Noise-Assisted Metastability: From Lévy Flights to Memristors, Quantum Escape, and Josephson-based Axion Searches

TL;DR

This review develops a unifying framework for noise-assisted stabilization of metastable states across classical and quantum systems, emphasizing non-Gaussian fluctuations such as symmetric $\alpha$-stable Lévy noise and their impact on residence times and switching statistics. It presents exact MRT results for arbitrary $\alpha$ and a closed quadrature for $\alpha=1$, illustrating how long jumps and boundary conditions shape metastable lifetimes. The discussion then connects these ideas to memristive devices, where noise can enhance stability and shift switching kinetics, and to driven quantum bistable systems described by the Caldeira–Leggett model, highlighting a quantum Zeno-like crossover at strong dissipation. Finally, it proposes axion-induced resonant activation in current-biased Josephson junctions as a practical switching-statistics approach to axion detection, demonstrating how a tunable energy ratio $\varepsilon$ can reveal resonant signatures in switching-time statistics. Together, these results offer a cohesive picture of how fluctuations can be harnessed to control metastability and enable novel sensing technologies across disciplines.

Abstract

Many-body and complex systems, both classical and quantum, often exhibit slow, nonlinear relaxation toward stationary states due to the presence of metastable configurations and environmental fluctuations. Nonlinear relaxation in a wide variety of natural systems proceeds through metastable states, which arise in condensed-matter physics as well as in fields ranging from cosmology and biology to high-energy physics. Moreover, noise-induced phenomena play a central role in shaping the dynamics of such systems far from equilibrium. This review develops a unifying perspective centered on noise-assisted stabilization and the statistical properties of metastable dynamics. We first discuss escape processes driven by Lévy flights in smooth metastable potentials, emphasizing the emergence of nonmonotonic residence-time behavior. We then connect these concepts to stochastic resistive switching in memristive devices, where noise-induced effects can enhance stability and reproducibility. We further examine driven dissipative quantum bistability, showing how the interplay between external driving and system-environment coupling reshapes escape pathways and lifetimes. Finally, we outline how switching-time statistics in current-biased Josephson junctions can provide an experimentally accessible strategy for axion detection, based on an axion-induced resonant-activation signature.

Figures (11)

• Figure 1: MRT for Cauchy noise ($\alpha=1$) in the cubic metastable potential $V(x)=-x^3/3+m^2x$ with $m=x_m=1$ and initial condition $x_0=2.1$. (a) MRT $\tau_{\mathrm{MRT}}(x_0)$ versus noise intensity $D_1$ for $L_1=-0.5$ and $L_2\in[2.2,7]$ in steps of $0.2$ (log-log scale, $D_1\in[10^{-3},10^{3}]$), highlighting the NES maximum and the large-$D_1$ power-law decay. (b) Normalized MRT $\tau_{\mathrm{MRT}}(x_0)/\tau_d(x_0)$ versus $D_1$ for $L_2=3$ and $L_1\in[-6,0]$ in steps of $0.2$, showing the NES maximum for all explored $L_1$ and the characteristic "duck-bill" structure associated with boundary-controlled trapping under Lévy flights. Here $\tau_d(x_0)$ denotes the deterministic transit time to $L_2$ for the noiseless overdamped dynamics, when this time is finite.
• Figure 2: Typical I--V curve of a memristive device based on a Ta/ZrO$_2$(Y)/Pt stack. The direction of the voltage sweep is shown by arrows. Inset: schematic representation of the oxygen ions drift under the action of an electric field in different directions. From Koryazhkina2022.
• Figure 3: A filament growth model for resistive random access memory switching.
• Figure 4: Memristance SNR vs. noise intensity experimentally obtained for the memristive device under study. From Mikhaylov2021.
• Figure 5: Temperature dependence of the relaxation time of the memristor during the switching from LRS to HRS. From Filatov2022.