Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-linear equation of motion for Page-Wootters mechanism with
  interaction and quasi-ideal clocks   Among the many proposals to approach the concept of time in quantum theory,
the Page-Wootters mechanism has attracted much attention in the last few years.
Originally, such a mechanism explored a stationary bipartite non-interacting
global system, i.e., a system of interest together with an ancillary clock, to
determine how the evolution in time can emerge as an equation of motion for a
quantum particle conditioned to the measurement of the state of the clock.
After the seminal proposal, many variations of it were considered, and
different aspects of the mechanism were elucidated. Our contribution to these
investigations is that we analyze such a timeless approach to quantum theory
but deriving an equation of motion for a mixed state system that evolves
according to its gravitationally induced interaction with a non-ideal quantum
clock. The interaction considered is known to describe the gravitational
decoherence mechanism, and the clock model is the recently proposed quasi-ideal
clock, i.e., one constructed to approximate the time-energy canonical
commutation relation. As a result of our considerations, we obtained an
equation of motion that is non-linear in nature, dependent on the system's
initial conditions.

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The categories of this paper are: math-ph
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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: atom-ph
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The categories of this paper are: physics
9
The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int