Shows Noise-Assisted Metastability Drives Lévy Flights and Quantum Escape Dynamics

Researchers are increasingly recognising the crucial role of noise in influencing the behaviour of metastable systems, from the microscopic world of materials science to macroscopic phenomena in cosmology. Claudio Guarcello (Università degli Studi di Salerno and INFN, Napoli), Alexander A. Dubkov (Lobachevsky State University), and Davide Valenti et al. (Università degli Studi di Palermo and Lobachevsky University) present a unifying theoretical framework demonstrating how noise can not only disrupt, but actively stabilise, dynamics in these complex systems. Their work, detailed in a new review, connects seemingly disparate areas, Lévy flight escape processes, the operation of memristors, and even the potential detection of axions via Josephson junctions, revealing a shared underlying mechanism of noise-assisted metastability and offering new insights into controlling and exploiting these phenomena.

Lévy Noise Stabilises Metastable States via Non-Gaussian Fluctuations in complex systems

Scientists have demonstrated a unifying perspective on noise-assisted stabilization and the statistical properties of metastable dynamics in both classical and quantum systems. This research addresses how many-body and complex systems exhibit slow, nonlinear relaxation due to metastable configurations and environmental fluctuations, a phenomenon observed across diverse fields from cosmology to high-energy physics.
The team achieved a deeper understanding of escape processes driven by Lévy flights in smooth metastable potentials, revealing nonmonotonic residence-time behaviour and highlighting the enhancement of stability induced by these fluctuations. Specifically, the study establishes that Lévy noise, characterised by rare but large events, fundamentally alters the stability of metastable states compared to Gaussian noise.

Researchers obtained exact results for the mean residence time of a particle in an arbitrary smooth potential under Lévy noise, with a closed expression derived for Cauchy noise in a cubic potential, analytically proving the enhancement of metastable stability. These findings broaden the theoretical framework and underscore the universality of noise-assisted stabilization phenomena, extending beyond traditional Gaussian stochastic dynamics.

Furthermore, the work connects these concepts to practical applications in memristive devices, demonstrating that noise-induced effects can enhance stability and reproducibility in stochastic resistive switching. Experiments on ZrO2(Y) memristors provided the first evidence of noise-enhanced stability, aligning with a stochastic model predicting a nonmonotonic dependence of relaxation time on fluctuation intensity.

This research reveals that noise can constructively influence memristive systems, either slowing down or accelerating switching depending on its characteristics. The study also extends to quantum systems, examining driven dissipative bistability and showing how the interplay between external driving and system, environment coupling reshapes escape pathways and lifetimes.

Valenti et al. (2018) demonstrated that increasing system, environment coupling drives a transition in escape dynamics, revealing a quantum analogue of noise-enhanced stability. Finally, the research outlines a novel strategy for axion detection using current-biased Josephson junctions, leveraging switching-time statistics and an axion-induced resonant-activation signature, potentially opening new avenues for particle physics investigations.

Quantifying Metastable Escape Times via Discretised Potential Well Population reveals key dynamical insights

Scientists investigated nonlinear relaxation phenomena in complex systems by focusing on noise-assisted stabilization and metastable dynamics. The study employed a discretized method to analyse escape times from metastable regions, building upon earlier work by Sargsyan et al. (2007). Researchers computed the population of the lower potential well, defined as Pright(t), by summing the populations of DVR states |q4>, |q5>, and |q6>, using the equation Pright(t) = 6X j=4 ρjj(t).

The escape time, τ, was then determined as the time required for Pright(t) to reach a threshold value of 0.95, signifying the particle’s escape from the metastable region. This approach enabled precise measurement of how driving frequency and coupling strength influence escape dynamics. The team fixed the coupling parameter, γ, at its lowest value and generated plots of escape time versus driving frequency (Ω/ω0) and coupling strength (γ/ω0) for amplitudes of A = 0.15 and 0.20.

They observed that as γ increased, the peaks and dips in τ smoothed out, eventually becoming independent of the driving frequency at a critical coupling value, γc = 0.75. This critical value marks the onset of a regime where the tunneling process is suppressed, preventing population transfer to the metastable region.

Furthermore, the research pioneered a strategy for axion detection using a current-biased Josephson junction (CBJJ) functioning as a threshold device. The study proposed that an axion field, if coupled to the Josephson phase, could act as a weak drive, modifying escape dynamics and creating a resonant-activation effect.

Scientists predicted this would manifest as a minimum in the mean switching time when the junction energy scale is tuned, alongside a corresponding structure in the switching-time distributions. The team harnessed the junction’s nonlinearity and low dissipation to propose a sensitive electrical readout for axion detection in superconducting circuits.

Lévy noise stabilises metastable states in quantum systems and memristive devices, enhancing their persistence

Scientists have demonstrated that noise can enhance the stability of metastable states in both quantum and classical systems, challenging the traditional view of noise as purely detrimental. Experiments revealed that Lévy noise, characterized by rare but large fluctuations, enhances metastable stability and exhibits asymptotic behaviour differing from Gaussian noise.

Researchers obtained exact results for the mean residence time (MRT) of a particle in an arbitrary smooth potential under Lévy noise, with the work addressing how this noise affects stability and yielding a closed expression in quadrature for the MRT with Cauchy noise in a cubic potential. The team measured a nonmonotonic dependence of relaxation time on fluctuation intensity in ZrO2(Y) memristors, providing the first experimental evidence of noise-enhanced stability in these devices.

Data shows that noise can either accelerate or slow down switching, depending on its strength, and can genuinely contribute to memristive system function. Furthermore, stochastic resonance was experimentally observed in metal-oxide memristive devices, demonstrating another noise-induced phenomenon. Investigations into quantum systems revealed that external driving and dissipation can stabilize quantum metastable states, rather than solely causing decoherence.

Measurements confirm that the interplay between coherent driving, dissipation, and quantum fluctuations can prolong the lifetime of these states, mirroring noise-enhanced stability observed classically. Specifically, the escape time exhibited a nonmonotonic dependence on bath coupling, temperature, and driving frequency, indicating a transition in escape dynamics and a single peak followed by a steep decrease. These results outline how switching-time statistics in current-biased Josephson junctions could provide an experimentally accessible strategy for axion detection, based on an axion-induced resonant-activation signature.

Harnessing Stochasticity for Stabilised Metastability in Nonlinear Systems offers novel control strategies

Scientists have demonstrated that metastability in nonlinear systems can be actively controlled and, in certain conditions, even strengthened by fluctuations, dissipation, and time-dependent perturbations. Beginning with an analysis of barrier crossing driven by Lévy flights, the research highlights how heavy-tailed noise fundamentally alters escape dynamics, resulting in finite residence times dependent on boundary conditions and a distinct, nonmonotonic relationship between mean residence time and noise intensity.

This extends the concept of noise-enhanced stability beyond traditional Gaussian noise models. The study connects these theoretical findings to practical applications, notably memristors and Josephson junctions. In memristive devices, the inherent stochasticity of resistive switching can be harnessed through controlled fluctuations to improve operational stability, reproducibility, and switching kinetics for neuromorphic computing and memory technologies.

Furthermore, the research explores driven dissipative bistable systems, revealing a crossover in escape dynamics governed by system-bath coupling, analogous to noise-assisted control where dissipation can be engineered to modify metastable lifetimes. A potential application of these principles lies in axion detection, where modifications to Josephson junction switching statistics, induced by axions, could be identified through careful parameter scans and statistical analysis of switching times.

The authors acknowledge that the effectiveness of coupling-induced signatures in Josephson junctions is most pronounced in the underdamped regime, becoming negligible with strong damping. Future research could focus on exploring these dynamics in more complex systems and refining the statistical protocols for detecting subtle signals, such as those potentially arising from axion interactions. These findings establish a unifying framework for understanding metastability across diverse physical settings, demonstrating that noise and dissipation are not merely disruptive forces but can be actively leveraged to control and enhance system behaviour.