Zin Lin, Joseph Schindler, Fred M. Ellis, Tsampikos Kottos

We investigate experimentally parity-time \({\cal PT}\) symmetric scattering using \(LRC\) circuits in an inductively coupled \({\cal PT}\)- symmetric pair connected to transmission line leads. In the single-lead case, the \({\cal PT}\)-symmetric circuit acts as a simple dual device – an amplifier or an absorber depending on the orientation of the lead. When a second lead is attached, the system exhibits unidirectional transparency for some characteristic frequencies. This non-reciprocal behavior is a consequence of generalized (non-unitary) conservation relations satisfied by the scattering matrix.

http://arxiv.org/abs/1205.2176

Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

Emanuela Caliceti, Sandro Graffi, Michael Hitrik, Johannes Sjoestrand

It is established that a PT-symmetric elliptic quadratic differential operator with real spectrum is similar to a self-adjoint operator precisely when the associated fundamental matrix has no Jordan blocks.

http://arxiv.org/abs/1204.6605

Mathematical Physics (math-ph); Quantum Physics (quant-ph)

Jun-Qing Li, Qian Li, Yan-Gang Miao

Two non-Hermitian PT-symmetric Hamiltonian systems are reconsidered by means of the algebraic method which was originally proposed for the pseudo-Hermitian Hamiltonian systems rather than for the PT-symmetric ones. Compared with the way converting a non-Hermitian Hamiltonian to its Hermitian counterpart, this method has the merit that keeps the Hilbert space of the non-Hermitian PT-symmetric Hamiltonian unchanged. In order to give the positive definite inner product for the PT-symmetric systems, a new operator V, instead of C, can be introduced. The operator V has the similar function to the operator C adopted normally in the PT-symmetric quantum mechanics, however, it has the advantage that V can be constructed directly in terms of Hamiltonians. The spectra of the two non-Hermitian PT-symmetric systems are obtained, which coincide with that given in literature, and in particular, the Hilbert spaces associated with positive definite inner products are worked out.

http://arxiv.org/abs/1204.6544

Quantum Physics (quant-ph); High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph)