Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Observation of phase synchronization and alignment during free induction
  decay of quantum spins with Heisenberg interactions   Equilibration of observables in closed quantum systems that are described by
a unitary time evolution is a meanwhile well-established phenomenon apart from
a few equally well-established exceptions. Here we report the surprising
theoretical observation that integrable as well as non-integrable spin rings
with nearest-neighbor or long-range isotropic Heisenberg interaction not only
equilibrate but moreover also synchronize the directions of the expectation
values of the individual spins. We highlight that this differs from spontaneous
synchronization in quantum dissipative systems. Here, we observe mutual
synchronization of local spin directions in closed systems under unitary time
evolution. Contrary to dissipative systems, this synchronization is independent
of whether the interaction is ferro- or antiferromagnetic. In our numerical
simulations, we investigate the free induction decay (FID) of an ensemble of up
to $N = 25$ quantum spins with $s = 1/2$ each by solving the time-dependent
Schr\"odinger equation numerically exactly. Our findings are related to, but
not fully explained by conservation laws of the system. The synchronization is
very robust against for instance random fluctuations of the Heisenberg
couplings and inhomogeneous magnetic fields. Synchronization is not observed
with strong enough symmetry-breaking interactions such as the dipolar
interaction. We also compare our results to closed-system classical spin
dynamics which does not exhibit phase synchronization due to the lack of
entanglement. For classical spin systems the fixed magnitude of individual
spins effectively acts like additional $N$ conservation laws.

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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: math
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The categories of this paper are: ao-sci
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The categories of this paper are: econ