383 research outputs found
Measurement, Decoherence and Chaos in Quantum Pinball
The effect of introducing measuring devices in a ``quantum pinball'' system
is shown to lead to a chaotic evolution for the particle position as defined in
Bohm's approach to Quantum Mechanics.Comment: Latex, uses ioplppt style, two figures. Also can be ftp'd anonymously
from: ftp://zaphod.phys.port.ac.uk/pub/papers/paper2
A non-local, Lorentz-invariant, hidden-variable interpretation of relativistic quantum mechanics based on particle trajectories
We demonstrate how to construct a lorentz-invariant, hidden-variable
interpretation of relativistic quantum mechanics based on particle
trajectories. The covariant theory that we propose employs a multi-time
formalism and a lorentz-invariant rule for the coordination of the space-time
points on the individual particle trajectories. In this way we show that there
is no contradiction between nonlocality and lorentz invariance in quantum
mechanics. The approach is illustrated for relativistic bosons, using a simple
model to discuss the individual non-locally correlated particle motion which
ensues when the wavefunction is entangled. A simple example of measurement is
described.Comment: 12 pages, 2 figure
Bohm's interpretation and maximally entangled states
Several no-go theorems showed the incompatibility between the locality
assumption and quantum correlations obtained from maximally entangled spin
states. We analyze these no-go theorems in the framework of Bohm's
interpretation. The mechanism by which non-local correlations appear during the
results of measurements performed on distant parts of entangled systems is
explicitly put into evidence in terms of Bohmian trajectories. It is shown that
a GHZ like contradiction of the type+1=-1 occurs for well-chosen initial
positions of the Bohmian trajectories and that it is this essential
non-classical feature that makes it possible to violate the locality condition.Comment: 18 page
Spin-dependent Bohm trajectories associated with an electronic transition in hydrogen
The Bohm causal theory of quantum mechanics with spin-dependence is used to
determine electron trajectories when a hydrogen atom is subjected to
(semi-classical) radiation. The transition between the 1s ground state and the
2p0 state is examined. It is found that transitions can be identified along
Bohm trajectories. The trajectories lie on invariant hyperboloid surfaces of
revolution in R^3. The energy along the trajectories is also discussed in
relation to the hydrogen energy eigenvalues.Comment: 18 pages, 8 figure
A relativistically covariant version of Bohm's quantum field theory for the scalar field
We give a relativistically covariant, wave-functional formulation of Bohm's
quantum field theory for the scalar field based on a general foliation of
space-time by space-like hypersurfaces. The wave functional, which guides the
evolution of the field, is space-time-foliation independent but the field
itself is not. Hence, in order to have a theory in which the field may be
considered a beable, some extra rule must be given to determine the foliation.
We suggest one such rule based on the eigen vectors of the energy-momentum
tensor of the field itself.Comment: 1 figure. Submitted to J Phys A. 20/05/04 replacement has additional
references and a few minor changes made for clarity. Accepted by J Phys
Time-like flows of energy-momentum and particle trajectories for the Klein-Gordon equation
The Klein-Gordon equation is interpreted in the de Broglie-Bohm manner as a
single-particle relativistic quantum mechanical equation that defines unique
time-like particle trajectories. The particle trajectories are determined by
the conserved flow of the intrinsic energy density which can be derived from
the specification of the Klein-Gordon energy-momentum tensor in an
Einstein-Riemann space. The approach is illustrated by application to the
simple single-particle phenomena associated with square potentials.Comment: 14 pages, 11 figure
The density matrix in the de Broglie-Bohm approach
If the density matrix is treated as an objective description of individual
systems, it may become possible to attribute the same objective significance to
statistical mechanical properties, such as entropy or temperature, as to
properties such as mass or energy. It is shown that the de Broglie-Bohm
interpretation of quantum theory can be consistently applied to density
matrices as a description of individual systems. The resultant trajectories are
examined for the case of the delayed choice interferometer, for which Bell
appears to suggest that such an interpretation is not possible. Bell's argument
is shown to be based upon a different understanding of the density matrix to
that proposed here.Comment: 15 pages, 4 figure
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