Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Salecker-Wigner-Peres clock, Feynman paths, and a tunnelling time
  that should not exist   The Salecker-Wigner-Peres (SWP) clock is often used to determine the duration
a quantum particle is supposed to spend is a specified region of space $\Om$.
By construction, the result is a real positive number, and the method seems to
avoid the difficulty of introducing complex time parameters, which arises in
the Feynman paths approach. However, it tells little about about the particle's
motion. We investigate this matter further, and show that the SWP clock, like
any other Larmor clock, correlates the rotation of its angular momentum with
the durations, $\tau$, which the Feynman paths spend in $\Om$, thereby
destroying interference between different durations. An inaccurate weakly
coupled clock leaves the interference almost intact, and the need to resolve
the resulting "which way?" problem is one of the main difficulties at the
centre of the "tunnelling time" controversy. In the absence of a probability
distribution for the values of $\tau$, the SWP results are expressed in terms
of moduli of the "complex times", given by the weighted sums of the
corresponding probability amplitudes. It is shown that over-interpretation of
these results, by treating the SWP times as physical time intervals, leads to
paradoxes and should be avoided. We also analyse various settings of the SWP
clock, different calibration procedures, and the relation between the SWP
results and the quantum dwell time. The cases of stationary tunnelling and
tunnel ionisation are considered in some detail. Although our detailed analysis
addresses only one particular definition of the duration of a tunnelling
process, it also points towards the impossibility of uniting various time
parameters, which may occur in quantum theory, within the concept of a single
"tunnelling time".

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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: math
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin