Non-Hermitian coherent states for finite-dimensional systems

Abstract

We introduce Gilmore-Perelomov coherent states for non-unitary representations of non-compact groups, and discuss the main similarities and differences with respect to ordinary unitary Gilmore-Perelomov coherent states. The example of coherent states for the non-unitary finite dimensional representations of $SU(1,1)$ is considered and they are used to describe the propagation of light in coupled PT-symmetric optical devices.

16 pages, 2 figures, to appear as Chapter 10 of "Coherent States and Their Applications", Springer Proceedings in Physics 205, J.-P. Antoine et al. (eds.)

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Cited by in corpus (1)

• Geometric Dynamics of a Harmonic Oscillator, Arbitrary Minimal Uncertainty States and the Smallest Step 3 Nilpotent Lie Group