August 2014
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Month August 2014

PT-/non-PT-Symmetric and non-Hermitian Hellmann Potential: Approximate Bound and Scattering States with Any \(\ell\)-Values

Altug Arda, Ramazan Sever

We investigate the approximate bound state solutions of the Schrodinger equation for the PT-/non-PT-symmetric and non Hermitian Hellmann potential. Exact energy eigenvalues and corresponding normalized wave functions are obtained. Numerical values of energy eigenvalues for the bound states are compared with the ones obtained before. Scattering state solutions are also studied. Phase shifts of the potential are written in terms of the angular momentum quantum number \(\ell\).
Quantum Physics (quant-ph)

Three-level \(\Lambda\)-type atomic systems with a Pseudo-Hermitian PT-symmetric Hamiltonian

Amarendra K. Sarma, Balla Prannay

We have studied a three-level \(\Lambda\)-type atomic system with all the energy levels exhibiting decay. The system is described by a pseudo-Hermitian Hamiltonian and subject to certain conditions, the Hamiltonian shows parity-time (PT) symmetry. The probability amplitudes of various atomic levels both below and above the PT-theshold is worked out.
Quantum Physics (quant-ph); Optics (physics.optics)

Unbreakable PT-symmetry of solitons supported by inhomogeneous defocusing nonlinearity

Yaroslav V. Kartashov, Boris A. Malomed, Lluis Torner

We consider bright solitons supported by a symmetric inhomogeneous defocusing nonlinearity growing rapidly enough toward the periphery of the medium, combined with an antisymmetric gain-loss profile. Despite the absence of any symmetric modulation of the linear refractive index, which is usually required to establish a PT-symmetry in the form of a purely real spectrum of modes, we show that the PT-symmetry is never broken in the present system, and that the system always supports stable bright solitons, fundamental and multi-pole ones. Such phenomenon is connected to non-linearizability of the underlying evolution equation. The increase of the gain-losses strength results, in lieu of the PT-symmetry breaking, in merger of pairs of different soliton branches, such as fundamental and dipole, or tripole and quadrupole ones. The fundamental and dipole solitons remain stable for all values of the gain-loss coefficient.
Optics (physics.optics); Pattern Formation and Solitons (nlin.PS)

Elementary modes of coupled oscillators with balanced loss and gain

Rabin Banerjee, Pradip Mukherjee

We provide a reduction of a set of two coupled oscillators with balanced loss and gain in their elementary modes. A possible method of quantization based on these elementary modes, in the framework of PT symmetric quantum mechanics is indicated.
High Energy Physics – Theory (hep-th)

PT-symmetry in macroscopic magnetic structures

J. M. Lee, T. Kottos, B. Shapiro

We introduce the notion of PT-symmetry in magnetic nanostructures and show that they can support a new type of non-Hermitian dynamics. Using the simplest possible set-up consisting of two coupled ferromagnetic films, one with loss and another one with a balanced amount of gain, we demonstrate the existence of a spontaneous PT-symmetry breaking point where both the eigenfrequencies and eigenvectors are degenerate. Below this point the frequency spectrum is real indicating stable dynamics while above this point it is complex signaling unstable dynamics.
Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Mathematical Physics (math-ph); Chaotic Dynamics (nlin.CD)

PT-symmetry in optics beyond the paraxial approximation

Changming Huang, Fangwei Ye, Yaroslav V. Kartashov, Boris A Malomed, Xianfeng Chen

The concept of the PT-symmetry, originating from the quantum field theory, has been intensively investigated in optics, stimulated by the similarity between the Schr\”odinger equation and the paraxial wave equation that governs the propagation of light in a guiding structure. We go beyond the bounds of the paraxial approximation and demonstrate, using the solution of the Maxwell’s equations for light beams propagating in deeply subwavelength waveguides and periodic lattices with “balanced” gain and loss, that the PT symmetry may stay unbroken in this setting. Moreover, the PT-symmetry in subwavelength optical structures may be restored after being initially broken upon the increase of gain and loss. Critical gain/loss levels, at which the breakup and subsequent restoration of the PT symmetry occur, strongly depend on the scale of the structure.
Optics (physics.optics); Pattern Formation and Solitons (nlin.PS)

Infinitely many inequivalent field theories from one Lagrangian

Carl M. Bender, Daniel W. Hook, Nick E. Mavromatos, Sarben Sarkar

Logarithmic time-like Liouville quantum field theory has a generalized PT invariance, where T is the time-reversal operator and P stands for an S-duality reflection of the Liouville field \(\phi\). In Euclidean space the Lagrangian of such a theory, \(L=\frac{1}{2}(\nabla\phi)^2−ig\phi \exp(ia\phi)\), is analyzed using the techniques of PT-symmetric quantum theory. It is shown that L defines an infinite number of unitarily inequivalent sectors of the theory labeled by the integer n. In one-dimensional space (quantum mechanics) the energy spectrum is calculated in the semiclassical limit and the \(m\)th energy level in the \(n\)th sector is given by \(E_{m,n}∼(m+1/2)^2a^2/(16n^2)\).
High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)

Light transport in PT-invariant photonic structures with hidden symmetries

M.H. Teimourpour, R. El-Ganainy, A. Eisfeld, A. Szameit, D.N Christodoulides

We introduce a recursive bosonic quantization technique for generating classical PT photonic structures that possess hidden symmetries and higher order exceptional points. We study light transport in these geometries and we demonstrate that perfect state transfer is possible only for certain initial conditions. Moreover, we show that for the same propagation direction, left and right coherent transports are not symmetric with field amplitudes following two different trajectories. A general scheme for identifying the conservation laws in such PT-symmetric photonic networks is also presented.
Optics (physics.optics); Quantum Physics (quant-ph)

On Symmetries and Exact Solutions of a Class of Non-local Non-linear Schrodinger Equations with Self-induced PT-symmetric Potential

Debdeep Sinha, Pijush K. Ghosh

A class of non-local non-linear Schrodinger equations(NLSE) is considered in an external potential with space-time modulated coefficient of the nonlinear interaction term as well as confining and/or loss-gain terms. This is a generalization of a recently introduced integrable non-local NLSE with self induced potential that is PT symmetric in the corresponding stationary problem. Exact soliton solutions are obtained for the inhomogeneous and/or non autonomous non-local NLSE by using similarity transformation and the method is illustrated with a few examples. It is found that only those transformations are allowed for which the transformed spatial coordinate is odd under the parity transformation of the original one. It is shown that the non-local NLSE without the external potential and a \(d+1\) dimensional generalization of it, admits all the symmetries of the \(d+1\) dimensional Schrodinger group. The conserved Noether charges associated with the time-translation, dilatation and special conformal transformation are shown to be real-valued in spite of being non-hermitian. Finally, dynamics of different moments are studied with an exact description of the time-evolution of the “pseudo-width” of the wave-packet for the special case when the system admits a \(O(2,1)\) conformal symmetry.
Exactly Solvable and Integrable Systems (nlin.SI); High Energy Physics – Theory (hep-th)

Symmetry breaking of solitons in one-dimensional parity-time-symmetric optical potentials

Jianke Yang

Symmetry breaking of solitons in a class of one-dimensional parity-time (PT) symmetric complex potentials with cubic nonlinearity is reported. In generic PT symmetric potentials, such symmetry breaking is forbidden. However, in a special class of PT-symmetric potentials \(V(x)=g^2(x)+αg(x)+ig′(x)\), where \(g(x)\) is a real and even function and α a real constant, symmetry breaking of solitons can occur. That is, a branch of non-PT-symmetric solitons can bifurcate out from the base branch of PT-symmetric solitons when the base branch’s power reaches a certain threshold. At the bifurcation point, the base branch changes stability, and the bifurcated branch can be stable.
Optics (physics.optics); Pattern Formation and Solitons (nlin.PS)