Correspondence in Quasiperiodic and Chaotic Maps: Quantization via the von Neumann Equation

A generalized approach to the quantization of a large class of maps on a torus, i.e. quantization via the von Neumann Equation, is described and a number of issues related to the quantization of model systems are discussed. The approach yields well behaved mixed quantum states for tori for which the corresponding Schrodinger equation has no solutions, as well as an extended spectrum for tori where the Schrodinger equation can be solved. Quantum-classical correspondence is demonstrated for the class of mappings considered, with the Wigner-Weyl density $\rho(p,q,t)$ going to the correct classical limit. An application to the cat map yields, in a direct manner, nonchaotic quantum dynamics, plus the exact chaotic classical propagator in the correspondence limit.Comment: 36 pages, RevTex preprint forma

Exponential Divergence and Long Time Relaxation in Chaotic Quantum Dynamics

Phase space representations of the dynamics of the quantal and classical cat map are used to explore quantum--classical correspondence in a K-system: as $\hbar \to 0$, the classical chaotic behavior is shown to emerge smoothly and exactly. The quantum dynamics near the classical limit displays both exponential separation of adjacent distributions and long time relaxation, two characteristic features of classical chaotic motion.Comment: 10 pages, ReVTeX, to appear in Phys. Rev. Lett. 13 figures NOT included. Available either as LARGE (uuencoded gzipped) postscript files or hard-copies from [email protected]

You should go for diversity, but I'd rather stay with similar others: Social distance modulates the preference for diversity

Organizations often state that they value diversity. The workforce, however, is often quite homogeneous, reflecting a striking mismatch between aspirations and reality. Based on the distinction between desirability and feasibility concerns, we provide a psychological argument for this mismatch. We hypothesize that social distance influences individuals' choices regarding diversity. When being socially more distant, individuals prefer to assemble a diverse team, due to a stronger impact of pro-diversity desirability concerns. In contrast, when being socially close, individuals prefer similar team members, due to a stronger weighing of anti-diversity feasibility concerns. Four studies investigate the different decision outcomes when being socially distant compared to close. Study 1 shows that working in a diverse group is perceived as desirable, but less feasible. Study 2 investigates the impact of psychological distance on individuals' choices of working with a more different (when being socially distant) or similar partner (when being socially close). Study 3 shows that participants created a more diverse team for another person (distance condition) than for themselves (proximity condition). In Study 4, participants did not create a more diverse group for a stranger (distance condition) than for a friend (adjusted proximity condition), however, participants weighted feasibility concerns less strongly for strangers than for friends. Implications for diversity research and practice are discussed

Stochastic Transition States: Reaction Geometry amidst Noise

Classical transition state theory (TST) is the cornerstone of reaction rate theory. It postulates a partition of phase space into reactant and product regions, which are separated by a dividing surface that reactive trajectories must cross. In order not to overestimate the reaction rate, the dynamics must be free of recrossings of the dividing surface. This no-recrossing rule is difficult (and sometimes impossible) to enforce, however, when a chemical reaction takes place in a fluctuating environment such as a liquid. High-accuracy approximations to the rate are well known when the solvent forces are treated using stochastic representations, though again, exact no-recrossing surfaces have not been available. To generalize the exact limit of TST to reactive systems driven by noise, we introduce a time-dependent dividing surface that is stochastically moving in phase space such that it is crossed once and only once by each transition path

From Heisenberg matrix mechanics to EBK quantization: theory and first applications

Despite the seminal connection between classical multiply-periodic motion and Heisenberg matrix mechanics and the massive amount of work done on the associated problem of semiclassical (EBK) quantization of bound states, we show that there are, nevertheless, a number of previously unexploited aspects of this relationship that bear on the quantum-classical correspondence. In particular, we emphasize a quantum variational principle that implies the classical variational principle for invariant tori. We also expose the more indirect connection between commutation relations and quantization of action variables. With the help of several standard models with one or two degrees of freedom, we then illustrate how the methods of Heisenberg matrix mechanics described in this paper may be used to obtain quantum solutions with a modest increase in effort compared to semiclassical calculations. We also describe and apply a method for obtaining leading quantum corrections to EBK results. Finally, we suggest several new or modified applications of EBK quantization.Comment: 37 pages including 3 poscript figures, submitted to Phys. Rev.

The XXL Survey: XII. Optical spectroscopy of X-ray-selected clusters and the frequency of AGN in superclusters

This article belongs to the first series of XXL publications. It presents multifibre spectroscopic observations of three 0.55 sq.deg. fields in the XXL Survey, which were selected on the basis of their high density of X-ray-detected clusters. The observations were obtained with the AutoFib2+WYFFOS (AF2) wide-field fibre spectrograph mounted on the 4.2m William Herschel Telescope. The paper first describes the scientific rationale, the preparation, the data reduction, and the results of the observations, and then presents a study of active galactic nuclei (AGN) within three superclusters. We obtained redshifts for 455 galaxies in total, 56 of which are counterparts of X-ray point-like sources. We were able to determine the redshift of the merging supercluster XLSSC-e, which consists of six individual clusters at z~0.43, and we confirmed the redshift of supercluster XLSSC-d at z~0.3. More importantly, we discovered a new supercluster, XLSSC-f, that comprises three galaxy clusters also at z~0.3. We find a significant 2D overdensity of X-ray point-like sources only around the supercluster XLSSC-f. This result is also supported by the spatial (3D) analysis of XLSSC-f, where we find four AGN with compatible spectroscopic redshifts and possibly one more with compatible photometric redshift. In addition, we find two AGN (3D analysis) at the redshift of XLSSC-e, but no AGN in XLSSC-d. Comparing these findings with the optical galaxy overdensity we conclude that the total number of AGN in the area of the three superclusters significantly exceeds the field expectations. The difference in the AGN frequency between the three superclusters cannot be explained by the present study because of small number statistics. Further analysis of a larger number of superclusters within the 50 sq. deg. of the XXL is needed before any conclusions on the effect of the supercluster environment on AGN can be reached.Comment: 11 pages, published by A&

GASP XVIII: Star formation quenching due to AGN feedback in the central region of a jellyfish galaxy

We report evidence for star formation quenching in the central 8.6 kpc region of the jellyfish galaxy JO201 which hosts an active galactic nucleus, while undergoing strong ram pressure stripping. The ultraviolet imaging data of the galaxy disk reveal a region with reduced flux around the center of the galaxy and a horse shoe shaped region with enhanced flux in the outer disk. The characterization of the ionization regions based on emission line diagnostic diagrams shows that the region of reduced flux seen in the ultraviolet is within the AGN-dominated area. The CO J$_{2-1}$ map of the galaxy disk reveals a cavity in the central region. The image of the galaxy disk at redder wavelengths (9050-9250 \overset{\lower.5em\circ}{\mathrm{A}}) reveals the presence of a stellar bar. The star formation rate map of the galaxy disk shows that the star formation suppression in the cavity occurred in the last few 10$^8$ yr. We present several lines of evidence supporting the scenario that suppression of star formation in the central region of the disk is most likely due to the feedback from the AGN. The observations reported here make JO201 a unique case of AGN feedback and environmental effects suppressing star formation in a spiral galaxy.Comment: Author's accepted manuscrip

GASP IV: A muse view of extreme ram-pressure stripping in the plane of the sky: the case of jellyfish galaxy JO204

In the context of the GAs Stripping Phenomena in galaxies with Muse (GASP) survey, we present the characterization of JO204, a jellyfish galaxy in A957, a relatively low-mass cluster with $M=4.4 \times10^{14}M_\odot$. This galaxy shows a tail of ionized gas that extends up to 30 kpc from the main body in the opposite direction of the cluster center. No gas emission is detected in the galaxy outer disk, suggesting that gas stripping is proceeding outside-in. The stellar component is distributed as a regular disk galaxy; the stellar kinematics shows a symmetric rotation curve with a maximum radial velocity of 200km/s out to 20 kpc from the galaxy center. The radial velocity of the gas component in the central part of the disk follows the distribution of the stellar component; the gas kinematics in the tail retains the rotation of the galaxy disk, indicating that JO204 is moving at high speed in the intracluster medium. Both the emission and radial velocity maps of the gas and stellar components indicate ram-pressure as the most likely primary mechanism for gas stripping, as expected given that JO204 is close to the cluster center and it is likely at the first infall in the cluster. The spatially resolved star formation history of JO204 provides evidence that the onset of ram-pressure stripping occurred in the last 500 Myr, quenching the star formation activity in the outer disk, where the gas has been already completely stripped. Our conclusions are supported by a set of hydrodynamic simulations.Comment: accepted for publication in Ap

Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape

Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events by crossing periodic orbit around saddles. Both of these frameworks require computation with curves represented by millions of points-computing intersection points between these curves and area bounded by the segments of these curves-for quantifying the transport and escape rate. We present a theory for computing these intersection points and the area bounded between the segments of these curves based on a classification of the intersection points using equivalence class. We also present an alternate theory for curves with nontransverse intersections and a method to increase the density of points on the curves for locating the intersection points accurately.The numerical implementation of the theory presented herein is available as an open source software called Lober. We used this package to demonstrate the application of the theory to lobe dynamics that arises in fluid mechanics, and rate of escape from a potential well that arises in ship dynamics.Comment: 33 pages, 17 figure

Geometrical Models of the Phase Space Structures Governing Reaction Dynamics

Hamiltonian dynamical systems possessing equilibria of ${saddle} \times {centre} \times...\times {centre}$ stability type display \emph{reaction-type dynamics} for energies close to the energy of such equilibria; entrance and exit from certain regions of the phase space is only possible via narrow \emph{bottlenecks} created by the influence of the equilibrium points. In this paper we provide a thorough pedagogical description of the phase space structures that are responsible for controlling transport in these problems. Of central importance is the existence of a \emph{Normally Hyperbolic Invariant Manifold (NHIM)}, whose \emph{stable and unstable manifolds} have sufficient dimensionality to act as separatrices, partitioning energy surfaces into regions of qualitatively distinct behavior. This NHIM forms the natural (dynamical) equator of a (spherical) \emph{dividing surface} which locally divides an energy surface into two components (`reactants' and `products'), one on either side of the bottleneck. This dividing surface has all the desired properties sought for in \emph{transition state theory} where reaction rates are computed from the flux through a dividing surface. In fact, the dividing surface that we construct is crossed exactly once by reactive trajectories, and not crossed by nonreactive trajectories, and related to these properties, minimizes the flux upon variation of the dividing surface. We discuss three presentations of the energy surface and the phase space structures contained in it for 2-degree-of-freedom (DoF) systems in the threedimensional space $\R^3$, and two schematic models which capture many of the essential features of the dynamics for $n$-DoF systems. In addition, we elucidate the structure of the NHIM.Comment: 44 pages, 38 figures, PDFLaTe