4,383 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
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
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
Collapse models with non-white noises
We set up a general formalism for models of spontaneous wave function
collapse with dynamics represented by a stochastic differential equation driven
by general Gaussian noises, not necessarily white in time. In particular, we
show that the non-Schrodinger terms of the equation induce the collapse of the
wave function to one of the common eigenstates of the collapsing operators, and
that the collapse occurs with the correct quantum probabilities. We also
develop a perturbation expansion of the solution of the equation with respect
to the parameter which sets the strength of the collapse process; such an
approximation allows one to compute the leading order terms for the deviations
of the predictions of collapse models with respect to those of standard quantum
mechanics. This analysis shows that to leading order, the ``imaginary'' noise
trick can be used for non-white Gaussian noise.Comment: Latex, 20 pages;references added and minor revisions; published as J.
Phys. A: Math. Theor. {\bf 40} (2007) 15083-1509
Effect of metal clusters on the swelling of gold-fluorocarbon-polymer composite films
We have investigated the phenomenon of swelling due to acetone diffusion in
fluorocarbon polymer films doped with different gold concentrations below the
percolation threshold. The presence of the gold clusters in the polymer is
shown to improve the mixing between the fluorocarbon polymer and the acetone,
which is not a good solvent for this kind of polymers. In order to explain the
experimental results the stoichiometry and the morphology of the polymer--metal
system have been studied and a modified version of the Flory--Huggins model has
been developed
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
On the long time behavior of Hilbert space diffusion
Stochastic differential equations in Hilbert space as random nonlinear
modified Schroedinger equations have achieved great attention in recent years;
of particular interest is the long time behavior of their solutions. In this
note we discuss the long time behavior of the solutions of the stochastic
differential equation describing the time evolution of a free quantum particle
subject to spontaneous collapses in space. We explain why the problem is subtle
and report on a recent rigorous result, which asserts that any initial state
converges almost surely to a Gaussian state having a fixed spread both in
position and momentum.Comment: 6 pages, EPL2-Te
Breaking quantum linearity: constraints from human perception and cosmological implications
Resolving the tension between quantum superpositions and the uniqueness of
the classical world is a major open problem. One possibility, which is
extensively explored both theoretically and experimentally, is that quantum
linearity breaks above a given scale. Theoretically, this possibility is
predicted by collapse models. They provide quantitative information on where
violations of the superposition principle become manifest. Here we show that
the lower bound on the collapse parameter lambda, coming from the analysis of
the human visual process, is ~ 7 +/- 2 orders of magnitude stronger than the
original bound, in agreement with more recent analysis. This implies that the
collapse becomes effective with systems containing ~ 10^4 - 10^5 nucleons, and
thus falls within the range of testability with present-day technology. We also
compare the spectrum of the collapsing field with those of known cosmological
fields, showing that a typical cosmological random field can yield an efficient
wave function collapse.Comment: 13 pages, LaTeX, 3 figure
Are collapse models testable with quantum oscillating systems? The case of neutrinos, kaons, chiral molecules
Collapse models provide a theoretical framework for understanding how
classical world emerges from quantum mechanics. Their dynamics preserves
(practically) quantum linearity for microscopic systems, while it becomes
strongly nonlinear when moving towards macroscopic scale. The conventional
approach to test collapse models is to create spatial superpositions of
mesoscopic systems and then examine the loss of interference, while
environmental noises are engineered carefully. Here we investigate a different
approach: We study systems that naturally oscillate --creating quantum
superpositions-- and thus represent a natural case-study for testing quantum
linearity: neutrinos, neutral mesons, and chiral molecules. We will show how
spontaneous collapses affect their oscillatory behavior, and will compare them
with environmental decoherence effects. We will show that, contrary to what
previously predicted, collapse models cannot be tested with neutrinos. The
effect is stronger for neutral mesons, but still beyond experimental reach.
Instead, chiral molecules can offer promising candidates for testing collapse
models.Comment: accepted by NATURE Scientific Reports, 12 pages, 1 figures, 2 table
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