The PT Symmeter » ETH Zurich

The real spectrum of the imaginary cubic oscillator: An expository proof

dwh — Wed, 30 Oct 2013 10:39:53 +0000

Ilario Giordanelli, Gian Michele Graf

We give a partially alternate proof of the reality of the spectrum of the imaginary cubic oscillator in quantum mechanics.

http://arxiv.org/abs/1310.7767
Mathematical Physics (math-ph)

Pump-induced Exceptional Points in Lasers above Threshold

dwh — Mon, 05 Sep 2011 21:55:35 +0000

M. Liertzer, Li Ge, A. Cerjan, A. D. Stone, H. E. Türeci, S. Rotter

We demonstrate that the above-threshold behavior of a laser can be strongly affected by exceptional points which are induced by pumping the laser non-uniformly. At these singularities the eigenstates of the non-Hermitian operator which describes the lasing modes coalesce. In the vicinity of these points the laser may turn off even when the overall pump power deposited in the system is increased. We suggest that such signatures of a pump-induced exceptional point can be experimentally probed with coupled ridge or microdisk lasers.

http://arxiv.org/abs/1109.0454
Optics (physics.optics)

http://arxiv.org/abs/1109.0454

Galois Conjugates of Topological Phases

dwh — Tue, 21 Jun 2011 07:57:58 +0000

Michael H. Freedman, Jan Gukelberger, Matthew B. Hastings, Simon Trebst, Matthias Troyer, Zhenghan Wang

Galois conjugation relates unitary conformal field theories (CFTs) and topological quantum field theories (TQFTs) to their non-unitary counterparts. Here we investigate Galois conjugates of quantum double models, such as the Levin-Wen model. While these Galois conjugated Hamiltonians are typically non-Hermitian, we find that their ground state wave functions still obey a generalized version of the usual code property (local operators do not act on the ground state manifold) and hence enjoy a generalized topological protection. The key question addressed in this paper is whether such non-unitary topological phases can also appear as the ground states of Hermitian Hamiltonians. Specific attempts at constructing Hermitian Hamiltonians with these ground states lead to a loss of the code property and topological protection of the degenerate ground states. Beyond this we rigorously prove that no local change of basis can transform the ground states of the Galois conjugated doubled Fibonacci theory into the ground states of a topological model whose Hermitian Hamiltonian satisfies Lieb-Robinson bounds. These include all gapped local or quasi-local Hamiltonians. A similar statement holds for many other non-unitary TQFTs. One consequence is that the “Gaffnian” wave function cannot be the ground state of a gapped fractional quantum Hall state.

http://arxiv.org/abs/1106.3267
Strongly Correlated Electrons (cond-mat.str-el); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Mathematical Physics (math-ph)