wiener-Hermite expansion; both are standard techniques applied directly to the given non-Hermitian Hamiltonian and do not reduce to any fitted parameter or self-defined quantity. The colored-noise regime is handled by direct numerical diagonalization of instantaneous eigenvalues, with exceptional-point identification presented as an output of that computation rather than an input. No self-citation is invoked as a load-bearing uniqueness theorem, no ansatz is smuggled via prior work, and no prediction is shown to be equivalent to a fit by construction. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Abstract-only review limits visibility into specific parameters; the model introduces a nonreciprocity parameter and colored noise characteristics as central elements, with standard quantum mechanics as background.

free parameters (2)
  • nonreciprocity parameter
    Controls the degree of nonreciprocity and is central to triggering multiple exceptional points and noise insensitivity.
  • amplitude and correlation time of colored noise
    Characterize the heat-bath noise and are varied to produce phase diagrams.
axioms (2)
  • domain assumption System dynamics follow a time-dependent nonreciprocal Hamiltonian under stochastic noise
    Basis for both numerical energy level calculations and analytical tunneling probability expressions.
  • domain assumption Colored noise is modeled with finite correlation time from a heat bath
    Used to distinguish from white-noise limit in the approximate solution.

pith-pipeline@v0.9.1-grok · 5724 in / 1379 out tokens · 53102 ms · 2026-06-30T00:54:18.711891+00:00 · methodology

0 comments
read the original abstract

In this work, we investigate the effects of heat-bath-induced colored noise on nonreciprocal Landau-Zener tunneling. We perform numerical calculations of the instantaneous energy levels and find that noise induces stochastic fluctuations in these levels. Beyond such fluctuations, sufficiently large nonreciprocity parameters enable noise to further trigger the emergence of multiple exceptional points. The corresponding tunneling probability is significantly modified by colored noise. On the one hand, colored noise generally enhances the tunneling probability under nonadiabatic sweeping. On the other hand, it can break the reciprocity of Landau-Zener tunneling in the adiabatic limit. In particular, for large nonreciprocity parameters, the adiabatic tunneling probability is insensitive to noise and determined by exceptional points. We plot the phase diagram of tunneling probability as a function of the sweep rate and nonreciprocity parameter, for different amplitudes and correlation times of colored noise. Analytically, we derive the exact expression for the tunneling probability in the absence of noise and an approximate solution in the white-noise limit, employing Weber functions and the Wiener-Hermite expansion method. Some implications of our theory are discussed.

Figures

Figures reproduced from arXiv: 2605.25008 by Jie Liu, Yi Cao.

Figure 1
Figure 1. Figure 1: FIG. 1. Instantaneous energy levels for various nonrecipro [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Sweep-rate-dependent tunneling probabilities wit [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Phase diagram of the tunneling probability with re [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Comparison of three types of solutions as functions o [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

discussion (0)

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Reference graph

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