4,139 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
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
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
Entangling macroscopic diamonds at room temperature: Bounds on the continuous-spontaneous-localization parameters
A recent experiment [K. C. Lee et al., Science 334, 1253 (2011)] succeeded in
detecting entanglement between two macroscopic specks of diamonds, separated by
a macroscopic distance, at room temperature. This impressive results is a
further confirmation of the validity of quantum theory in (at least parts of)
the mesoscopic and macroscopic domain, and poses a challenge to collapse
models, which predict a violation of the quantum superposition principle, which
is the bigger the larger the system. We analyze the experiment in the light of
such models. We will show that the bounds placed by experimental data are
weaker than those coming from matter-wave interferometry and
non-interferometric tests of collapse models.Comment: 7 pages, 3 figures, v2: close to the published version, LaTe
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
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
Collapse models with non-white noises II: particle-density coupled noises
We continue the analysis of models of spontaneous wave function collapse with
stochastic dynamics driven by non-white Gaussian noise. We specialize to a
model in which a classical "noise" field, with specified autocorrelator, is
coupled to a local nonrelativistic particle density. We derive general results
in this model for the rates of density matrix diagonalization and of state
vector reduction, and show that (in the absence of decoherence) both processes
are governed by essentially the same rate parameters. As an alternative route
to our reduction results, we also derive the Fokker-Planck equations that
correspond to the initial stochastic Schr\"odinger equation. For specific
models of the noise autocorrelator, including ones motivated by the structure
of thermal Green's functions, we discuss the qualitative and qantitative
dependence on model parameters, with particular emphasis on possible
cosmological sources of the noise field.Comment: Latex, 43 pages; versions 2&3 have minor editorial revision
Local Fields without Restrictions on the Spectrum of 4-Momentum Operator and Relativistic Lindblad Equation
Quantum theory of Lorentz invariant local scalar fields without restrictions
on 4-momentum spectrum is considered. The mass spectrum may be both discrete
and continues and the square of mass as well as the energy may be positive or
negative. Such fields can exist as part of a hidden matter in the Universe if
they interact with ordinary fields very weakly. Generalization of
Kallen-Lehmann representation for propagators of these fields is found. The
considered generalized fields may violate CPT- invariance. Restrictions on
mass-spectrum of CPT-violating fields are found. Local fields that annihilate
vacuum state and violate CPT- invariance are constructed in this scope. Correct
local relativistic generalization of Lindblad equation for density matrix is
written for such fields. This generalization is particulary needed to describe
the evolution of quantum system and measurement process in a unique way.
Difficulties arising when the field annihilating the vacuum interacts with
ordinary fields are discussed.Comment: Latex 23 pages, sent to "Foundations of Physics
Role of the anterior temporal lobes in semantic representations: paradoxical results of a cTBS study
According to the 'Semantic Hub' model, which was developed from data gathered in the moderate to advanced stages of semantic dementia (SD), a unitary amodal mechanism, located in the anterior parts of both temporal lobes (ATLs), should support the interactive activation of semantic representations in all modalities and for all semantic categories. This model has been challenged by clinical findings, which show that in the early stages of SD, when important asymmetries can be observed at the level of the right and left ATLs, the semantic impairment can be modality-specific, mainly affecting lexical-semantic knowledge when the left temporal lobe is more atrophic and pictorial representations when atrophy prevails on the right side. On the other hand, findings of experiments conducted in normal subjects with repetitive transcranial magnetic stimulations (rTMS), support the unitary model. In the most compelling of these studies, rTMS was used to investigate the role of right and left ATLs directly, by comparing semantic processing of the same concepts, presented as written words or pictures. The efficiency of semantic processing for words and pictures was reduced to the same degree by rTMS applied to the left and right ATLs. However, to consider more in depth some methodological inconsistencies of these studies and with the aim of discussing the effects of rTMS on high-level cognitive functions, we decided to repeat that experimental paradigm, using the continuous theta burst stimulation (cTBS) protocol over the right ATL, left ATL and vertex (as control site). A significant interaction was found between side of cTBS application and type of stimulus, but, contrary to our predictions, we observed significantly faster (rather than slower) responses to pictures after application of cTBS to the right ATL and no difference between responses to written words after application of cTBS to the left ATL in comparison with the vertex. These unexpected results are discussed with respect to the nature of the semantic representations supported by the right and left ATLs and to re-appraisal of the 'virtual lesion' account to explain results obtained with rTMS experiments on high-level cognitive functions
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