A theory of non-local linear drift wave transport

Transport events in turbulent tokamak plasmas often exhibit non-local or non-diffusive action at a distance features that so far have eluded a conclusive theoretical description. In this paper a theory of non-local transport is investigated through a Fokker-Planck equation with fractional velocity derivatives. A dispersion relation for density gradient driven linear drift modes is derived including the effects of the fractional velocity derivative in the Fokker-Planck equation. It is found that a small deviation (a few percent) from the Maxwellian distribution function alters the dispersion relation such that the growth rates are substantially increased and thereby may cause enhanced levels of transport.Comment: 22 pages, 2 figures. Manuscript submitted to Physics of Plasma

A Fractional Fokker-Planck Model for Anomalous Diffusion

In this paper we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality observing the transition from a Gaussian distribution to a L\'evy distribution. The statistical properties of the distribution functions are assessed by a generalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.Comment: 22 pages, 14 figure

Levy statistics and anomalous transport in quantum-dot arrays

A novel model of transport is proposed to explain power law current transients and memory phenomena observed in partially ordered arrays of semiconducting nanocrystals. The model describes electron transport by a stationary Levy process of transmission events and thereby requires no time dependence of system properties. The waiting time distribution with a characteristic long tail gives rise to a nonstationary response in the presence of a voltage pulse. We report on noise measurements that agree well with the predicted non-Poissonian fluctuations in current, and discuss possible mechanisms leading to this behavior.Comment: 7 pages, 2 figure

Generic Continuous Spectrum for Ergodic Schr"odinger Operators

We consider discrete Schr"odinger operators on the line with potentials generated by a minimal homeomorphism on a compact metric space and a continuous sampling function. We introduce the concepts of topological and metric repetition property. Assuming that the underlying dynamical system satisfies one of these repetition properties, we show using Gordon's Lemma that for a generic continuous sampling function, the associated Schr"odinger operators have no eigenvalues in a topological or metric sense, respectively. We present a number of applications, particularly to shifts and skew-shifts on the torus.Comment: 14 page

Accurate thermal conductivities from optimally short molecular dynamics simulations

The evaluation of transport coefficients in extended systems, such as thermal conductivity or shear viscosity, is known to require impractically long simulations, thus calling for a paradigm shift that would allow to deploy state-of-the-art quantum simulation methods. We introduce a new method to compute these coefficients from optimally short molecular dynamics simulations, based on the Green-Kubo theory of linear response and the cepstral analysis of time series. Information from the full sample power spectrum of the relevant current for a single and relatively short trajectory is leveraged to evaluate and optimally reduce the noise affecting its zero-frequency value, whose expectation is proportional to the corresponding conductivity. Our method is unbiased and consistent, in that both the resulting bias and statistical error can be made arbitrarily small in the long-time limit. A simple data-analysis protocol is proposed and validated with the calculation of thermal conductivities in the paradigmatic cases of elemental and molecular fluids (liquid Ar and H2O) and of crystalline and glassy solids (MgO and a-SiO2). We find that simulation times of one to a few hundred picoseconds are sufficient in these systems to achieve an accuracy of the order of 10% on the estimated thermal conductivities

Quantum Rings in Electromagnetic Fields

This is the author accepted manuscript. The final version is available from Springer via the DOI in this recordThis chapter is devoted to optical properties of so-called Aharonov-Bohm quantum rings (quantum rings pierced by a magnetic flux resulting in AharonovBohm oscillations of their electronic spectra) in external electromagnetic fields. It studies two problems. The first problem deals with a single-electron AharonovBohm quantum ring pierced by a magnetic flux and subjected to an in-plane (lateral) electric field. We predict magneto-oscillations of the ring electric dipole moment. These oscillations are accompanied by periodic changes in the selection rules for inter-level optical transitions in the ring allowing control of polarization properties of the associated terahertz radiation. The second problem treats a single-mode microcavity with an embedded Aharonov-Bohm quantum ring which is pierced by a magnetic flux and subjected to a lateral electric field. We show that external electric and magnetic fields provide additional means of control of the emission spectrum of the system. In particular, when the magnetic flux through the quantum ring is equal to a half-integer number of the magnetic flux quanta, a small change in the lateral electric field allows for tuning of the energy levels of the quantum ring into resonance with the microcavity mode, thus providing an efficient way to control the quantum ring-microcavity coupling strength. Emission spectra of the system are discussed for several combinations of the applied magnetic and electric fields

Physical Processes in Star Formation

© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s11214-020-00693-8.Star formation is a complex multi-scale phenomenon that is of significant importance for astrophysics in general. Stars and star formation are key pillars in observational astronomy from local star forming regions in the Milky Way up to high-redshift galaxies. From a theoretical perspective, star formation and feedback processes (radiation, winds, and supernovae) play a pivotal role in advancing our understanding of the physical processes at work, both individually and of their interactions. In this review we will give an overview of the main processes that are important for the understanding of star formation. We start with an observationally motivated view on star formation from a global perspective and outline the general paradigm of the life-cycle of molecular clouds, in which star formation is the key process to close the cycle. After that we focus on the thermal and chemical aspects in star forming regions, discuss turbulence and magnetic fields as well as gravitational forces. Finally, we review the most important stellar feedback mechanisms.Peer reviewedFinal Accepted Versio