Pt Symmetry and Supersymmetry 1. Supersymmetry for Pedestrians, or Bosons and Fermions in Witten's Picture
Pseudo-Hermitian (so called PT symmetric) Hamiltonians are featured within a re-formulated Witten's supersymmetric quantum mechanics. An unusual form of the supersymmetric partnership between the spiked harmonic oscillators is described. In the review [1] of the Witten's (or so called supersymmetric) quantum mechanics one finds the specific Fock vacuum q|0 = exp(−q 2 /2)/ √ π 0 , q ∈ (−∞, ∞). (1) In the upper line we recognize the ground state of the one-dimensional harmonic oscillator H (HO) = p 2 + q 2 and see that " bosons " may be created/annihilated by the action of the respective operators −∂ r + q and ∂ r + q (to be denoted as B (−1/2) and A (−1/2) here). The solvable harmonic-oscillator character of this elementary model enables us to define the three two-by-two matrices F † = 0 0 1 0 , F = 0 1 0 0 , N F = 0 0 0 1 (2) which create and annihilate a " fermion " and determine the fermionic number, respectively. Formally, this enables us to introduce the two partner Hamiltonians H (L) = H (HO) − 1, H (R) = H (HO) + 1 and identify the underlying symmetry with the superalgebra sl(1/1) generated by the following three operator matrices
Supersymmetry in the half oscillator: Revisited
Following a recent study by Das and Pernice [Nucl. Phys. B561, (1999) 357], we have carefully analyzed the half-harmonic oscillator. In contrast to their observations, our analysis reveals that the spectrum does not allow for a zero energy ground state and hence the supersymmetry is broken when the domain is restricted to the positive half of the real axis.
Strategies for glass based photonic system integration
There is a clear tendency to integrate more and more opto-electronic and micro-optical components like optical fibers, laser diodes, modulators, isolators, beam-splitting components and micro lenses in also increasingly dense and complex assemblies. The paper will discuss thin glass as a very promising base material for that kind of photonic packaging on interposer and board level including optical interconnection using fibers.