Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator

We study quench dynamics in the many-body Hilbert space using two isolated systems with a finite number of interacting particles: a paradigmatic model of randomly interacting bosons and a dynamical (clean) model of interacting spins-$1/2$. For both systems in the region of strong quantum chaos, the number of components of the evolving wave function, defined through the number of principal components $N_{pc}$ (or participation ratio), was recently found to increase exponentially fast in time [Phys. Rev. E 99, 010101R (2019)]. Here, we ask whether the out-of-time ordered correlator (OTOC), which is nowadays widely used to quantify instability in quantum systems, can manifest analogous time-dependence. We show that $N_{pc}$ can be formally expressed as the inverse of the sum of all OTOC's for projection operators. While none of the individual projection-OTOC's shows an exponential behavior, their sum decreases exponentially fast in time. The comparison between the behavior of the OTOC with that of the $N_{pc}$ helps us better understand wave packet dynamics in the many-body Hilbert space, in close connection with the problems of thermalization and information scrambling.Comment: 11 pages, 7 figure

Quantum interference-induced stability of repulsively bound pairs of excitations

We study the dynamics of two types of pairs of excitations which are bound despite their strong repulsive interaction. One corresponds to doubly occupied sites in one-dimensional Bose-Hubbard systems, the so-called doublons. The other is pairs of neighboring excited spins in anisotropic Heisenberg spin-1/2 chains. We investigate the possibility of decay of the bound pairs due to resonant scattering by a defect or due to collisions of the pairs. We find that the amplitudes of the corresponding transitions are very small. This is a result of destructive quantum interference and explains the stability of the bound pairs.Comment: 12 pages, 3 figure

Einstein Observatory solid state spectrometer observations of M87 and the Virgo cluster

X-ray observations of the galaxy M87 and of a region in the Virgo cluster displaced 7 minutes from the center of M87 are presented. X-ray spectra are obtained at these two locations with the slid state spectrometer onboard the Einstein Observatory. Emission lines were observed in both locations, indicating the presence of heavy elements at abundances approximately solar (to within a factor of 2). A temperature gradient, T increases from approximately 1.4 keV at the position of M87 to T approximately 3.35 keV 7' away, was detected. There is lower temperature thermal emission at the center of M87 with T approximately 0.6 keV, consistent with models for cooling flows in this cluster. In addition to the thermal emission, a power law component in the spectrum of M87, was detected consistent with that observed by HEAO-1, indicating that this component probably originates in the galaxy itself. The presence of intracluster gas having density approximately .001 cu cm and temperature approximately 30 million K is indicated

Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems

We study how the proximity to an integrable point or to localization as one approaches the atomic limit, as well as the mixing of symmetries in the chaotic domain, may affect the onset of thermalization in finite one-dimensional systems. We consider systems of hard-core bosons at half-filling with nearest neighbor hopping and interaction, and next-nearest neighbor interaction. The latter breaks integrability and induces a ground-state superfluid to insulator transition. By full exact diagonalization, we study chaos indicators and few-body observables. We show that when different symmetry sectors are mixed, chaos indicators associated with the eigenvectors, contrary to those related to the eigenvalues, capture the onset of chaos. The results for the complexity of the eigenvectors and for the expectation values of few-body observables confirm the validity of the eigenstate thermalization hypothesis in the chaotic regime, and therefore the occurrence of thermalization. We also study the properties of the off-diagonal matrix elements of few-body observables in relation to the transition from integrability to chaos and from chaos to localization.Comment: 12 pages, 13 figures, as published (Fig.09 was corrected in this final version

Biodiversity of Spongosorites coralliophaga (Stephens, 1915) on coral rubble at two contrasting cold-water coral reef settings

The authors would like to thank Bill Richardson (Master), the crew of the RRS James Cook, Will Handley and the Holland-I ROV team. We also thank all the specialists in taxonomy that provided important help with identification of species: Professor Paul Tyler (ophiuroids), Dr. Tammy Horton (amphipods), Dr. Graham Oliver (bivalves), Dr. Rob van Soest (sponges), Susan Chambers, Peter Garwood, Sue Hamilton, Raimundo Blanco Pérez (polychaetes). Also we would like to thank Val Johnston (University of Aberdeen) for her contribution to cruise preparations and John Polanski (University of Aberdeen) for his help onboard the RRS James Cook. Special thanks to Dr. Alexios P. Lolas (University of Thessaly, Greece) for all the artwork. Funding for the JC073 cruise was provided by the Natural Environment Research Council (NERC) UK Ocean Acidification (UKOA) research programme’s Benthic Consortium project (NE/H017305/1 to JMR). JMR acknowledges support from Heriot-Watt University’s Environment and Climate Change theme. GK was funded by a Marine Alliance for Science and Technology for Scotland (MASTS) Ph.D. scholarship.Peer reviewedPublisher PD

Fluctuations of a Greenlandic tidewater glacier driven by changes in atmospheric forcing : observations and modelling of Kangiata Nunaata Sermia, 1859–present

Acknowledgements. The authors wish to thank Stephen Price, Mauri Pelto, and the anonymous reviewer for their reviews and comments that helped to improve the manuscript. RACMO2.1 data were provided by Jan van Angelen and Michiel van den Broeke, IMAU, Utrecht University. MAR v3.2 data used for runoff calculations were provided by Xavier Fettweis, Department of Geography, University of Liège. The photogrammetric DEM used in Figs. 1 and 3 was provided by Kurt H. Kjær, Centre for GeoGenetics, University of Copenhagen. This research was financially supported by J. M. Lea’s PhD funding, NERC grant number NE/I528742/1. Support for F. M. Nick was provided through the Conoco-Phillips/Lundin Northern Area Program CRIOS project (Calving Rates and Impact on Sea Level).Peer reviewedPublisher PD

Domain wall dynamics in integrable and chaotic spin-1/2 chains

We study the time evolution of correlation functions, spin current, and local magnetization in an isolated spin-1/2 chain initially prepared in a sharp domain wall state. The results are compared with the level of spatial delocalization of the eigenstates of the system which is measured using the inverse participation ratio. Both integrable and non-integrable regimes are considered. Non-integrability is introduced to the integrable Hamiltonian with nearest neighbor couplings by adding a single site impurity field or by adding next-nearest-neighbor couplings. A monotonic correspondence between the enhancement of the level of delocalization, spin current and magnetization dynamics occurs in the integrable domain. This correspondence is however lost for chaotic models with weak Ising interactions.Comment: 9 pages, 5 figures, 1 tabl

An introduction to the spectrum, symmetries, and dynamics of spin-1/2 Heisenberg chains

Quantum spin chains are prototype quantum many-body systems. They are employed in the description of various complex physical phenomena. The goal of this paper is to provide an introduction to the subject by focusing on the time evolution of a Heisenberg spin-1/2 chain and interpreting the results based on the analysis of the eigenvalues, eigenstates, and symmetries of the system. We make available online all computer codes used to obtain our data.Comment: 8 pages, 3 figure

Exponentially fast dynamics of chaotic many-body systems

We demonstrate analytically and numerically that in isolated quantum systems of many interacting particles, the number of many-body states participating in the evolution after a quench increases exponentially in time, provided the eigenstates are delocalized in the energy shell. The rate of the exponential growth is defined by the width $\Gamma$ of the local density of states (LDOS) and is associated with the Kolmogorov-Sinai entropy for systems with a well defined classical limit. In a finite system, the exponential growth eventually saturates due to the finite volume of the energy shell. We estimate the time scale for the saturation and show that it is much larger than $\hbar/\Gamma$. Numerical data obtained for a two-body random interaction model of bosons and for a dynamical model of interacting spin-1/2 particles show excellent agreement with the analytical predictions.Comment: 11 pages, 5 figures (as published