The band spectrum of periodic potentials with PT - symmetry
نویسنده
چکیده
A real band condition is shown to exist for one dimensional periodic complex non-hermitian potentials exhibiting PT-symmetry. We use an exactly solvable ultralocal periodic potential to obtain the band structure and discuss some spectral features of the model, specially those concerning the role of the imaginary parameters of the couplings. Analytical results as well as some numerical examples are provided. The band spectrum of periodic potentials with PT-symmetry 2
منابع مشابه
The energy spectrum of complex periodic potentials of the Kronig-Penney type
We consider a complex periodic PT-symmetric potential of the Kronig-Penney type, in order to elucidate the peculiar properties found by Bender et al. for potentials of the form V = i(sin x)2N+1, and in particular the absence of anti-periodic solutions. In this model we show explicitly why these solutions disappear as soon as V (x) 6= V (x), and spell out the consequences for the form of the dis...
متن کاملAnalytically Solvable PT-Invariant Periodic Potentials
Associated Lamé potentials V (x) = a(a + 1)msn2(x,m) + b(b + 1)mcn2(x,m)/dn(x,m) are used to construct complex, PT-invariant, periodic potentials using the anti-isospectral transformation x→ ix+ β, where β is any nonzero real number. These PT-invariant potentials are defined by V PT (x) ≡ −V (ix + β), and have a different real period from V (x). They are analytically solvable potentials with a ...
متن کاملPT-Invariant Periodic Potentials with a Finite Number of Band Gaps
We obtain the band edge eigenstates and the mid-band states for the complex, PT-invariant generalized associated Lamé potentials V PT (x) = −a(a + 1)m sn2(y,m) − b(b + 1)m sn2(y +K(m),m) − f(f+1)m sn2(y +K(m) + iK (m),m)−g(g+1)m sn2(y + iK (m),m), where y ≡ ix+β, and there are four parameters a, b, f, g. This work is a substantial generalization of previous work with the associated Lamé potenti...
متن کاملObservation of defect states in PT-symmetric optical lattices.
We provide the first experimental demonstration of defect states in parity-time (PT) symmetric mesh-periodic potentials. Our results indicate that these localized modes can undergo an abrupt phase transition in spite of the fact that they remain localized in a PT-symmetric periodic environment. Even more intriguing is the possibility of observing a linearly growing radiation emission from such ...
متن کاملHoneycomb Lattice Potentials and Dirac Points
In this article we study the spectral properties of the Schrödinger operator HV “ ́Δ ` V pxq, x P R, where the potential, V , is periodic and has honeycomb structure symmetry. For general periodic potentials the spectrum of HV , considered as an operator on LpRq, is the union of closed intervals of continuous spectrum called the spectral bands. Associated with each spectral band are a band dispe...
متن کامل