6,630 research outputs found
Dynamical Reduction Models: present status and future developments
We review the major achievements of the dynamical reduction program, showing
why and how it provides a unified, consistent description of physical
phenomena, from the microscopic quantum domain to the macroscopic classical
one. We discuss the difficulties in generalizing the existing models in order
to comprise also relativistic quantum field theories. We point out possible
future lines of research, ranging from mathematical physics to phenomenology.Comment: 12 pages. Contribution to the Proceedings of the "Third International
Workshop DICE2006", Castello di Piombino (Tuscany), September 11-15, 2006.
Minor changes mad
On the Electromagnetic Properties of Matter in Collapse Models
We discuss the electromagnetic properties of both a charged free particle,
and a charged particle bounded by an harmonic potential, within collapse
models. By choosing a particularly simple, yet physically relevant, collapse
model, and under only the dipole approximation, we are able to solve the
equation of motion exactly. In this way, both the finite time and large time
behavior can be analyzed accurately. We discovered new features, which did not
appear in previous works on the same subject. Since, so far, the spontaneous
photon emission process places the strongest upper bounds on the collapse
parameters, our results call for a further analysis of this process for those
atomic systems which can be employed in experimental tests of collapse models,
as well as of quantum mechanics.Comment: 17 pages, LaTeX, updated version with minor change
The quantum theory of measurement within dynamical reduction models
We analyze in mathematical detail, within the framework of the QMUPL model of
spontaneous wave function collapse, the von Neumann measurement scheme for the
measurement of a 1/2 spin particle. We prove that, according to the equation of
the model: i) throughout the whole measurement process, the pointer of the
measuring device is always perfectly well localized in space; ii) the
probabilities for the possible outcomes are distributed in agreement with the
Born probability rule; iii) at the end of the measurement the state of the
microscopic system has collapsed to the eigenstate corresponding to the
measured eigenvalue. This analysis shows rigorously how dynamical reduction
models provide a consistent solution to the measurement problem of quantum
mechanics.Comment: 24 pages, RevTeX. Minor changes mad
On the spontaneous emission of electromagnetic radiation in the CSL model
Spontaneous photon emission in the Continuous Spontaneous Localization (CSL)
model is studied one more time. In the CSL model each particle interacts with a
noise field that induces the collapse of its wave function. As a consequence of
this interaction, when the particle is electrically charged, it radiates. As
discussed in [1], the formula for the emission rate, to first perturbative
order, contains two terms: One is proportional to the Fourier component of the
noise field at the same frequency as that of the emitted photon and one is
proportional to the zero Fourier component of the noise field. As discussed in
previous works, this second term seems unphysical. In [1], it was shown that
the unphysical term disappears when the noises is confined to a bounded region
and the final particle's state is a wave packet. Here we investigate the origin
of the unphysical term and why it vanishes according to the previous
prescription. For this purpose, the electrodynamic part of the equation of
motion is solved exactly while the part due to the noise is treated
perturbatively. We show that the unphysical term is connected to exponentially
decaying function of time which dies out in the large time limit, however,
approximates to 1 in the first perturbative order in the electromagnetic field.Comment: 10 pages, 1 figure, LaTe
Towards Quantum Superpositions of a Mirror: an Exact Open Systems Analysis - Calculational Details
We give details of calculations analyzing the proposed mirror superposition
experiment of Marshall, Simon, Penrose, and Bouwmeester within different
stochastic models for state vector collapse. We give two methods for exactly
calculating the fringe visibility in these models, one proceeding directly from
the equation of motion for the expectation of the density matrix, and the other
proceeding from solving a linear stochastic unravelling of this equation. We
also give details of the calculation that identifies the stochasticity
parameter implied by the small displacement Taylor expansion of the CSL model
density matrix equation. The implications of the two results are briefly
discussed. Two pedagogical appendices review mathematical apparatus needed for
the calculations.Comment: 9 pages, LaTeX. Minor changes mad
A 1D Model for N-level Atoms Coupled to an EM Field
We construct a model for n-level atoms coupled to quantized electromagnetic
fields in a fibrillar geometry. In the slowly varying envelope and rotating
wave approximations, the equations of motion are shown to satisfy a zero
curvature representation, implying integrability of the quantum system.Comment: 8 pages, Plain Te
The Hilbert space operator formalism within dynamical reduction models
Unlike standard quantum mechanics, dynamical reduction models assign no
particular a priori status to `measurement processes', `apparata', and
`observables', nor self-adjoint operators and positive operator valued measures
enter the postulates defining these models. In this paper, we show why and how
the Hilbert-space operator formalism, which standard quantum mechanics
postulates, can be derived from the fundamental evolution equation of dynamical
reduction models. Far from having any special ontological meaning, we show that
within the dynamical reduction context the operator formalism is just a compact
and convenient way to express the statistical properties of the outcomes of
experiments.Comment: 25 pages, RevTeX. Changes made and two figures adde
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