Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relational evolution with oscillating clocks   A fundamental description of time can be consistent not only with the usual
monotonic behavior but also with a periodic physical clock variable, coupled to
the degrees of freedom of a system evolving in time. Generically, one would in
fact expect some kind of oscillating motion of a system that is dynamical and
interacts with its surroundings, as required for a fundamental clock that can
be noticed by any other system. Unitary evolution does not require a monotonic
clock variable and can be achieved more generally by formally unwinding the
periodic clock movement, keeping track not only of the value of the clock
variable but also of the number of cycles it has gone through at any moment. As
a result, the clock is generically in a quantum state with a superposition of
different clock cycles, a key feature that distinguishes oscillating clocks
from monotonic time. Because the clock and an evolving system have a common
conserved energy, the clock is in different cycles for different energy
eigenstates of the system state. Coherence could therefore be lost faster than
observed, for instance if a system that would be harmonic in isolation is made
anharmonic by interactions with a fundamental clock, implying observational
bounds on fundamental clocks. Numerical computations show that coherence is
almost maintained over long time scales provided the clock period is much
smaller than the system period. Since the precision of atomic clocks could not
be achieved if atomic frequencies would be subject to additional variations
from coupling to a fundamental clock, an upper bound on the clock period can be
obtained that turns out to be much smaller than currently available direct or
indirect measurements of time. (abbreviated)

22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph