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Related papers: Real Spectra in PT Symmetry Hamiltonians using Tri…

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If a Hamiltonian is PT symmetric, there are two possibilities: Either the eigenvalues are entirely real, in which case the Hamiltonian is said to be in an unbroken-PT-symmetric phase, or else the eigenvalues are partly real and partly…

Mathematical Physics · Physics 2015-06-05 Carl M. Bender , Bjorn K. Berntson , David Parker , E. Samuel

Non-Hermitian systems with parity-time symmetry have been developed rapidly and hold great promise for future applications. Unlike most existing works considering the symmetry of the free energy terms (e.g., gain-loss system), in this…

Quantum Physics · Physics 2017-11-21 Wenlin Li , Chong Li , Heshan Song

The local reggeon field theory is studied perturbatively taking advantage of the PT symmetry in the Hamiltonian formulation. In the lowest non trivial order we show that the pomeron interactions renormalize the slope. In the same order we…

High Energy Physics - Phenomenology · Physics 2010-04-21 M. A. Braun , G. P. Vacca

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 comprehensive and essentially self-contained review…

Quantum Physics · Physics 2015-05-13 Ali Mostafazadeh

This paper deals with the mathematical spectral analysis and physical interpretation of a fermionic system described by a non-Hermitian Hamiltonian possessing real eigenvalues. A statistical thermodynamical description of such a system is…

Effective non-Hermitian Hamiltonians are obtained to describe coherent perfect absorbing and lasing boundary conditions. PT -symmetry of the Hamiltonians enables to design configurations which perfectly absorb at multiple frequencies.…

Classical Physics · Physics 2017-04-19 V. Achilleos , G. Theocharis , O. Richoux , V. Pagneux

Non-hermitian, $\mathcal{PT}$-symmetric Hamiltonians, experimentally realized in optical systems, accurately model the properties of open, bosonic systems with balanced, spatially separated gain and loss. We present a family of exactly…

Quantum Physics · Physics 2015-12-17 Kaustubh S. Agarwal , Rajeev K. Pathak , Yogesh N. Joglekar

While dealing in [1] with the supersymmetry of a tridiagonal Hamiltonian H, we have proved that its partner Hamiltonian H(+) also have a tridiagonal matrix representation in the same basis and that the polynomials associated with the…

Mathematical Physics · Physics 2017-04-05 Hashim A Yamani , Zouhair Mouayn

We study a general class of PT-symmetric tridiagonal Hamiltonians with purely imaginary interaction terms in the quasi-hermitian representation of quantum mechanics. Our general Hamiltonian encompasses many previously studied lattice models…

Quantum Physics · Physics 2016-04-05 Frantisek Ruzicka

Version 1: The well known Eckart's singular s-wave potential is PT-symmetrically regularized and continued to the whole real line. The new model remains exactly solvable and its bound states remain proportional to Jacobi polynomials. Its…

Quantum Physics · Physics 2009-10-31 Miloslav Znojil

One of the most used approaches in simulating materials is the tight-binding approximation. When using this method in a material simulation, it is necessary to compute the eigenvalues and eigenvectors of the Hamiltonian describing the…

Numerical Analysis · Computer Science 2009-10-29 Matthias Petschow , Edoardo Di Napoli , Paolo Bientinesi

The energy spectrum of the three-particle Hamiltonian obtained by replacing the two-body trigonometric potential of the Sutherland problem by a three-body one of a similar form is derived. When expressed in appropriate variables, the…

High Energy Physics - Theory · Physics 2009-10-30 C. Quesne

Bootstrapping in Quantum Mechanics uses positivity condition to derive the Eigenspectum. For non-hermitian systems usual positivity condition does not work. In this paper we define positivity condition for special class of non-hermitian…

Quantum Physics · Physics 2022-10-05 Sakil Khan , Yuv Agarwal , Devjyoti Tripathy , Sachin Jain

We review various attempts to localize the discrete spectra of semirelativistic Hamiltonians of the form H = \beta \sqrt{m^2 + p^2} + V(r) (w.l.o.g. in three spatial dimensions) as entering, for instance, in the spinless Salpeter equation.…

High Energy Physics - Theory · Physics 2014-11-18 Richard Hall , Wolfgang Lucha , F. F. Schoeberl

A real potential Hamiltonian has real energy bound states below the scattering threshold and complex energy resonances above it. Scattering states are not square integrable, being instead delta function normalized. This lack of square…

Quantum Physics · Physics 2026-05-06 Philip D. Mannheim

A complexified von Roos Hamiltonian is considered and a Hermitian first-order intertwining differential operator is used to obtain the related position dependent mass $\eta$-weak-pseudo-Hermitian Hamiltonians. Using a Liouvillean-type…

Quantum Physics · Physics 2009-11-13 Omar Mustafa , S. Habib Mazharimousavi

We provide a reviewlike introduction into the quantum mechanical formalism related to non-Hermitian Hamiltonian systems with real eigenvalues. Starting with the time-independent framework we explain how to determine an appropriate domain of…

Quantum Physics · Physics 2015-06-26 Carla Figueira de Morisson Faria , Andreas Fring

We demonstrate that non-Hermitian Hamiltonian systems with spontaneously broken PT-symmetry and partially complex eigenvalue spectrum can be made meaningful in a quantum mechanical sense when introducing some explicit time-dependence into…

Quantum Physics · Physics 2017-06-06 Andreas Fring , Thomas Frith

A class of three-dimensional models which satisfy supersymmetric intertwining relations with the simplest - oscillator-like - variant of shape invariance is constructed. It is proved that the models are not amenable to conventional…

High Energy Physics - Theory · Physics 2015-06-12 M. S. Bardavelidze , F. Cannata , M. V. Ioffe , D. N. Nishnianidze

We study Hamiltonian systems with point interactions and give a systematic description of the corresponding boundary conditions and the spectrum properties for self-adjoint, PT-symmetric systems and systems with real spectra. The…

Quantum Physics · Physics 2009-11-10 Shao-Ming Fei