Transfer matrices as nonunitary S matrices, multimode unidirectional invisibility, and perturbative inverse scattering

@article{Mostafazadeh2014TransferMA,
  title={Transfer matrices as nonunitary S matrices, multimode unidirectional invisibility, and perturbative inverse scattering},
  author={Ali Mostafazadeh},
  journal={Physical Review A},
  year={2014},
  volume={89},
  pages={012709}
}
  • A. Mostafazadeh
  • Published 7 November 2013
  • Physics, Mathematics
  • Physical Review A
We show that in one dimension the transfer matrix M of any scattering potential v coincides with the S-matrix of an associated time-dependent non-Hermitian 2 x 2 matrix Hamiltonian H(\tau). If v is real-valued, H(\tau) is pseudo-Hermitian and its exceptional points correspond to the classical turning points of v. Applying time-dependent perturbation theory to H(\tau) we obtain a perturbative series expansion for M and use it to study the phenomenon of unidirectional invisibility. In particular… 

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References

SHOWING 1-10 OF 38 REFERENCES
Pseudo-Hermitian Representation of Quantum Mechanics
A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a
A Dynamical Formulation of One-Dimensional Scattering Theory and Its Applications in Optics
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are
Quantum Theory of Fields
To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject. But it is a very good and most useful book. The original was
An introduction to electromagnetic inverse scattering
Preface. 1. Introduction. 2. Mathematics of Electromagnetic Waves. 3. Linearized Inverse Solutions. 4. Higher Order Integral Solutions. 5. Higher Order Differential Solutions. 6. Exact Solutions. 7.
Modern Quantum Mechanics
1. Fundamental Concepts. 2. Quantum Dynamics. 3. Theory of Angular Momentum. 4. Symmetry in Quantum Mechanics. 5. Approximation Methods. 6. Identical Particles. 7. Scattering Theory. Appendices.
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
Ann
Aaron Beck’s cognitive therapy model has been used repeatedly to treat depression and anxiety. The case presented here is a 34-year-old female law student with an adjustment disorder with mixed
A 44
  • 392001 (2011); Phil. Trans. R. Soc. A 371, 20120044,
  • 2013
Nature Materials 12
  • 108
  • 2013
Nature Materials 12
  • 175
  • 2013
...
1
2
3
4
...