arXiv subjects

Lior Zarfaty

Publications and source records attributed to Lior Zarfaty.

6 recordsLinked to original sources

arXiv2025

Black hole optical analogue: photon sphere microlasers

The bell-like ringdown of the gravitational field in the last stage of the merging of massive black holes is now routinely detected on earth by the last generation of gravitational wave detectors. Its spectrum is interpreted as a sum of damped sinusoidal vibrations of the spacetime in the vicinity of the black hole. These so-called quasinormal modes are currently the subject of extensive studies, yet, their true nature remains elusive. Here, we emulate, in the laboratory, genuine four-dimension black hole metrics by two-dimensional optical curved surfaces that preserve the features of lightlike geodesics. %We establish the analogy with gravitational waves radiated by relaxing black holes, and We analytically compute the optical quasinormal modes and show that they are confined around the photon sphere, the unstable region around a black hole where spacetime curvature traps light in circular orbits. By 3D-printing non-Euclidean dye-doped microcavities, we demonstrate lasing at the photon sphere with a mode profile that closely matches the analytical prediction. These results paves the way for observing astrophysical phenomena in tabletop setups and is likely to inspire innovative designs in photonics.

physics.optics↗

arXiv2022

Discrete Sampling of Extreme Events Modifies Their Statistics

Extreme value (EV) statistics of correlated systems are widely investigated in many fields, spanning the spectrum from weather forecasting to earthquake prediction. Does the unavoidable discrete sampling of a continuous correlated stochastic process change its EV distribution? We explore this question for correlated random variables modeled via Langevin dynamics for a particle in a potential field. For potentials growing at infinity faster than linearly and for long measurement times, we find that the EV distribution of the discretely sampled process diverges from that of the full continuous dataset and converges to that of independent and identically distributed random variables drawn from the process's equilibrium measure. However, for processes with sublinear potentials, the long-time limit is the EV statistics of the continuously sampled data. We treat processes whose equilibrium measures belong to the three EV attractors: Gumbel, Fréchet, and Weibull. Our work shows that the EV statistics can be extremely sensitive to the sampling rate of the data.

cond-mat.stat-mech↗

arXiv2021

Discrete sampling of correlated random variables modifies the long-time behavior of their extreme value statistics

We consider the extreme value statistics of correlated random variables that arise from a Langevin equation. Recently, it was shown that the extreme values of the Ornstein-Uhlenbeck process follow a different distribution than those originating from its equilibrium measure, composed of independent and identically distributed Gaussian random variables. Here, we first focus on the discretely sampled Ornstein-Uhlenbeck process, which interpolates between these two limits. We show that in the limit of large times, its extreme values converge to those of the equilibrium distribution, instead of those of the continuously sampled process. This finding folds for any positive sampling interval, with an abrupt transition at zero. We then analyze the Langevin equation for any force that gives rise to a stable equilibrium distribution. For forces which asymptotically grow with the distance from the equilibrium point, the above conclusion continues to hold, and the extreme values for large times correspond to those of independent variables drawn from the equilibrium distribution. However, for forces which asymptotically decay to zero with the distance, the discretely sampled extreme value statistics at large times approach those of the continuously sampled process.

cond-mat.stat-mech↗

arXiv2021

Accurately approximating extreme value statistics

We consider the extreme value statistics of $N$ independent and identically distributed random variables, which is a classic problem in probability theory. When $N\to\infty$, fluctuations around the maximum of the variables are described by the Fisher-Tippett-Gnedenko theorem, which states that the distribution of maxima converges to one out of three limiting forms. Among these is the Gumbel distribution, for which the convergence rate with $N$ is of a logarithmic nature. Here, we present a theory that allows one to use the Gumbel limit to accurately approximate the exact extreme value distribution. We do so by representing the scale and width parameters as power series, and by a transformation of the underlying distribution. We consider functional corrections to the Gumbel limit as well, showing they are obtainable via Taylor expansion. Our method also improves the description of large deviations from the mean extreme value. Additionally, it helps to characterize the extreme value statistics when the underlying distribution is unknown, for example when fitting experimental data.

cond-mat.stat-mech↗

arXiv2019

Infinite horizon billiards: Transport at the border between Gauss and Lévy universality classes

We consider transport in two billiard models, the infinite horizon Lorentz gas and the stadium channel, presenting analytical results for the spreading packet of particles. We first obtain the cumulative distribution function of traveling times between collisions, which exhibits non-analytical behavior. Using a renewal assumption and the Lévy walk model, we obtain the particles' probability density. For the Lorentz gas, it shows a distinguished difference when compared with the known Gaussian propagator, as the latter is valid only for extremely long times. In particular, we show plumes of particles spreading along the infinite corridors, creating power-law tails of the density. We demonstrate the slow convergence rate via summation of independent identically distributed random variables on the border between Lévy and Gauss laws. The renewal assumption works well for the Lorentz gas with intermediately sized scattering centers, but fails for the stadium channel due to strong temporal correlations. Our analytical results are supported with numerical samplings.

cond-mat.stat-mech↗

arXiv2016

Statistics of large currents in the Kipnis-Marchioro-Presutti model in a ring geometry

We use the macroscopic fluctuation theory to determine the statistics of large currents in the Kipnis-Marchioro-Presutti (KMP) model in a ring geometry. About 10 years ago this simple setting was instrumental in identifying a breakdown of the additivity principle in a class of lattice gases at currents exceeding a critical value. Building on earlier work, we assume that, for supercritical currents, the optimal density profile, conditioned on the given current, has the form of a traveling wave (TW). For the KMP model we find this TW analytically, in terms of elliptic functions, for any supercritical current $I$. Using this TW solution, we evaluate, up to a pre-exponential factor, the probability distribution $P(I)$. We obtain simple asymptotics of the TW and of $P(I)$ for currents close to the critical current, and for currents much larger than the critical current. In the latter case we show that $-\ln P (I) \sim I\ln I$, whereas the optimal density profile acquires a soliton-like shape. Our analytic results are in a very good agreement with Monte-Carlo simulations and numerical solutions of Hurtado and Garrido (2011).

cond-mat.stat-mech↗