On the correspondence principle : implications from a study of the nonlinear dynamics of a macroscopic quantum device
Mark Everitt
2134/4081
https://repository.lboro.ac.uk/articles/journal_contribution/On_the_correspondence_principle_implications_from_a_study_of_the_nonlinear_dynamics_of_a_macroscopic_quantum_device/9409232
The recovery of classical nonlinear and chaotic dynamics from
quantum systems has long been a subject of interest. Furthermore, recent work
indicates that quantum chaos may well be significant in quantum information
processing. In this paper, we discuss the quantum to classical crossover of
a superconducting quantum interference device (SQUID) ring. Such devices
comprise a thick superconducting loop enclosing a Josephson weak link and are
currently strong candidates for many applications in quantum technologies. The
weak link brings with it a nonlinearity such that semiclassical models of this
system can exhibit nonlinear and chaotic dynamics. For many similar systems
an application of the correspondence principle together with the inclusion of
environmental degrees of freedom through a quantum trajectories approach can
be used to effectively recover classical dynamics. Here we show (i) that the
standard expression of the correspondence principle is incompatible with the
ring Hamiltonian and we present a more pragmatic and general expression which
finds application here and (ii) that practical limitations to circuit parameters
of the SQUID ring prevent arbitrarily accurate recovery of classical nonlinear
dynamics.
2009-01-08 14:28:17
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Physical Sciences not elsewhere classified