Carl M. Bender, Bjorn K. Berntson, David Parker, E. Samuel

If a Hamiltonian is PT symmetric, there are two possibilities: Either the eigenvalues are entirely real, in which case the Hamiltonian is said to be in an unbroken-PT-symmetric phase, or else the eigenvalues are partly real and partly complex, in which case the Hamiltonian is said to be in a broken-PT-symmetric phase. As one varies the parameters of the Hamiltonian, one can pass through the phase transition that separates the unbroken and broken phases. This transition has recently been observed in a variety of laboratory experiments. This paper explains the phase transition in a simple and intuitive fashion and then describes an extremely elementary experiment in which the phase transition is easily observed.

http://arxiv.org/abs/1206.4972

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

Eva-Maria Graefe

The understanding of nonlinear PT-symmetric quantum systems, arising for example in the theory of Bose-Einstein condensates in PT-symmetric potentials, is widely based on numerical investigations, and little is known about generic features induced by the interplay of PT-symmetry and nonlinearity. To gain deeper insights it is important to have analytically solvable toy-models at hand. In the present paper the stationary states of a simple toy-model of a PT-symmetric system are investigated. The model can be interpreted as a simple description of a Bose-Einstein condensate in a PT-symmetric double well trap in a two-mode approximation. The eigenvalues and eigenstates of the system can be explicitly calculated in a straight forward manner; the resulting structures resemble those that have recently been found numerically for a more realistic PT-symmetric double delta potential. In addition, a continuation of the system is introduced that allows an interpretation in terms of a simple linear matrix model.

http://arxiv.org/abs/1206.4806

Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas)

Carl M. Bender, Moshe Moshe, Sarben Sarkar

The conventional double-scaling limit of a quartic quantum field theory is inconsistent because the critical coupling constant is negative. Thus, at the critical coupling the Lagrangian appears to define a quantum theory whose energy is complex. Worse yet, the functional integral for the partition function of the theory does not exist. It is shown that one can avoid these difficulties if one approaches this correlated limit in a PT-symmetric fashion. The partition function is calculated explicitly in the double-scaling limit of an zero-dimensional O(N)-symmetric quartic model.

http://arxiv.org/abs/1206.4943

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