999 research outputs found
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
Reply to Comments of Steuernagel on the Afshar's Experiment
We respond to criticism of our paper "Paradox in Wave-Paricle Duality for
Non-Perturbative Measurements". We disagree with Steuernagel's derivation of
the visibility of the Afshar experiment. To calculate the fringe visibility,
Steuernagel utilizes two different experimental situations, i.e. the wire grid
in the pattern minima and in the pattern maxima. In our assessment, this
proceduere cannot lead to the correct result for the complementarity properties
of wave-particle in one particular experimental set-up
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
Seven Steps Towards the Classical World
Classical physics is about real objects, like apples falling from trees,
whose motion is governed by Newtonian laws. In standard Quantum Mechanics only
the wave function or the results of measurements exist, and to answer the
question of how the classical world can be part of the quantum world is a
rather formidable task. However, this is not the case for Bohmian mechanics,
which, like classical mechanics, is a theory about real objects. In Bohmian
terms, the problem of the classical limit becomes very simple: when do the
Bohmian trajectories look Newtonian?Comment: 16 pages, LaTeX, uses latexsy
On Epstein's trajectory model of non-relativistic quantum mechanics
In 1952 Bohm presented a theory about non-relativistic point-particles moving
along deterministic trajectories and showed how it reproduces the predictions
of standard quantum theory. This theory was actually presented before by de
Broglie in 1926, but Bohm's particular formulation of the theory inspired
Epstein to come up with a different trajectory model. The aim of this paper is
to examine the empirical predictions of this model. It is found that the
trajectories in this model are in general very different from those in the de
Broglie-Bohm theory. In certain cases they even seem bizarre and rather
unphysical. Nevertheless, it is argued that the model seems to reproduce the
predictions of standard quantum theory (just as the de Broglie-Bohm theory).Comment: 12 pages, no figures, LaTex; v2 minor improvement
Typicality vs. probability in trajectory-based formulations of quantum mechanics
Bohmian mechanics represents the universe as a set of paths with a
probability measure defined on it. The way in which a mathematical model of
this kind can explain the observed phenomena of the universe is examined in
general. It is shown that the explanation does not make use of the full
probability measure, but rather of a suitable set function deriving from it,
which defines relative typicality between single-time cylinder sets. Such a set
function can also be derived directly from the standard quantum formalism,
without the need of an underlying probability measure. The key concept for this
derivation is the {\it quantum typicality rule}, which can be considered as a
generalization of the Born rule. The result is a new formulation of quantum
mechanics, in which particles follow definite trajectories, but which is only
based on the standard formalism of quantum mechanics.Comment: 24 pages, no figures. To appear in Foundation of Physic
Emergent quantum Euler equation and Bose-Einstein condensates
In this paper, proceeding from the recently developed way of deriving the
quantum-mechanical equations from the classical ones, the complete system of
hydrodynamical equations, including the quantum Euler equation, is derived for
a perfect fluid and an imperfect fluid with pairwise interaction between the
particles. For the Bose-Einstein condensate of the latter one the Bogolyubov
spectrum of elementary excitations is easily reproduced in the acoustic
approximation.Comment: 10 page
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