LPTMC Seminars

A unifying approach to diffusive transport in annealed heterogeneous media

In this seminar, we will discuss the thermal diffusion in heterogeneous media through the lenses of stochastic processes. Transport as the mesoscopic scale is dominated by thermal fluctuations yielding stochastic motion. While stochastic motion in homogeneous media is understood since Einstein and his derivation of Brownian motion, its extension to heterogeneous media remains to elucidate. Heterogeneity induces induce statistical deviations from Brownian motion as will be discussed in the context of diffusion in living cells. The two main effects are anomalous diffusion where the mean squared displacement displays a power-law scaling and non-Gaussian displacement statistics which may occur at the same time. We will discuss how anomalous and non-Gaussian diffusion articulate. 

To do so, we introduce the concept of Randomly Modulated Gaussian Processes [1] as a unifying framework for modelling, analysing and classifying diffusion in heterogeneous media. This formulation incorporates correlations in the displacements together with correlated fluctuations of their amplitudes. Most known models of anomalous diffusion (including Continuous-Time Random Walk, fractional Brownian motion but also Lévy flights) and random diffusivity can be described and generalized within this framework. Moreover, the unified view identifies the main statistical properties to be probed experimentally for a reliable classification of diffusive dynamics.

Résumé sur https://sematomesfroids.sciencesconf.org/

Diffusion in a noisy trap: dynamics and thermodynamics of the OU^2 process

The Ornstein–Uhlenbeck (OU) process is the standard model for confined Langevin dynamics and is used throughout theoretical biology. However, in a number of scenarios including in active cellular environments and optical tweezer experiments, the OU process fails to capture the fluctuating nature of the confining potential itself. To capture these inherently out-of-equilibrium dynamics, we recently introduced the OU2 process, a natural extension where the stiffness of the harmonic trap undergoes its own OU-like fluctuations. In this talk, we explore the dynamics and thermodynamics of this model through a combination of analytical and numerical methods. First, we show that this dynamic probe-controller coupling fundamentally alters the system's dynamics. Unlike the Gaussian decay of the standard OU process, the OU2 probability density exhibits heavy power-law tails. We discuss how these asymptotics qualitatively change the system's trapping behavior, extreme value statistics, and crucially its first passage time (FPT) statistics. Secondly, we analyze the thermodynamic consequences of external driving. When the trap's fluctuations violate detailed balance, we reveal a breakdown of quasistatic (infinite-time) optimality. Instead, continuous work exchange between the probe and controller drives the emergence of finite-time optimal protocols. Ultimately, we hope that the introduction of the OU2 model provides a refined analytical framework for exploring the interplay of anomalous FPT statistics and non-equilibrium control in fluctuating biological systems.

Monitored Quantum Hitting Times on NISQ Platforms

We introduce a time-energy uncertainty relation within the context of monitored quantum dynamics [1] . Previous studies have established that the mean recurrence time, which represents the time taken to return to the initial state, is quantized as an integer multiple of the sampling time, displaying point-wise discontinuous transitions at resonances. Our findings demonstrate that the natural utilization of the restart mechanism in laboratory experiments [2], driven by finite data collection time spans, leads to a broadening effect on the transitions of the mean recurrence time. Our proposed uncertainty relation captures the underlying essence of these phenomena, by connecting the broadening of the mean hitting time near resonances, to the intrinsic energies of the quantum system and to the fluctuations of recurrence time. Our uncertainty relation has also been validated through remote experiments conducted on an International Business Machines Corporation (IBM) quantum computer. We then discuss ractional quantization of the recurrence time for interacting spin systems using sub-space measurements [3].

References
[1] R. Yin, Q. Wang, S. Tornow, and E. Barkai, Restart uncertainty relation for
monitored quantum dynamics Proceedings of the National Academy of
Sciences 122 (1) e2402912121, (2025).
[2] R. Yin, E. Barkai Restart expedites quantum walk hitting times Phys. Rev.
Lett. 130, 050802 (2023).
[3] Q. Liu, S. Tornow, D. Kessler, and E. Barkai Fractionally Quantized Recurrence
Detection Times in Monitored Quantum Many-Body Systems Proceedings of
the National Academy of Sciences 123 (22) e2529694123 (2026).