Noise and ergodic properties of Brownian motion in an optical tweezer: Looking at regime crossovers in an Ornstein-Uhlenbeck process.

We characterize throughout the spectral range of an optical trap the nature of the noise that drives the Brownian motion of an overdamped trapped single microsphere and its ergodicity, comparing experimental, analytical, and simulated data. We carefully analyze noise and ergodic properties (i) using the Allan variance for characterizing the noise and (ii) exploiting a test of ergodicity tailored for experiments done over finite times. We derive these two estimators in the Ornstein-Uhlenbeck low-frequency trapped-diffusion regime and study analytically their evolution toward the high-frequency Wiener-like free-diffusion regime, in very good agreement with simulated and experimental results. This study is performed comprehensively from the free-diffusion to the trapped-diffusion regimes. It also carefully looks at the specific signatures of the estimators at the crossover between the two regimes. This analysis is important to conduct when exploiting optical traps in a metrology context.

Searching for the Gardner Transition in Glassy Glycerol.

We search for a Gardner transition in glassy glycerol, a standard molecular glass, measuring the third harmonics cubic susceptibility χ_{3}^{(3)} from slightly below the usual glass transition temperature down to 10 K. According to the mean-field picture, if local motion within the glass were becoming highly correlated due to the emergence of a Gardner phase then χ_{3}^{(3)}, which is analogous to the dynamical spin-glass susceptibility, should increase and diverge at the Gardner transition temperature T_{G}. We find instead that upon cooling |χ_{3}^{(3)}| decreases by several orders of magnitude and becomes roughly constant in the regime 100-10 K. We rationalize our findings by assuming that the low temperature physics is described by localized excitations weakly interacting via a spin-glass dipolar pairwise interaction in a random magnetic field. Our quantitative estimations show that the spin-glass interaction is twenty to fifty times smaller than the local random field contribution, thus rationalizing the absence of the spin-glass Gardner phase. This hints at the fact that a Gardner phase may be suppressed in standard molecular glasses, but it also suggests ways to favor its existence in other amorphous solids and by changing the preparation protocol.

Primary Burkitt lymphoma of the thyroid.

Primary Burkitt lymphoma of the thyroid is extremely rare. The author describes a new case in a 15-year-old boy who presented with a rapidly enlarging thyroid mass and dyspnea.