Nonlinear unbalanced Bessel beams in the collapse of Gaussian beams arrested by nonlinear losses

Collapse of a Gaussian beam in self-focusing Kerr media arrested by nonlinear losses may lead to the spontaneous formation of a quasi-stationary nonlinear unbalanced Bessel beam with finite energy, which can propagate without significant distortion over tens of diffraction lengths, and without peak intensity attenuation while the beam power is drastically diminishing.Comment: 4 pages, 5 figure

The Flow Permanence Index: A Statistical Assessment of Flow Regime in Austin Streams

The report makes two explicit mentions of Waller Creek, briefly mentioning flow patterns and how they are highest near its mouth. In addition, the report contains valuable information concerning the importance of baseflow in the sustainability of a creek ecosystem.Flow permanence or the reliability of baseflow in a stream is an important metric in determining the potential of local streams to support aquatic life and can be used to provide an indication of future ecological changes. This report looks at quantifying the probabilities associated with permanent flow at all streams monitored for the City of Austin Environmental Integrity Index. Spatial patterns in flow permanence were examined, as well as the contributions of rainfall to flow permanence. Among the principal results is an index and ranking of streams with the most and least consistently flowing monitoring sites and a heuristic to calculate the probability of flow in a stream given the cumulative rainfall in the previous three months.Waller Creek Working Grou

Quantum chaotic fluctuation-dissipation theorem: effective Brownian motion in closed quantum systems

We analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable in terms of the rate of decay to equilibrium. Our result shows the emergence of a Fluctuation-Dissipation theorem corresponding to a classical Brownian process, specifically, the Ornstein-Uhlenbeck process. Our predictions can be tested in quantum simulation experiments, thus helping to bridge the gap between theoretical and experimental research in quantum thermalization. We test our analytic results by exact numerical experiments in a spin-chain. We argue that our Fluctuation-Dissipation relation can be used to measure the density of states involved in the non-equilibrium dynamics of an isolated quantum system

Ergodicity probes: using time-fluctuations to measure the Hilbert space dimension

Quantum devices, such as quantum simulators, quantum annealers, and quantum computers, may be exploited to solve problems beyond what is tractable with classical computers. This may be achieved as the Hilbert space available to perform such `calculations' is far larger than that which may be classically simulated. In practice, however, quantum devices have imperfections, which may limit the accessibility to the whole Hilbert space. We thus determine that the dimension of the space of quantum states that are available to a quantum device is a meaningful measure of its functionality, though unfortunately this quantity cannot be directly experimentally determined. Here we outline an experimentally realisable approach to obtaining the required Hilbert space dimension of such a device to compute its time evolution, by exploiting the thermalization dynamics of a probe qubit. This is achieved by obtaining a fluctuation-dissipation theorem for high-temperature chaotic quantum systems, which facilitates the extraction of information on the Hilbert space dimension via measurements of the decay rate, and time-fluctuations