Electrical conductivity of hot Abelian plasma with scalar charge carriers

We study the electrical conductivity of hot Abelian plasma containing scalar charge carriers in the leading logarithmic order in coupling constant $\alpha$ using the Boltzmann kinetic equation. The leading contribution to the collision integral is due to the M{\o}ller and Bhabha scattering of scalar particles with a singular cross section in the region of small momentum transfer. Regularizing this singularity by taking into account the hard thermal loop corrections to the propagators of intermediate particles, we derive the second order differential equation which determines the kinetic function. We solve this equation numerically and also use a variational approach in order to find a simple analytical formula for the conductivity. It has the standard parametric dependence on the coupling constant $\sigma\approx 2.38\, T/(\alpha \log\alpha^{-1})$ with the prefactor taking a somewhat lower value compared to the fermionic case. Finally, we consider the general case of hot Abelian plasma with an arbitrary number of scalar and fermionic particle species and derive the simple analytical formula for its conductivity.Comment: 36 pages, 2 figures, 4 table

Charging the Poor: Criminal Justice Debt & Modern-Day Debtors’ Prisons

Debtors’ prisons should no longer exist. While imprisonment for debt was common in colonial times in the United States, subsequent constitutional provisions, legislation, and court rulings all called for the abolition of incarcerating individuals to collect debt. Despite these prohibitions, individuals who are unable to pay debts are now regularly incarcerated, and the vast majority of them are indigent. In 2015, at least ten lawsuits were filed against municipalities for incarcerating individuals in modern-day debtors’ prisons. Criminal justice debt is the primary source for this imprisonment. Criminal justice debt includes fines, restitution charges, court costs, and fees. Monetary charges exist at all stages of the criminal justice system from pre-conviction to parole. They include a wide variety of items, such as fees for electronic monitoring, probation, and room and board. Forty-three states even charge fees for an indigent’s “free” public defender. With expanding incarceration rates and contracting state budgets, monetary sanctions have continued to escalate. Additionally, many states and localities are now outsourcing prison, probation, monitoring, and collection services to private companies, who add additional fees and charges to the criminal justice debt burden of defendants. The impact of criminal justice debt is especially severe on the poor and minorities as they are frequently assessed “poverty penalties” for interest, late fees, installment plans, and collection. Often they have to decide between paying criminal justice debt and buying family necessities. The deaths of Michael Brown in Ferguson, Eric Garner in New York, and Freddie Gray in Baltimore have prompted renewed calls for investigation of the adverse treatment of the poor and minorities in the criminal justice system. The fear of arrest, incarceration, and unfair treatment for those owing criminal justice debt creates distrust in the system. In February 2015, a class action complaint was filed against the City of Ferguson asserting that the city’s jails had become a “modern debtors’ prison scheme” that had “devastated the City’s poor, trapping them for years in a cycle of increased fees, debts, extortion, and cruel jailings.” Moreover, the Department of Justice’s report on the Ferguson Police Department presents a scathing indictment of a system apparently more concerned with revenue collection than justice. Unfortunately, as illustrated by recent lawsuits and investigations alleging debtors’ prisons in Alabama, Colorado, Georgia, Louisiana, Mississippi, New Hampshire, Ohio, Oklahoma, Tennessee, Texas, and Washington, the abuses are not limited to Ferguson, Missouri. The same concerns that led to the historical restrictions on debtors’ prisons have risen again with the growth of modern-day debtors’ prisons. Similar to the prisons in London during the eighteenth and nineteenth centuries that were criticized for using a privatized system that charged inmates for all services, including room and board, the current justice system improperly charges the poor. It is now time to revisit these concerns and implement effective restrictions to reduce the incidence of debtors’ prisons. To remedy these concerns, my Article proposes eliminating egregious sanctions, providing courts flexibility to base fines on earning levels, and establishing procedures to enforce restrictions against incarcerating those who are truly unable to pay their criminal justice debt

Foreign ownership of U.S. Treasury securities: what the data show and do not show

The Treasury Department makes available to the public considerable information about foreign holdings of its securities. Nevertheless, it is not possible to determine from the published data exactly which foreigners own U.S. Treasury debt and how much of this debt is in foreign hands.Treasury bills ; Investments, Foreign - United States

Kolmogorov equations in infinite dimensions: Well-posedness and regularity of solutions, with applications to stochastic generalized Burgers equations

We develop a new method to uniquely solve a large class of heat equations, so-called Kolmogorov equations in infinitely many variables. The equations are analyzed in spaces of sequentially weakly continuous functions weighted by proper (Lyapunov type) functions. This way for the first time the solutions are constructed everywhere without exceptional sets for equations with possibly nonlocally Lipschitz drifts. Apart from general analytic interest, the main motivation is to apply this to uniquely solve martingale problems in the sense of Stroock--Varadhan given by stochastic partial differential equations from hydrodynamics, such as the stochastic Navier--Stokes equations. In this paper this is done in the case of the stochastic generalized Burgers equation. Uniqueness is shown in the sense of Markov flows.Comment: Published at http://dx.doi.org/10.1214/009117905000000666 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org