Francisco M. Fernández, Javier Garcia

We show that a recently developed semiclassical expansion for the eigenvalues of PT-symmetric oscillators of the form \(V(x)=(ix)^{2N+1}+bix\) does not agree with an earlier WKB expression for \(V(x)=−(ix)^{2N+1}\) the case \(b=0\). The reason is due to the choice of different paths in the complex plane for the calculation of the WKB integrals. We compare the Stokes and anti-Stokes lines that apply to each case for the quintic oscillator and derive a general WKB expression that contains the two earlier ones.

http://arxiv.org/abs/1312.5117

Quantum Physics (quant-ph)

Stefano Longhi

We investigate the spectral and dynamical properties of a quantum particle constrained on a ring threaded by a magnetic flux in presence of a complex (non-Hermitian) potential. For a static magnetic flux, the quantum states of the particle on the ring can be mapped into the Bloch states of a complex crystal, and magnetic flux tuning enables to probe the spectral features of the complex crystal, including the appearance of exceptional points. For a time-varying (linearly-ramped) magnetic flux, Zener tunneling among energy states is realized owing to the induced electromotive force. As compared to the Hermitian case, striking effects are observed in the non-Hermitian case, such as a highly asymmetric behavior of particle motion when reversing the direction of the magnetic flux and field-induced delayed transparency.

http://arxiv.org/abs/1312.4693

Quantum Physics (quant-ph)

Konstantin Y. Bliokh, Yuri S. Kivshar, Franco Nori

We study the generic interaction of a monochromatic electromagnetic field with bi-isotropic nanoparticles. Such an interaction is described by dipole-coupling terms associated with the breaking of dual, P- and T-symmetries, including the chirality and the nonreciprocal magnetoelectric effect. We calculate absorption rates, radiation forces, and radiation torques for the nanoparticles and introduce novel characteristics of the field quantifying the transfer of energy, momentum, and angular-momentum in these interactions. In particular, we put forward the concept of ‘magnetoelectric energy density’, quantifying the local PT-symmetry of the field. Akin to the ‘super-chiral’ light suggested recently for sensitive local probing of molecular chirality [Phys. Rev. Lett. 104, 163901 (2010); Science 332, 333 (2011)], here we describe a complex field for sensitive probing of the nonreciprocal magnetoelectric effect in nanoparticles or molecules.

http://arxiv.org/abs/1312.4325

Optics (physics.optics); Other Condensed Matter (cond-mat.other); Quantum Physics (quant-ph)

Jianke Yang

Multi-dimensional complex optical potentials with partial parity-time (PT) symmetry are proposed. The usual PT symmetry requires that the potential is invariant under complex conjugation and simultaneous reflection in all spatial directions. However, we show that if the potential is only partially PT-symmetric, i.e., it is invariant under complex conjugation and reflection in a single spatial direction, then it can also possess all-real spectra and continuous families of solitons. These results are established analytically and corroborated numerically.

http://arxiv.org/abs/1312.3660

Pattern Formation and Solitons (nlin.PS); Optics (physics.optics)

K. Li, P. G. Kevrekidis, B. A. Malomed

The subject of the work are pairs of linearly coupled PT-symmetric dimers. Two different settings are introduced, namely, straight-coupled dimers, where each gain site is linearly coupled to one gain and one loss site, and cross-coupled dimers, with each gain site coupled to two lossy ones. The latter pair with equal coupling coefficients represents a “PT-hypersymmetric” quadrimer. We find symmetric and antisymmetric solutions in these systems, chiefly in an analytical form, and explore the existence, stability and dynamical behavior of such solutions by means of numerical methods. We thus identify bifurcations occurring in the systems, including spontaneous symmetry breaking and saddle-center bifurcations. Simulations demonstrate that evolution of unstable branches typically leads to blowup. However, in some cases unstable modes rearrange into stable ones.

http://arxiv.org/abs/1312.3376

Pattern Formation and Solitons (nlin.PS); Optics (physics.optics)

Yi-Chan Lee, Min-Hsiu Hsieh, Steven T. Flammia, Ray-Kuang Lee

Bender et al. have developed PT-symmetric quantum theory as an extension of quantum theory to non-Hermitian Hamiltonians. We show that when this model has a local PT symmetry acting on composite systems it violates the non-signaling principle of relativity. Since the case of global PT symmetry is known to reduce to standard quantum mechanics, this shows that the PT-symmetric theory is either a trivial extension or likely false as a fundamental theory.

http://arxiv.org/abs/1312.3395

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

Bhabani Prasad Mandal, Sushant S. Mahajan

We consider a Parity-time (PT) invariant non-Hermitian quasi-exactly solvable (QES) potential which exhibits PT phase transition. We numerically study this potential in a complex plane classically to demonstrate different quantum effects. The particle with real energy makes closed orbits around one of the periodic wells of the complex potential depending on the initial condition. However interestingly the particle can have open orbits even with real energy if it is initially placed in certain region between the two wells on the same side of the imaginary axis. On the other hand when the particle energy is complex the trajectory is open and the particle tunnels back and forth between two wells which are separated by a classically forbidden path. The tunneling time is calculated for different pair of wells and is shown to vary inversely with the imaginary component of energy. At the classical level unlike the analogous quantum situation we do not see any qualitative differences in the features of the particle dynamics for PT symmetry broken and unbroken phases.

http://arxiv.org/abs/1312.0757

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