Universality of spectra for interacting quantum chaotic systems

We analyze a model quantum dynamical system subjected to periodic interaction with an environment, which can describe quantum measurements. Under the condition of strong classical chaos and strong decoherence due to large coupling with the measurement device, the spectra of the evolution operator exhibit an universal behavior. A generic spectrum consists of a single eigenvalue equal to unity, which corresponds to the invariant state of the system, while all other eigenvalues are contained in a disk in the complex plane. Its radius depends on the number of the Kraus measurement operators, and determines the speed with which an arbitrary initial state converges to the unique invariant state. These spectral properties are characteristic of an ensemble of random quantum maps, which in turn can be described by an ensemble of real random Ginibre matrices. This will be proven in the limit of large dimension.Comment: 11 pages, 10 figure

Plankton lattices and the role of chaos in plankton patchiness

Spatiotemporal and interspecies irregularities in planktonic populations have been widely observed. Much research into the drivers of such plankton patches has been initiated over the past few decades but only recently have the dynamics of the interacting patches themselves been considered. We take a coupled lattice approach to model continuous-in-time plankton patch dynamics, as opposed to the more common continuum type reaction-diffusion-advection model, because it potentially offers a broader scope of application and numerical study with relative ease. We show that nonsynchronous plankton patch dynamics (the discrete analog of spatiotemporal irregularity) arise quite naturally for patches whose underlying dynamics are chaotic. However, we also observe that for parameters in a neighborhood of the chaotic regime, smooth generalized synchronization of nonidentical patches is more readily supported which reduces the incidence of distinct patchiness. We demonstrate that simply associating the coupling strength with measurements of (effective) turbulent diffusivity results in a realistic critical length of the order of 100 km, above which one would expect to observe unsynchronized behavior. It is likely that this estimate of critical length may be reduced by a more exact interpretation of coupling in turbulent flows