Fluctuation Theorem for Quasi-Integrable Systems

A Fluctuation Theorem (FT), both Classical and Quantum, describes the large-deviations in the approach to equilibrium of an isolated quasi-integrable system. Two characteristics make it unusual: (i) it concerns the internal dynamics of an isolated system without external drive, and (ii) unlike the usual FT, the system size, or the time, need not be small for the relation to be relevant, provided the system is close to integrability. As an example, in the Fermi-Pasta-Ulam chain, the relation gives information on the ratio of probability of death to resurrection of solitons. For a coarse-grained system the FT describes how the system `skis' down the (minus) entropy landscape: always descending but generically not along a gradient line.Comment: 11 pages (6 main text + 5 supplemental material); 4 figure

Recombination Effects on Supernova Light Curves

The light curves of type-II supernovae (SNe) are believed to be highly affected by recombination of hydrogen that takes place in their envelopes. In this work, we analytically investigate the transition from a fully ionized envelope to a partially recombined one and its effects on the SN light curve. The motivation is to establish the underlying processes that dominate the evolution at late times when recombination takes place in the envelope, yet early enough so that $^{56}$Ni decay is a negligible source of energy. We consider the diffusion of photons through the envelope while analyzing the ionization fraction and the coupling between radiation and gas, and find that the main effect of recombination is on the evolution of the observed temperature. Before recombination the temperature decreases relatively fast, while after recombination starts it significantly reduces the rate at which the observed temperature drops with time. This behaviour is the main cause for the observed flattening in the optical bands, where for a typical red supergiant explosion, the recombination wave affects the bolometric luminosity only mildly during most of the photospheric phase. Moreover, the plateau phase observed in some type-II SNe is not a generic result of recombination, and it also depends on the density structure of the progenitor. This is one possible explanation to the different light curve decay rates observed in type II (P and L) SNe.Comment: Submitted to ApJ, after first referee report. This is a major revision of arXiv:1404.631

Quantum Kolmogorov-Sinai entropy and Pesin relation

International audienceWe discuss a quantum Kolmogorov-Sinai entropy defined as the entropy production per unit time resulting from coupling the system to a weak, auxiliary bath. The expressions we obtain are fully quantum but require that the system is such that there is a separation between the Ehrenfest and the correlation timescales. We show that they reduce to the classical definition in the semiclassical limit, one instance where this separation holds. We show a quantum (Pesin) relation between this entropy and the sum of positive eigenvalues of a matrix describing phase-space expansion. Generalizations to the case where entropy grows sublinearly with time are possible

Out-of-time-order correlator in weakly perturbed integrable systems

Classical quasi-integrable systems are known to have Lyapunov times much shorter than their ergodicity time, but the situation for their quantum counterparts is less well understood. As a first example, we examine the quantum Lyapunov exponent -- defined by the evolution of the 4-point out-of-time-order correlator (OTOC) -- of integrable systems which are weakly perturbed by an external noise, a setting that has proven to be illuminating in the classical case. In analogy to the tangent space in classical systems, we derive a linear superoperator equation which dictates the OTOC dynamics. We find that {\em i)} in the semi-classical limit the quantum Lyapunov exponent is given by the classical one: it scales as $\epsilon^{1/3}$, with $\epsilon$ being the variance of the random drive, leading to short Lyapunov times compared to the diffusion time (which is $\sim \epsilon^{-1}$). {\em ii)} in the highly quantal regime the Lyapunov instability is suppressed by quantum fluctuations, and {\em iii)} for sufficiently small perturbations the $\epsilon^{1/3}$ dependence is also suppressed -- another purely quantum effect which we explain. Several numerical examples which demonstrate the theoretical predictions are given. The implication for the results to the behavior of real near-integrable systems, and for quantum limits on chaos are briefly discussed

Quasi-integrable systems are slow to thermalize but may be good scramblers

Classical quasi-integrable systems are known to have Lyapunov times orders of magnitude shorter than their ergodic time, the most clear example being the Solar System. This puzzling fact may be understood by considering the simple situation of an integrable system perturbed by a weak, random noise: there is no KAM regime and the Lyapunov instability may be shown to happen almost tangent to the tori. We extend here this analysis to the quantum case, and show that the discrepancy between Lyapunov and ergodicity times still holds. Quantum mechanics limits the Lyapunov regime by spreading wavepackets on a torus up to a {\em prescrambling time}. Still, the system is a relatively good scrambler in the sense that $\lambda \hbar/ T$ is finite, at low temperature $T$. The essential features of the problem, both classical and quantum, are already present in a rotor that is kicked {\em weakly} but {\em randomly}