Hidden variable theories and quantum nonlocality

We clarify the meaning of Bell's theorem and its implications for the construction of hidden variable theories by considering an example system consisting of two entangled spin-1/2 particles. Using this example, we present a simplified version of Bell's theorem and describe several hidden variable theories that agree with the predictions of quantum mechanics. These example theories clarify some subtle points, which are often misunderstood, regarding what it is that Bell's theorem actually establishes

Simulating a toy model of electrodynamics in (1 + 1) dimensions

We show how to simulate a toy model of electrodynamics in (1+1) dimensions and describe several numerical experiments. The toy model is much simpler than ordinary electrodynamics, but shares many of the same physical features. For example, there are analogs to the electric and magnetic fields, and these fields generate forces between charged particles and support freely propagating radiation. Unlike electrodynamics, however, the toy model is not Lorentz invariant, gives an attractive force between charges of the same sign, and yields a radiation reaction force that depends on the particle velocity

A toy model of electrodynamics in (1 + 1) dimensions

A model is presented that describes a scalar field interacting with a point particle in (1+1) dimensions. The model exhibits many of the same phenomena that appear in classical electrodynamics, such as radiation and radiation damping, yet has a much simpler mathematical structure. By studying these phenomena in a highly simplified model, the physical concepts involved may be more easily understood

Quantum field theory in (0 + 1) dimensions

We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In addition, working in (0 + 1) dimensions considerably simplifies the mathematics, allowing the physical concepts involved to be exhibited more clearly

Laserlike and atomlike regimes in a one-atom laser

We consider a three-level model of a one-atom laser, and show that there are two limiting regimes of parameter space, one in which the system behaves like a conventional laser and one in which the system exhibits novel quantum properties. We show that in the first limiting regime, the model can be approximated by semiclassical laser theory, and in the second limiting regime the model can be approximated as an effective two-level atom. We also perform numerical simulations that confirm the limiting behaviors predicted by these approximate descriptions

Simulating a one-dimensional plasma

We describe a dynamical model of a one-dimensional plasma and present a simple algorithm for simulating the model on a computer. We use the algorithm to perform several numerical experiments that illustrate collective effects in plasma physics such as Debye screening and plasma oscillations

Fast magnetic reconnection and the ideal evolution of a magnetic field

Regardless of how small non-ideal effects may be, phenomena associated with changes in magnetic field line connections are frequently observed to occur on an Alfv\'enic time scale. Since it is mathematically impossible for magnetic field line connections to change when non-ideal effects are identically zero, an ideal evolution must naturally lead to states of unbounded sensitivity to non-ideal effects. That such an evolution is natural is demonstrated using Lagrangian coordinates based on the flow velocity of the magnetic field lines. The Lagrangian representation of an evolving magnetic field is highly constrained when neither the magnetic field strength nor the forces exerted by the magnetic field increase exponentially with time. The development of a state of fast reconnection consistent with these constraints (1) requires a three-dimensional evolution, (2) has an exponentially increasing sensitivity to non-ideal effects, and (3) has a parallel current density, which lies in exponentially thinning but exponentially widening ribbons, with a magnitude that is limited to a slow growth. The implication is that exponential growth in sensitivity is the cause of fast magnetic reconnection when non-ideal effects are sufficiently small. The growth of the non-ideal effect of the resistivity multiplied by the parallel current density is far too slow to be competitive.Comment: 13 pages, no figure

Periodic lattices in Minkowski space

We describe a set of periodic lattices in (1+1)-dimensional Minkowski space, where each lattice has an associated symmetry group consisting of inhomogeneous Lorentz transformations that map the lattice onto itself. Our results show how ideas of crystal structure in Euclidean space generalize to Minkowski space and provide an example that illustrates basic concepts of spacetime symmetry