The stationary Boltzmann equation for hard and soft forces in the context of a two component gas is considered in the slab when the molecular masses of the 2 component are different. An L existence theorem is proved when one component satisfies a given indata profile and the other component satisfies diffuse reflection at the boundaries. Weak L compactness is extracted from the control of the e...

Solving the Dirac equation is a formidable task due to the high frequency and the degrees of freedom involved. However, this high frequency allows one to obtain an approximation to the equation. Here, we directly solve the Dirac equation using an envelope method and derive analytical solutions of Dirac wave packets to first order for the small momentum spread. We apply the insight gained from t...

The measure problem of cosmology is how to obtain normalized probabilities of observations from the quantum state of the universe. This is particularly a problem when eternal inflation leads to a universe of unbounded size so that there are apparently infinitely many realizations or occurrences of observations of each of many different kinds or types, making the ratios ambiguous. There is also ...

A graph technique analogous to the usual Feynman technique in field theory is developed for calculating Green's functions for particles in a statistical system which under the action of an external field deviates to any arbitrary extent from the state of thermodynamic equilibrium. It is found that in order to describe such a system it is necessary to introduce two Green's functions for each typ...

The problem of computing the electrostatic energy of a large molecule is considered. It is reduced to solving the Poisson equation inside and the linear Poisson-Boltzmann equation in the exterior, coupled by boundary conditions. A Monte Carlo estimate for the potential point values, their derivatives, and the energy is constructed. The estimate is based on the walk on spheres and Green’s functi...

The formalism of graded Poisson-sigma models allows the construction of N = (2, 2) dilaton supergravity in terms of a minimal number of fields. For the gauged chiral U(1) symmetry the full action, involving all fermionic contributions , is derived. The twisted chiral case follows by simple redefinition of fields. The equivalence of our approach to the standard second order one in terms of super...