October 2011
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Day October 12, 2011

Stabilization of solitons in PT models with supersymmetry by periodic management

R. Driben, B. A. Malomed

We introduce a system based on dual-core nonlinear waveguides with the balanced gain and loss acting separately in the cores. The system features a “supersymmetry” when the gain and loss are equal to the inter-core coupling. This system admits a variety of exact solutions (we focus on solitons), which are subject to a specific subexponential instability. We demonstrate that the application of a “management”, in the form of periodic simultaneous switch of the sign of the gain, loss, and inter-coupling, effectively stabilizes solitons, without destroying the supersymmetry. The management turns the solitons into attractors, for which an attraction basin is identified. The initial amplitude asymmetry and phase mismatch between the components transforms the solitons into quasi-stable breathers.

http://arxiv.org/abs/1110.2409
Optics (physics.optics); Pattern Formation and Solitons (nlin.PS)

Spontaneous breaking of permutation symmetry in pseudo-hermitian quantum mechanics

Jun-Qing Li, Yan-Gang Miao

By adding an imaginary potential proportional to \(ip_1p_2\) to the hamiltonian of an anisotropic planar oscillator, we construct a model which is described by a non-hermitian hamiltonian with PT pseudo-hermiticity. We introduce the mechanism of the spontaneous breaking of permutation symmetry of the hamiltonian for diagonalizing the hamiltonian. By applying the definition of annihilation and creation operators which are PT pseudo-hermitian adjoint to each other, we give the real spectra.

http://arxiv.org/abs/1110.2312
Quantum Physics (quant-ph)

Jun-Qing Li, Yan-Gang Miao

By adding an imaginary potential proportional to ip_1p_2 to the hamiltonian of an anisotropic planar oscillator, we construct a model which is described by a non-hermitian hamiltonian with PT pseudo-hermiticity. We introduce the mechanism of the spontaneous breaking of permutation symmetry of the hamiltonian for diagonalizing the hamiltonian. By applying the definition of annihilation and creation operators which are PT pseudo-hermitian adjoint to each other, we give the real spectra.

http://arxiv.org/abs/1110.2312

Quantum Physics (quant-ph)