Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum asymptotic phase reveals signatures of quantum synchronization   We propose a fully quantum-mechanical definition of the asymptotic phase for
quantum nonlinear oscillators. The asymptotic phase function of the system is
introduced in terms of the eigenoperator of the adjoint Liouville superoperator
associated with the fundamental frequency. This quantum asymptotic phase yields
appropriate phase values of the system even in the strong quantum regime, while
reproducing the conventional asymptotic phase in the semiclassical regime. We
analyze a quantum van der Pol oscillator with Kerr effect and show that several
dominant eigenoperators with different fundamental frequencies exist in the
strong quantum regime. Using the quantum asymptotic phase functions with
respective fundamental frequencies, we reveal that the multiple phase locking
of the system with a harmonic drive at several different frequencies, an
explicit quantum signature observed only in the strong quantum regime, can be
interpreted as synchronization on a torus rather than a simple limit cycle.

12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin