Fermionic stochastic differential equations and the index of Fredholm operators

The index of a Fredholm operator associated to a-summable Fredholm module is expressed in terms of the vacuum expectation value of a unitary operator-valued stochastic process which satisfies a stochastic differential equation with unbounded coefficients driven by fermion noise.     

Plasma Photocathodes

Plasma wakefield accelerators offer accelerating and focusing electric fields three to four orders of magnitude larger than state-of-the-art radiofrequency cavity-based accelerators. Plasma photocathodes can release ultracold electron populations within such plasma waves and thus open a path toward tunable production of well-defined, compact electron beams with normalized emittance and brightness many orders of magnitude better than state-of-the-art. Such beams will have far-reaching impact for applications such as light sources, but also open up new vistas on high energy and high field physics. This paper reviews the innovation of plasma photocathodes, and reports on the experimental progress, challenges, and future prospects of the approach. Details of the proof-of-concept demonstration of a plasma photocathode in 90° geometry at SLAC FACET within the E-210: Trojan Horse program are described. Using this experience, alongside theoretical and simulation-supported advances, an outlook is given on future realizations of plasma photocathodes such as the upcoming E-310: Trojan Horse-II program at FACET-II with prospects toward excellent witness beam parameter quality, tunability, and stability. Future installations of plasma photocathodes also at compact, hybrid plasma wakefield accelerators, will then boost capacities and open up novel capabilities for experiments at the forefront of interaction of high brightness electron and photon beams.     

On a Class of Non-Translation Invariant Feller Semigroups on Lie Groups

We consider a class of Feller semigroups on Lie groups which fail to commute with left translation due to the existence of a cocycle h which is identically one for Lévy processes. Under certain conditions, we are able to show that the infinitesimal generator of such a semigroup has the Lévy–Khintchine–Hunt form but with variable characteristics, thus we obtain an extension of classical work in Euclidean space by Courrège.     

On a class of stochastic flows driven by quantum Brownian motion

A class of quantum stochastic flows on^*-algebras is introduced which includes both classical flows on Riemannian manifolds and flows induced by Lie group actions onC ^*-algebras. Criteria are established to determine those flows which are unitarily equivalent to ones driven by classical Brownian motion. It is shown that taking complex combinations of the driving coefficients of such flows gives rise to flows which are not of Evans-Hudson type (i.e., all driving coefficients do not preserve the relevant algebra).     

Unusual transformations of the chrysanthemic nitrile skeleton by sodium hydride in n,n-dimethylformamide

It is shown that the title transformations occurred through basecatalyzed opening of the cyclopropane ring into the dienic nitrile $\text{4}$which then reacted with the in situ formed formaldehyde to yield the bicyclic compound $\text{5}$.     

Notes on plane partitions VI

We consider the problem of plane partitions with given minimal differences between parts along rows and columns. We obtain a formula for the generating function in the two row case.     

Novel electrophoresis mechanism based on synchronous alternating drag perturbation

We present a novel means of transporting molecules in solution by applying a zero-time-average alternating motive force to the molecules, and perturbing the molecular drag coefficient synchronously with the applied force, thus causing a net drift in a direction determined by the phase of the alternating drag perturbation relative to the alternating force. We apply an electrophoretic form of the method to transport and concentrate DNA in a gel, such that all molecules migrate on average away from the nearest electrode and toward a central region. Since an electrode does not occupy this central region, this method presents the possibility of transporting and focusing DNA and other charged molecules in regions free from electrodes and the associated electrochemistry.