PT symmetry, namely, a combined parity and time-reversal symmetry can make non-unitary quantum walks exhibit entirely real eigenenergy. However, it is known that the concept of PT symmetry can be generalized and an arbitrary anti-unitary symmetry has a possibility to substitute PT symmetry. The aim of the present work is to seek such non-unitary quantum walks with generalized PT symmetry by focusing on effects of spatially random disorder which breaks PT symmetry. We numerically find non-unitary quantum walks whose quasi-energy is entirely real despite PT symmetry is broken.PT symmetry, namely, a combined parity and time-reversal symmetry can make non-unitary quantum walks exhibit entirely real eigenenergy. However, it is known that the concept of PT symmetry can be generalized and an arbitrary anti-unitary symmetry has a possibility to substitute PT symmetry. The aim of the present work is to seek such non-unitary quantum walks with generalized PT symmetry by focusing on effects of spatially random disorder which breaks PT symmetry. We numerically find non-unitary quantum walks whose quasi-energy is entirely real despite PT symmetry is broken.

arXiv:1608.00719Interdisciplinary Information SciencesJan 1, 20177 citations

Remarks on Effect Algebras

W. A. Majewski, Tomasz I. Tylec

International Journal of Theoretical PhysicsDec 15, 20091 citation

\mathcal {P}\mathcal {T}-symmetry, Cartan decompositions, Lie triple systems and Krein space-related Clifford algebras

Uwe Günther, Sergiusz Kużel

Gauged PT quantum mechanics (PTQM) and corresponding Krein space setups are studied. For models with constant non-Abelian gauge potentials and extended parity inversions compact and noncompact Lie group components are analyzed via Cartan decompositions. A Lie triple structure is found and an interpretation as PT-symmetrically generalized Jaynes-Cummings model is possible with close relation to recently studied cavity QED setups with transmon states in multilevel artificial atoms. For models with Abelian gauge potentials a hidden Clifford algebra structure is found and used to obtain the fundamental symmetry of Krein space related J-selfadjoint extensions for PTQM setups with ultra-localized potentials.Gauged PT quantum mechanics (PTQM) and corresponding Krein space setups are studied. For models with constant non-Abelian gauge potentials and extended parity inversions compact and noncompact Lie group components are analyzed via Cartan decompositions. A Lie triple structure is found and an interpretation as PT-symmetrically generalized Jaynes-Cummings model is possible with close relation to recently studied cavity QED setups with transmon states in multilevel artificial atoms. For models with Abelian gauge potentials a hidden Clifford algebra structure is found and used to obtain the fundamental symmetry of Krein space related J-selfadjoint extensions for PTQM setups with ultra-localized potentials.

arXiv:1006.1134Journal of Physics A Mathematical and TheoreticalSep 1, 201018 citations

On Realization of Generalized Effect Algebras

Jan Paseka

arXiv:1208.1450Reports on Mathematical PhysicsDec 1, 20127 citations

What is PT symmetry

Miloslav Znojil

The recently proposed complexification of Hamiltonians which keeps the spectra real (and is usually called PT symmetry) is re-interpreted here as a certain natural linear-algebraic alternative to Hermiticity. The juxtaposition is mediated by the Feshbachian projection on a model space which reduces the difference just to a sign of a propagator in the effective Hamiltonian. The problem of norms and orthogonality is clarified and a few perturbation aspects are mentioned. A remarkable simplicity of the secular polynomial is conjectured. The mechanism of the PT symmetry breaking is clarified via a separable approximation scheme.The recently proposed complexification of Hamiltonians which keeps the spectra real (and is usually called PT symmetry) is re-interpreted here as a certain natural linear-algebraic alternative to Hermiticity. The juxtaposition is mediated by the Feshbachian projection on a model space which reduces the difference just to a sign of a propagator in the effective Hamiltonian. The problem of norms and orthogonality is clarified and a few perturbation aspects are mentioned. A remarkable simplicity of the secular polynomial is conjectured. The mechanism of the PT symmetry breaking is clarified via a separable approximation scheme.

Mar 12, 20017 citations

\mathcal{PT}

-Symmetry in (Generalized) Effect Algebras