19 research outputs found
Entanglement Dynamics between Inertial and Non-uniformly Accelerated Detectors
We study the time-dependence of quantum entanglement between two Unruh-DeWitt
detectors, one at rest in a Minkowski frame, the other non-uniformly
accelerated in some specified way. The two detectors each couple to a scalar
quantum field but do not interact directly. The primary challenge in problems
involving non-uniformly accelerated detectors arises from the fact that an
event horizon is absent and the Unruh temperature is ill-defined. By numerical
calculation we demonstrate that the correlators of the accelerated detector in
the weak coupling limit behaves like those of an oscillator in a bath of
time-varying "temperature" proportional to the instantaneous proper
acceleration of the detector, with oscillatory modifications due to
non-adiabatic effects. We find that in this setup the acceleration of the
detector in effect slows down the disentanglement process in Minkowski time due
to the time dilation in that moving detectorComment: 20 pages, 15 figures; References added; More analysis given in
Appendix C; Typos correcte
Higher Order Quantum Superintegrability: a new "Painlev\'e conjecture"
We review recent results on superintegrable quantum systems in a
two-dimensional Euclidean space with the following properties. They are
integrable because they allow the separation of variables in Cartesian
coordinates and hence allow a specific integral of motion that is a second
order polynomial in the momenta. Moreover, they are superintegrable because
they allow an additional integral of order . Two types of such
superintegrable potentials exist. The first type consists of "standard
potentials" that satisfy linear differential equations. The second type
consists of "exotic potentials" that satisfy nonlinear equations. For , 4
and 5 these equations have the Painlev\'e property. We conjecture that this is
true for all . The two integrals X and Y commute with the Hamiltonian,
but not with each other. Together they generate a polynomial algebra (for any
) of integrals of motion. We show how this algebra can be used to calculate
the energy spectrum and the wave functions.Comment: 23 pages, submitted as a contribution to the monographic volume
"Integrability, Supersymmetry and Coherent States", a volume in honour of
Professor V\'eronique Hussin. arXiv admin note: text overlap with
arXiv:1703.0975