Quantum graphs: PT -symmetry and reflection symmetry of the spectrum
نویسندگان
چکیده
منابع مشابه
Time-dependent quantum systems and PT symmetry
In this work we intend to study a class of time-dependent quantum systems with nonHermitian Hamiltonians, particularly those whose Hermitian counterpart are important for the comprehension of posed problems in quantum optics and quantum chemistry, which consists of an oscillator with time-dependent mass and frequency under the action of a time-dependent imaginary potential. We obtain the propag...
متن کاملThe band spectrum of periodic potentials with PT - symmetry
A real band condition is shown to exist for one dimensional periodic complex non-hermitian potentials exhibiting PT-symmetry. We use an exactly solvable ultralocal periodic potential to obtain the band structure and discuss some spectral features of the model, specially those concerning the role of the imaginary parameters of the couplings. Analytical results as well as some numerical examples ...
متن کاملBroken spectral reflection symmetry in a solvable PT −symmetric model
Any non-Hermitian PT −symmetric quantum Hamiltonian H remains physical in a domain of parameters D where the spectrum is real and, hence, measurable. It has been conjectured and verified, recently, that the postulate of a self-duality of the spectrum Ej = −EN+1−j could simplify the structure of the manifold D. An independent constructive support of the plausibility of such a relationship is giv...
متن کاملWhat Is Pt Symmetry?
The recently proposed complexification of Hamiltonians which keeps the spectra real (and is usually called PT symmetry) is re-interpreted as a certain natural linearalgebraic alternative to Hermiticity. PACS 03.65.Bz, 03.65.Ca 03.65.Fd March 15, 2008, whatis.tex file, J. Phys. A (lett.) Formalism of quantum mechanics is often illustrated by the harmonic oscillator H = p + q. Its eigenstates for...
متن کاملDetecting Broken PT-Symmetry
A fundamental problem in the theory of PT-invariant quantum systems is to determine whether a given system “respects” this symmetry or not. If not, the system usually develops non-real eigenvalues. It is shown in this contribution how to algorithmically detect the existence of complex eigenvalues for a given PT-symmetric matrix. The procedure uses classical results from stability theory which q...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2017
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.4975757