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Non-Markovian Effects in Quantum Tunneling from a Minimal Memory Kernel Model

Piermario Bondi

Published Mar 31, 2026• 0 citations
Publisher

Abstract

We introduce a minimal non-Markovian extension of a scalar field model by including a temporal memory kernel with finite relaxation time. The resulting dynamics can be reformulated as a local system with an additional internal degree of freedom. We show that this modification induces history-dependent corrections to quantum tunneling probabilities, leading to a hysteresis effect. An order-of-magnitude estimate suggests that the effect may be observable in tunneling-dominated systems such as nuclear decay.

DOI
10.5281/zenodo.19347855

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We introduce a minimal non-Markovian extension of a scalar field model by including a temporal memory kernel with finite relaxation time. The resulting dynamics can be reformulated as a local system with an additional internal degree of freedom. We show that this modification induces history-dependent corrections to quantum tunneling probabilities, leading to a hysteresis effect. An order-of-magnitude estimate suggests that the effect may be observable in tunneling-dominated systems such as nuclear decay.
We propose an effective field-theoretic framework for open quantum systems in which decoherence dynamics are influenced by an auxiliary scalar field acting as an informational memory degree of freedom. This additional field induces intrinsically non-Markovian behavior, leading to structured noise spectra and deviations from standard exponential decay. The resulting reduced dynamics are governed by a non-local memory kernel, capturing temporal correlations beyond conventional approaches. We show that the model predicts oscillatory modulations in coherence decay and provides improved fits to simulated qubit data compared to both exponential and stretched-exponential models. The framework also reproduces nontrivial residual structures and spectral features that are not accounted for in standard decoherence theories. To test these predictions, we propose an experimental protocol using superconducting qubits, where systems initialized under identical environmental conditions but with different controlled histories exhibit distinguishable decoherence dynamics. This history dependence offers a potential experimental signature of the proposed mechanism. Overall, this work provides a phenomenological extension of decoherence theory and highlights the role of memory effects and informational degrees of freedom in open quantum systems, suggesting new directions for both theoretical and experimental investigation.
This work proposes a falsifiable extension of quantum tunneling in which the tunneling rate depends not only on the instantaneous state, but also on the history of prior interactions. A minimal kernel-based formulation is introduced, leading to a clear experimental prediction: systems prepared through different temporal protocols, yet brought to identical final conditions, may exhibit different tunneling rates. A concrete experimental implementation based on Josephson junctions is proposed, providing a controllable platform to test this prediction. The outcome of such experiments would directly constrain the validity of intrinsic-memory extensions of quantum dynamics.
We present a simple framework for classical and quantum ``memory'' in which the Hamiltonian at time ttt depends on past values of a control Hamiltonian through a causal kernel. This structure naturally describes finite-bandwidth or filtered control channels and provides a clean way to distinguish between memory in the control and genuine non-Markovian dynamics of the state. We focus on models where H(t)=H0+∫−∞tK(t−s) H1(s) dsH(t)=H_0+\int_{-\infty}^{t}K(t-s)\,H_1(s)\,dsH(t)=H0​+∫−∞t​K(t−s)H1​(s)ds, and illustrate the framework on single-qubit examples such as H(t)=σz+Φ(t)σxH(t)=σ_z+Φ(t)σ_xH(t)=σz​+Φ(t)σx​ with Φ(t)=∫−∞tK(t−s) u(s) dsΦ(t)=\int_{-\infty}^{t}K(t-s)\,u(s)\,dsΦ(t)=∫−∞t​K(t−s)u(s)ds. We derive basic properties of such dynamics, discuss conditions for unitarity, give an equivalent time-local description for exponential kernels, and show explicitly how hysteresis arises in the response of a driven qubit.
Abstract We propose a population-level description of cross-time memory effects in macroscopic quantum tunneling of a current-biased Josephson junction subject to a dynamically suppressed interval [t1,t2][t_1,t_2][t1​,t2​] . Starting from the Caldeira–Leggett influence functional, we identify the controlled approximations under which bath-mediated correlations between instantons can be coarse-grained into a Volterra equation for the survival probability S ( t ). The resulting cross-time kernel couples pre-window times t′<t1t'<t_1t′<t1​ to post-window times t>t2t>t_2t>t2​ with an amplitude proportional to e−λcΔtbMpree^{-\lambda _c\Delta t_b}M_\textrm{pre}e−λc​Δtb​Mpre​ , where Δtb=t2−t1\Delta t_b=t_2-t_1Δtb​=t2​−t1​ and MpreM_\textrm{pre}Mpre​ is a history-weighted pre-window survival functional. The switching distribution P(t)=−S˙(t)P(t)=-\dot{S}(t)P(t)=−S˙(t) then contains a Markovian clustering peak at t2t_2t2​ and a non-Markovian post-window tail. We clarify that the kernel is a controlled phenomenological reduction, not an exact microscopic identity, and we state explicit positivity, validity, and thermal-crossover conditions. Numerical diagnostics are reformulated in terms of S ( t ) and show how the full switching distribution changes with barrier duration and pre-barrier history. The analysis indicates that ordinary resistively shunted junctions have too short a memory time for nanosecond barriers, whereas engineered high- Q resonator environments provide a plausible route to testing the predicted peak-plus-tail signatures.
Non-Markovian processes may arise in physics due to memory effects of environmental degrees of freedom. For quantum non-Markovianity, it is an ongoing debate to clarify whether such memory effects have a verifiable quantum origin, or whether they might equally be modeled by a classical memory. In this contribution, we propose a criterion to test locally for a truly quantum memory. The approach is agnostic with respect to the environment, as it solely depends on the local dynamics of the system of interest. Experimental realizations are particularly easy, as only single-time measurements on the system itself have to be performed. We study memory in a variety of physically motivated examples, both for a time-discrete case, and for time-continuous dynamics. For the latter, we are able to provide an interesting class of non-Markovian master equations with classical memory that allows for a physically measurable quantum trajectory representation.
The dynamics of an open quantum system is non-Markovian when memory effect is non-negligible. The quantum memory effect is a very complex issue and presently there is no universally accepted method to quantify it. By examining the memory kernel of the Nakajima-Zwanzig master equation, we study the memory effect in a theoretical model consisting of a spin coupled to an environment of an Ising spin chain subject to a transverse field. We find that it can be dictated by either the time correlation in the environment, or the system-environment correlation, depending on the strength of the transverse field and the state of the environment. We analyze the information loss to the environment and backflow from it, and discover that the information flow is not always a reliable indicator for the nature of the dynamics.