2,194 research outputs found
Non-unitarity and non-reciprocity in scattering from real potentials in presence of confined non-linearity
Investigations of scattering in presence of non-linearity which have just
begun require the confinement of both the potential, , and the
non-linearity, . There could be two options for the
confinement. One is the finite support on and the other one is
on . Here, we consider real Hermitian potentials and report a
surprising disparate behaviour of these two types of confinements. We prove
that in the first option the symmetric potential enjoys reciprocity of both
reflectivity () and transmitivity () and their unitarity. More
interestingly, the asymmetry in causes non-unitarity () and
the non-reciprocity (reciprocity) of . On the other hand, the second
option of confinement gives rise to an essential non-unitarity even when
is symmetric about a point in . In the absence of symmetry there occurs
non-reciprocity of both and .Comment: 8 pages, Five Figures each with three parts a.b.
Gaussian-random Ensembles of Pseudo-Hermitian Matrices
Attention has been brought to the possibility that statistical fluctuation
properties of several complex spectra, or, well-known number sequences may
display strong signatures that the Hamiltonian yielding them as eigenvalues is
PT-symmetric (Pseudo-Hermitian). We find that the random matrix theory of
pseudo-Hermitian Hamiltonians gives rise to new universalities of level-spacing
distributions other than those of GOE, GUE and GSE of Wigner and Dyson. We call
the new proposals as Gaussian Pseudo-Orthogonal Ensemble and Gaussian
Pseudo-Unitary Ensemble. We are also led to speculate that the enigmatic
Riemann-zeros ( would rather correspond to some
PT-symmetric (pseudo-Hermitian) Hamiltonian.Comment: Invited Talk Delivered in II International Workshop on
`Pseudo-Hermitian Hanmiltonians in Physics' at Prague, June 14-16, 200
PT-symmetry and Transparency
It is known that the perfect absorption of two identical waves incident on a
complex potential from left and right can occur at a fixed real energy and that
the time-reversed setting of this system would act as a laser at threshold at
the same energy. Here, we argue and show that PT-symmetric potentials are
exceptional in this regard which do not allow Coherent Perfect Absorption
without lasing as the modulus of the determinant of the -matrix, ,
becomes 1, for all positive energies. Next we show that in the parametric
regimes where the PT-symmetry is unbroken, the eigenvalues, of , can
become unitary (uni-modular) for all energies. Then the potential becomes
coherent perfect emitter on both sides for any energy of coherent injection. We
call this property Transparency.Comment: 8 pages no Figure This paper is being withdrawn since we used an
in-appropriate s-matrix for transparency for coherent injection. We will soon
submit our investigation of transparency here and elsewher
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