Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lectures on dynamical models for quantum measurements   In textbooks, ideal quantum measurements are described in terms of the tested
system only by the collapse postulate and Born's rule. This level of
description offers a rather flexible position for the interpretation of quantum
mechanics. Here we analyse an ideal measurement as a process of interaction
between the tested system S and an apparatus A, so as to derive the properties
postulated in textbooks. We thus consider within standard quantum mechanics the
measurement of a quantum spin component $\hat s_z$ by an apparatus A, being a
magnet coupled to a bath. We first consider the evolution of the density
operator of S+A describing a large set of runs of the measurement process. The
approach describes the disappearance of the off-diagonal terms ("truncation")
of the density matrix as a physical effect due to A, while the registration of
the outcome has classical features due to the large size of the pointer
variable, the magnetisation. A quantum ambiguity implies that the density
matrix at the final time can be decomposed on many bases, not only the one of
the measurement. This quantum oddity prevents to connect individual outcomes to
measurements, a difficulty known as the "measurement problem". It is shown that
it is circumvented by the apparatus as well, since the evolution in a small
time interval erases all decompositions, except the one on the measurement
basis. Once one can derive the outcome of individual events from quantum
theory, the so-called "collapse of the wave function" or the "reduction of the
state" appears as the result of a selection of runs among the original large
set. Hence nothing more than standard quantum mechanics is needed to explain
features of measurements. The employed statistical formulation is advocated for
the teaching of quantum theory.

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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ