47 research outputs found
Modified Sch\"odinger dynamics with attractive densities
The linear Schr\"{o}dinger equation does not predict that macroscopic bodies
should be located at one place only. Quantum mechanics textbooks generally
solve the problem by introducing the projection postulate, which forces
definite values to emerge during position measurements; many other
interpretations have also been proposed.\ Here, in the same spirit as the GRW
and CSL theories, we modify the Schr\"{o}dinger equation in a way that
efficiently cancels macroscopic density fluctuations in space.\ Instead of
introducing the stochastic dynamics of GRW or CSL, we assume a deterministic
dynamics that includes an attraction term towards the density in space of the
de Broglie-Bohm position of particles. This automatically ensures macroscopic
uniqueness, so that the state vector can be considered as a direct
representation of physical reality.Comment: 14 pages, no figure. This is the version accepted by the European
Physical Journal, with a few additions in the text and a few more references.
A typo has been corrected in Eq (4
Quantum collapse dynamics with attractive densities
We discuss a model of spontaneous collapse of the quantum state that does not
require adding any stochastic processes to the standard dynamics. The
additional ingredient with respect to the wave function is a position in the
configuration space, which drives the collapse in a completely deterministic
way. This new variable is equivalent to a set of positions of all the
particles, i.e. a set of Bohmian positions, which obey the usual guiding
equation of Bohmian theory. Any superposition of quantum states of a
macroscopic object occupying different regions of space is projected by a
localization process onto the region occupied by the positions. Since the
Bohmian positions are well defined in a single realization of the experiment, a
space localization into one region is produced. The mechanism is based on the
correlations between these positions arising from the cohesive forces inside
macroscopic objects.
The model introduces two collapse parameters, which play a very similar role
to those of the GRW and CSL theories. With appropriate values of these
parameters, we check that the corresponding dynamics rapidly projects
superpositions of macroscopic states localized in different regions of space
into a single region, while is keeps a negligible effect in all situations
where the predictions of standard quantum dynamics are known to be correct. The
possible relations with gravity are briefly speculated. We then study the
evolution of the density operator and a mean-field approximation of the
dynamical equations of this model, as well as the change of the evolution of
the momentum introduced by the localization process. Possible theoretical
interpretations are finally discussed. Generally speaking, this model
introduces a sharper border between the quantum and classical world than the
GRW and CSL theories, and leaves a broader range of acceptable values for the
parameters.Comment: 21 pages, 45 ref
Statistical Estimation of Mechanical Parameters of Clarinet Reeds Using Experimental and Numerical Approaches
A set of 55 clarinet reeds is observed by holography, collecting 2 series of
measurements made under 2 different moisture contents, from which the resonance
frequencies of the 15 first modes are deduced. A statistical analysis of the
results reveals good correlations, but also significant differences between
both series. Within a given series, flexural modes are not strongly correlated.
A Principal Component Analysis (PCA) shows that the measurements of each series
can be described with 3 factors capturing more than of the variance: the
first is linked with transverse modes, the second with flexural modes of high
order and the third with the first flexural mode. A forth factor is necessary
to take into account the individual sensitivity to moisture content. Numerical
3D simulations are conducted by Finite Element Method, based on a given reed
shape and an orthotropic model. A sensitivity analysis revels that, besides the
density, the theoretical frequencies depend mainly on 2 parameters: and
. An approximate analytical formula is proposed to calculate the
resonance frequencies as a function of these 2 parameters. The discrepancy
between the observed frequencies and those calculated with the analytical
formula suggests that the elastic moduli of the measured reeds are frequency
dependent. A viscoelastic model is then developed, whose parameters are
computed as a linear combination from 4 orthogonal components, using a standard
least squares fitting procedure and leading to an objective characterization of
the material properties of the cane \textit{Arundo donax}