Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System

It was proposed recently that the out-of-time-ordered four-point correlator (OTOC) may serve as a useful characteristic of quantum-chaotic behavior, because in the semi-classical limit, $\hbar \to 0$, its rate of exponential growth resembles the classical Lyapunov exponent. Here, we calculate the four-point correlator, $C(t)$, for the classical and quantum kicked rotor -- a textbook driven chaotic system -- and compare its growth rate at initial times with the standard definition of the classical Lyapunov exponent. Using both quantum and classical arguments, we show that the OTOC's growth rate and the Lyapunov exponent are in general distinct quantities, corresponding to the logarithm of phase-space averaged divergence rate of classical trajectories and to the phase-space average of the logarithm, respectively. The difference appears to be more pronounced in the regime of low kicking strength $K$, where no classical chaos exists globally. In this case, the Lyapunov exponent quickly decreases as $K \to 0$, while the OTOC's growth rate may decrease much slower showing higher sensitivity to small chaotic islands in the phase space. We also show that the quantum correlator as a function of time exhibits a clear singularity at the Ehrenfest time $t_E$: transitioning from a time-independent value of $t^{-1} \ln{C(t)}$ at $t < t_E$ to its monotonous decrease with time at $t>t_E$. We note that the underlying physics here is the same as in the theory of weak (dynamical) localization [Aleiner and Larkin, Phys. Rev. B 54, 14423 (1996); Tian, Kamenev, and Larkin, Phys. Rev. Lett. 93, 124101 (2004)] and is due to a delay in the onset of quantum interference effects, which occur sharply at a time of the order of the Ehrenfest time.Comment: 5+2 pages, 5+2 figures; accepted for publication in Phys. Rev. Lett., Vol. 118 (2017

3-D characterization of weathered building limestones by high resolution synchrotron X-ray microtomography

International audienceUnderstanding the weathering processes of building stones and more generally of their transfer properties requires detailed knowledge of the porosity characteristics. This study aims at analyzing three-dimensional images obtained by X-ray microtomography of building stones. In order to validate these new results a weathered limestone previously characterised (Rozenbaum et al., 2007) by two-dimensional image analysis was selected. The 3-D images were analysed by a set of mathematical tools that enable the description of the pore and solid phase distribution. Results show that 3-D image analysis is a powerful technique to characterise the morphological, structural and topological differences due to weathering. The paper also discusses criteria for mathematically determining whether a stone is weathered or not

Registration and Fusion of Multi-Spectral Images Using a Novel Edge Descriptor

In this paper we introduce a fully end-to-end approach for multi-spectral image registration and fusion. Our method for fusion combines images from different spectral channels into a single fused image by different approaches for low and high frequency signals. A prerequisite of fusion is a stage of geometric alignment between the spectral bands, commonly referred to as registration. Unfortunately, common methods for image registration of a single spectral channel do not yield reasonable results on images from different modalities. For that end, we introduce a new algorithm for multi-spectral image registration, based on a novel edge descriptor of feature points. Our method achieves an accurate alignment of a level that allows us to further fuse the images. As our experiments show, we produce a high quality of multi-spectral image registration and fusion under many challenging scenarios

The thiourea carrier in human erythrocytes

The main purpose of this work is to determine the characteristics of the thiourea carrier in human erythrocytes taking into consideration the two parameters of transfer (half-saturation constant and maximum transport rate) and the energy of dissociation of the carrier complex. In the president experiment, the problem has been approached by observing the exit of thiourea, from cells previously equilibrated with thiourea, into a saline medium containing different concentrations of thiourea. The most important advantages of this method are the rapidity of the exit process and the fact that it can be easily measured