Out-of-time-order correlators in quantum mechanics

The out-of-time-order correlator (OTOC) is considered as a measure of quantum chaos. We formulate how to calculate the OTOC for quantum mechanics with a general Hamiltonian. We demonstrate explicit calculations of OTOCs for a harmonic oscillator, a particle in a one-dimensional box, a circle billiard and stadium billiards. For the first two cases, OTOCs are periodic in time because of their commensurable energy spectra. For the circle and stadium billiards, they are not recursive but saturate to constant values which are linear in temperature. Although the stadium billiard is a typical example of the classical chaos, an expected exponential growth of the OTOC is not found. We also discuss the classical limit of the OTOC. Analysis of a time evolution of a wavepacket in a box shows that the OTOC can deviate from its classical value at a time much earlier than the Ehrenfest time.Comment: 30 pages, 13 figure

An Overlooked Excerpt of the Chronicle of George the Monk in Codex Parisinus Suppl. gr. 1238

This article identifies two hitherto unidentified texts on fols. 4v–8r of the codex Parisinus Suppl. gr. 1238 that are, in fact, a sequential excerpt from the Vulgate version of the Chronicle of George the Monk. The excerpt, which had become independent presumably at an early stage of the Chronicle’s textual transmission, offers an example indicating the Chronicle was used as a source of Byzantine legal practices

Meson turbulence at quark deconfinement from AdS/CFT

Based on the QCD string picture at confining phase, we conjecture that the deconfinement transition always accompanies a condensation of higher meson resonances with a power-law behavior, "meson turbulence". We employ the AdS/CFT correspondence to calculate the meson turbulence for $\mathcal{N}=2$ supersymmetric QCD at large $N_c$ and at strong coupling limit, and find that the energy distribution to each meson level $n$ scales as $n^\alpha$ with the universal scaling $\alpha=-5$. The universality is checked for various ways to attain the quark deconfinement: a static electric field below/around the critical value, a time-dependent electric field quench, and a time-dependent quark mass quench, all result in the turbulent meson condensation with the universal power $\alpha=-5$ around the deconfinement.Comment: 20 pages, 17 figure