Non-equilibrium statistical mechanics of one-dimensional gases confined by perfectly reflecting walls
In this paper, we study the time evolution of confined one-dimensional gases. We deal with both one-dimensional ideal gases and non-ideal gases confined by perfectly reflecting walls. A major theme of the paper is the use of analytical approaches for studying the effects of smoothness conditions on the time evolution of these systems. We derive analytical expressions for the time evolution of the density distribution, momentum current, local kinetic energy density, and, when possible, the reduced single-particle momentum distribution function of confined one-dimensional gases. In the first half of the paper, we use two approaches to analyze the confined ideal gas: multiple reflection expansions and an approach using Fourier series and generating functions. In the second half of the paper, we use the method of iterative projections to study the time evolution of confined one-dimensional non-ideal gases with short range interactions. In analyzing confined non-ideal gases with short range interactions, we adapt analytical results on transport phenomena in the presence of external fields derived in previous work.