Exceptional points and pseudo-Hermiticity in real potential scattering
- URL: http://arxiv.org/abs/2110.05884v3
- Date: Mon, 11 Apr 2022 14:33:39 GMT
- Title: Exceptional points and pseudo-Hermiticity in real potential scattering
- Authors: Farhang Loran and Ali Mostafazadeh
- Abstract summary: We study a class of scattering setups modeled by real potentials in two dimensions.
Our results reveal the relevance of the concepts of pseudo-Hermitian operator and exceptional point in the standard quantum mechanics of closed systems.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We employ a recently-developed transfer-matrix formulation of scattering
theory in two dimensions to study a class of scattering setups modeled by real
potentials. The transfer matrix for these potentials is related to the
time-evolution operator for an associated pseudo-Hermitian Hamiltonian operator
$\widehat{\mathbf{H}}$ which develops an exceptional point for a discrete set
of incident wavenumbers. We use the spectral properties of this operator to
determine the transfer matrix of these potentials and solve their scattering
problem. We apply our general results to explore the scattering of waves by a
waveguide of finite length in two dimensions, where the source of the incident
wave and the detectors measuring the scattered wave are positioned at spatial
infinities while the interior of the waveguide, which is filled with an
inactive material, forms a finite rectangular region of the space. The study of
this model allows us to elucidate the physical meaning and implications of the
presence of the real and complex eigenvalues of $\widehat{\mathbf{H}}$ and its
exceptional points. Our results reveal the relevance of the concepts of
pseudo-Hermitian operator and exceptional point in the standard quantum
mechanics of closed systems where the potentials are required to be real.
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