In recent years, open systems with equal loss and gain have been investigated via their symmetry properties under combined parity and time-reversal (\(\mathcal{PT}\)) operations. We numerically investigate \(\mathcal{PT}\)-symmetry properties of an incompressible, viscous fluid with “balanced” inflow-outflow configurations. We define configuration-dependent asymmetries in velocity, kinetic energy density, and vorticity fields, and find that all asymmetries scale quadratically with the Reynolds number. Our proposed configurations have asymmetries that are orders of magnitude smaller than the asymmetries that occur in traditional configurations at low Reynolds numbers. Our results show that \(\mathcal{PT}\)-symmetric fluid flow configurations, which are defined here for the first time, offer a hitherto unexplored avenue to tune fluid flow properties.

http://arxiv.org/abs/1304.5348

Fluid Dynamics (physics.flu-dyn); Quantum Physics (quant-ph)

Adiabatic processes driven by non-Hermitian, time-dependent Hamiltonians may be sped up by generalizing inverse engineering techniques based on Berry’s transitionless driving algorithm or on dynamical invariants. We work out the basic theory and examples described by two-level Hamiltonians: the acceleration of rapid adiabatic passage with a decaying excited level and of the dynamics of a classical particle on an expanding harmonic oscillator.

http://arxiv.org/abs/1106.2776
Quantum Physics (quant-ph)