Pilot Wave model that includes creation and annihilation of particles

The purpose of this paper is to come up with a Pilot Wave model of quantum field theory that incorporates particle creation and annihilation without sacrificing determinism. This has been previously attempted in an article by the same author titled "Incorporating particle creation and annihilation in Pilot Wave model", in a much less satisfactory way. In this paper I would like to "clean up" some of the things. In particular, I would like to get rid of a very unnatural concept of "visibility" of particles, which makes the model much simpler. On the other hand, I would like to add a mechanism for decoherence, which was absent in the previous version.Comment: 9 pages, no figure

Rate of decoherence for an electron weakly coupled to a phonon gas

We study the dynamics of an electron weakly coupled to a phonon gas. The initial state of the electron is the superposition of two spatially localized distant bumps moving towards each other, and the phonons are in a thermal state. We investigate the dynamics of the system in the kinetic regime and show that the time evolution makes the non-diagonal terms of the density matrix of the electron decay, destroying the interference between the two bumps. We show that such a damping effect is exponential in time, and the related decay rate is proportional to the total scattering cross section of the electron-phonon interaction.Comment: 27 pages, 2 figure

Scaling tests with dynamical overlap and rooted staggered fermions

We present a scaling analysis in the 1-flavor Schwinger model with the full overlap and the rooted staggered determinant. In the latter case the chiral and continuum limit of the scalar condensate do not commute, while for overlap fermions they do. For the topological susceptibility a universal continuum limit is suggested, as is for the partition function and the Leutwyler-Smilga sum rule. In the heavy-quark force no difference is visible even at finite coupling. Finally, a direct comparison between the complete overlap and the rooted staggered determinant yields evidence that their ratio is constant up to $O(a^2)$ effects.Comment: 28 pages, 20 figures containg 37 graphs. v2: 6 new references, 2 new footnotes (to match published version

Bohmian Mechanics and Quantum Information

Many recent results suggest that quantum theory is about information, and that quantum theory is best understood as arising from principles concerning information and information processing. At the same time, by far the simplest version of quantum mechanics, Bohmian mechanics, is concerned, not with information but with the behavior of an objective microscopic reality given by particles and their positions. What I would like to do here is to examine whether, and to what extent, the importance of information, observation, and the like in quantum theory can be understood from a Bohmian perspective. I would like to explore the hypothesis that the idea that information plays a special role in physics naturally emerges in a Bohmian universe.Comment: 25 pages, 2 figure

Time and Ensemble Averages in Bohmian Mechanics

We show that in the framework of one-dimensional Bohmian Quantum Mechanics[1], for a particle subject to a potential undergoing a weak adiabatic change, the time averages of the particle's positions typically differ markedly from the ensemble averages. We Apply this result to the case where the weak perturbing potential is the back-action of a measuring device (i.e. a protective measurement). It is shown that under these conditions, most trajectories never cross the position measured (as already shown for a particular example in [3]).Comment: 6 page

On the zig-zag pilot-wave approach for fermions

We consider a pilot-wave approach for the Dirac theory that was recently proposed by Colin and Wiseman. In this approach, the particles perform a zig-zag motion, due to stochastic jumps of their velocity. We respectively discuss the one-particle theory, the many-particle theory and possible extensions to quantum field theory. We also discuss the non-relativistic limit of the one-particle theory. For a single particle, the motion is always luminal, a feature that persists in the non-relativistic limit. For more than one particle the motion is in general subluminal.Comment: 23 pages, no figures, LaTe

Comment on "Chiral anomalies and rooted staggered fermions"

In hep-lat/0701018, Creutz claims that the rooting trick used in simulations of staggered fermions to reduce the number of tastes misses key physics whenever the desired theory has an odd number of continuum flavors, and uses this argument to call into question the rooting trick in general. Here we show that his argument fails as the continuum limit is approached, and therefore does not imply any problem for staggered simulations. We also show that the cancellations necessary to restore unitarity in physical correlators in the continuum limit are a straightforward consequence of the restoration of taste symmetry.Comment: 11 pages, version 3 (4/13/07): Revisions to correspond to Creutz's latest posting, including a change in the title. Version to appear in Physics Letters

Comment on "Quantitative wave-particle duality in multibeam interferometers"

In a recent paper [Phys. Rev. {\bf A64}, 042113 (2001)] S. D\"urr proposed an interesting multibeam generalization of the quantitative formulation of interferometric wave-particle duality, discovered by Englert for two-beam interferometers. The proposed generalization is an inequality that relates a generalized measure of the fringe visibility, to certain measures of the maximum amount of which-way knowledge that can be stored in a which-way detector. We construct an explicit example where, with three beams in a pure state, the scheme proposed by D\"{u}rr leads to the possibility of an ideal which-way detector, that can achieve a better path-discrimination, at the same time as a better fringe visibility. In our opinion, this seems to be in contrast with the intuitive idea of complementarity, as it is implemented in the two-beams case, where an increase in path discrimination always implies a decrease of fringe visibility, if the beams and the detector are in pure states.Comment: 4 pages, 1 encapsulated figure. In press on Phys. Rev.

Multi-Player Diffusion Games on Graph Classes

We study competitive diffusion games on graphs introduced by Alon et al. [1] to model the spread of influence in social networks. Extending results of Roshanbin [8] for two players, we investigate the existence of pure Nash equilibria for at least three players on different classes of graphs including paths, cycles, grid graphs and hypercubes; as a main contribution, we answer an open question proving that there is no Nash equilibrium for three players on (m x n) grids with min(m, n) >= 5. Further, extending results of Etesami and Basar [3] for two players, we prove the existence of pure Nash equilibria for four players on every d-dimensional hypercube.Comment: Extended version of the TAMC 2015 conference version now discussing hypercube results (added details for the proof of Proposition 1