Yogesh N. Joglekar, Derek D. Scott, Avadh Saxena
We investigate the parity- and time-reversal (PT)-symmetry breaking in lattice models in the presence of long-ranged, non-hermitian, PT-symmetric potentials that remain finite or become divergent in the continuum limit. By scaling analysis of the fragile PT threshold for an open finite lattice, we show that continuum loss-gain potentials \(V_a(x)\sim i|x|^a{\rm sign}(x)\) have a positive PT-breaking threshold for \(\alpha>−2\), and a zero threshold for α≤−2. When α<0 localized states with complex (conjugate) energies in the continuum energy-band occur at higher loss-gain strengths. We investigate the signatures of PT-symmetry breaking in coupled waveguides, and show that the emergence of localized states dramatically shortens the relevant time-scale in the PT-symmetry broken region.
http://arxiv.org/abs/1403.4204
Quantum Physics (quant-ph); Optics (physics.optics)
D. Borisov
We consider a model of planar PT-symmetric waveguide and study the phenomenon of the eigenvalues collision under the perturbation of boundary conditions. This phenomenon was discovered numerically in previous works. The main result of this work is an analytic explanation of this phenomenon.
http://arxiv.org/abs/1401.6316
Spectral Theory (math.SP); Mathematical Physics (math-ph); Analysis of PDEs (math.AP)
E. M. Ferreira, J. Sesma
The spectrum of a one-dimensional Hamiltonian with potential V(x)=ix2 for negative x and \(V(x)=−ix^2\) for positive x is analyzed. The Schrodinger equation is algebraically solvable and the eigenvalues are obtained as the zeros of an expression explicitly given in terms of Gamma functions. The spectrum consists of one real eigenvalue and an infinite set of pairs of complex conjugate eigenvalues.
http://arxiv.org/abs/1401.5937
Quantum Physics (quant-ph)
The 11th Analytic and Algebraic Methods in Physics conference will be held at Villa Lanna, Prague, CZ between 30 October 2013 and 1 November 2013.
Details of the conference and registration may be found on:
http://gemma.ujf.cas.cz/~znojil/conf/micromeetingjedenact.html
V. N. Rodionov
The quantum-field model described by non-Hermitian, but a \({\cal PT}\)-symmetric Hamiltonian is considered. It is shown by the algebraic way that the limiting of the physical mass value \(m \leq m_{max}= {m_1}^2/2m_2\) takes place for the case of a fermion field with a \(\gamma_5\)-dependent mass term (\(m\rightarrow m_1 +\gamma_5 m_2 \)). In the regions of unbroken \(\cal PT\) symmetry the Hamiltonian \(H\) has another symmetry represented by a linear operator \( \cal C\). We exactly construct this operator by using a non-perturbative method. In terms of \( \cal C\) operator we calculate a time-independent inner product with a positive-defined norm. As a consequence of finiteness mass spectrum we have the \(\cal PT\)-symmetric Hamiltonian in the areas \((m\leq m_{max})\), but beyond this limits \(\cal PT\)-symmetry is broken. Thus, we obtain that the basic results of the fermion field model with a \(\gamma_5\)-dependent mass term is equivalent to the Model with a Maximal Mass which for decades has been developed by V.Kadyshevsky and his colleagues. In their numerous papers the condition of finiteness of elementary particle mass spectrum was introduced in a purely geometric way, just as the velocity of light is a maximal velocity in the special relativity. The adequate geometrical realization of the limiting mass hypothesis is added up to the choice of (anti) de Sitter momentum space of the constant curvature.
http://arxiv.org/abs/1207.5463
Mathematical Physics (math-ph); High Energy Physics – Theory (hep-th); Quantum Physics (quant-ph)
An article on a young mathematical prodigy on the 60 minutes news programme on US television shows him working on PT Symmetry with Prof YN Joglekar at IUPUI.
Their research article is available on arXiv at http://arxiv.org/abs/1108.6083, was published in Physical Review A (http://pra.aps.org/abstract/PRA/v84/i2/e024103), was reported on the PT-Symmeter (http://ptsymmetry.net/?p=552), and can now be seen as part of a documentary on the CBS 60 minutes website here:
http://www.cbsnews.com/video/watch/?id=7395214n&tag=re1.galleries
Huagang Li, Xiujuan Jiang, Xing Zhu, Zhiwei Shi
We numerically study the nonlocal gap solitons in parity-time (PT) symmetric optical lattices built into a nonlocal self-focusing medium. We state the existence, stability, and propagation dynamics of such PT gap solitons in detail. Simulated results show that there exist stable gap soltions. The influences of the degree of nonlocality on the soliton power, the energy flow density and the stable region of the PT gap solitons are also examined.
http://arxiv.org/abs/1109.4987
Optics (physics.optics)