Recent experiments have renewed interest in nonlocal interpretations of quantum mechanics. The experimental observation of the violation of Bell's inequalities implies the existence of nonlocality. Bohm expressed the nonlocal connection between quantum particles through the wave function and the quantum potential. This paper shows that a similar connection exists in a relativistic dynamical theory known as parametrized relativistic quantum theory (PRQT). We present an introduction to PRQT, derive the quantum potential for a system of relativistic scalar particles, and discuss alternative interpretations of nonlocality.

Nonlocality in Relativistic Dynamics

We study, by numerical and analytical means, the evolution of a uniform one-dimensional collisionless plasma initiated between plane absorbing walls. The ensuing flow is described by rarefaction waves that propagate symmetrically inward from the boundaries, interact, and eventually vanish after crossing through, leading up to the asymptotic phase.

Collisionless Adiabatic Afterglow.

We study, by numerical and analytical means, the evolution of a collisionless plasma initiated between absorbing walls. The ensuing flow is described by rarefaction waves that travel inward from the boundaries, interact, and eventually vanish after crossing through, leading up to the asymptotic stage of the decay. Particle simulations indicate that the kinetic evolution strongly resembles one found in isentropic gas dynamics. Namely, a very gradual density profile forms in the expanding central region where the rarefaction waves interact, with an accompanying linear velocity profile. Asymptotically, the density falls off as 1 / t. The density and the flux at the boundary show little variation over the period when rarefaction waves still exist. Plasma potential, on the other hand, drops quite rapidly (on the underlying ion-acoustic timescale) to less than initial electron temperature Te when over 70% of the particles still remain in the system. This is due to electron kinetics being governed by conservation of adiabatic invariant in a slowly varying potential well. Analytical model of the velocity distribution is presented to explain the simulations. The results have implications for afterglow plasmas used in material processing and also for ion-extraction devices. One property of potential interest is good uniformity of the decaying plasma that occurs after approximately one ion-acoustic time.

Collisionless Adiabatic Afterglow

A one‐dimensional gas flow is generated by a piston which moves at a constant velocity out of a pipe filled with gas. The piston causes a rarefaction wave which is reflected against the closed end of the pipe. According to the theory as described by Landau and Lifshitz the reflection process is governed by the solution of a linear partial differential equation with the adiabatic exponent γ as a parameter. Explicit solutions are obtained for γ=5/3 and γ=7/5, corresponding to the theoretical values for monoatomic and diatomic ideal gases, respectively. In this paper an explicit solution for arbitrary γ is given and applied specifically to the case γ=4/3, corresponding to a polyatomic ideal gas.

Björn Sundelius

Papers

Reflection of rarefaction wave in one‐dimensional gas flow