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It is shown that for a given Hermitian Hamiltonian possessing supersymmetry, there is alwayas a non-hermitian Jaynes-Cummings-type Hamiltonian(JCTH) admitting entirely real spectra. The parent supersymmetric Hamiltonian and the…

Quantum Physics · Physics 2009-11-11 Pijush K. Ghosh

The relevance of parity and time reversal (PT)-symmetric structures in optical systems is known for sometime with the correspondence existing between the Schrodinger equation and the paraxial equation of diffraction where the time parameter…

Quantum Physics · Physics 2014-01-21 Bijan Bagchi , Subhrajit Modak , Prasanta K. Panigrahi

Large families of Hamiltonians that are non-Hermitian in the conventional sense have been found to have all eigenvalues real, a fact attributed to an unbroken PT symmetry. The corresponding quantum theories possess an unconventional scalar…

Quantum Physics · Physics 2009-11-11 Zafar Ahmed , Carl M. Bender , M. V. Berry

We present a new approach to study a class of non-Hermitian (1+1)-dimensional Dirac Hamiltonian in the presence of local Fermi velocity. We apply the well known Nikiforov-Uvarov method to solve such a system. We discuss applications and…

Quantum Physics · Physics 2023-03-22 Rahul Ghosh

Two alternative scenarios are shown possible in Quantum Mechanics working with non-Hermitian $PT-$symmetric form of observables. While, usually, people assume that $P$ is a self-adjoint indefinite metric in Hilbert space (and that their…

Quantum Physics · Physics 2007-05-23 Miloslav Znojil

We extend the application of the techniques developed within the framework of the pseudo-Hermitian quantum mechanics to study a unitary quantum system described by an imaginary PT-symmetric potential v(x) having a continuous real spectrum.…

Quantum Physics · Physics 2009-11-11 Ali Mostafazadeh

The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge $e$ is taken to be imaginary. However, if one also specifies that the potential $A^\mu$ in such a theory transforms as a pseudovector…

High Energy Physics - Theory · Physics 2011-07-19 Carl M. Bender , Ines Cavero-Pelaez , Kimball A. Milton , K. V. Shajesh

In the conventional Schr\"{o}dinger's formulation of quantum mechanics the unitary evolution of a state $\psi$ is controlled, in Hilbert space ${\cal L}$, by a Hamiltonian $\mathfrak{h}$ which must be self-adjoint. In the recent,…

Quantum Physics · Physics 2023-12-21 Olaf Lechtenfeld , Miloslav Znojil

Manifestly non-Hermitian quantum graphs with real spectra are introduced and shown tractable as a new class of phenomenological models with several appealing descriptive properties. For illustrative purposes, just equilateral star-graphs…

High Energy Physics - Theory · Physics 2009-11-10 Miloslav Znojil

We study the Non-Hermitian quantum mechanics for the discrete system. This paper gives an exact analytic single-particle solution for an $N$-site tight-binding chain with two conjugated imaginary potentials $\pm i\gamma $ at two end sites,…

Quantum Physics · Physics 2011-07-04 L. Jin , Z. Song

The {\eta} pseudo PT symmetry theory, denoted by the symbol {\eta}, explores the conditions under which non-Hermitian Hamiltonians can possess real spectra despite the violation of PT symmetry, that is the adjoint of H, denoted H^{{\dag}}…

Quantum Physics · Physics 2024-01-09 Mustapha Maamache , Nour El Houda Absi

The overall principles of what is now widely known as PT-symmetric quantum mechanics are listed, explained and illustrated via a few examples. In particular, models based on an elementary local interaction V(x) are discussed as motivated by…

Quantum Physics · Physics 2015-11-06 Francisco M. Fernández , Javier Garcia , Iveta Semorádová , Miloslav Znojil

A $\mathcal{PT}$-symmetric, non-Hermitian Hamiltonian in the $\mathcal{PT}$-unbroken regime can lead to unitary dynamics under the appropriate choice of the Hilbert space. The Hilbert space is determined by a Hamiltonian-compatible inner…

Quantum Physics · Physics 2025-03-19 Himanshu Badhani , Subhashish Banerjee , C. M. Chandrashekar

A new proof is given for why the non-Hermitian, PT-Invariant cubic oscillator with imaginary coupling has real eigenvalues. The proof consists of two steps. In the first step, it is shown that for many PT-Invariant Hamiltonians, one can…

Mathematical Physics · Physics 2009-10-28 Scott Chapman

We introduce and study a class of non-Hermitian Hamiltonians which have velocity dependent potentials. Since stability can not be advocated directly from the classical potential, we show that the energy spectra are real and bounded from…

Quantum Physics · Physics 2015-02-11 Abouzeid Shalaby

Non-Hermiticity in quantum Hamiltonians leads to nonunitary time evolution and possibly complex energy eigenvalues, which can lead to a rich phenomenology with no Hermitian counterpart. In this work, we study the dynamics of an exactly…

Quantum Physics · Physics 2023-10-25 Karin Sim , Nicolò Defenu , Paolo Molignini , R. Chitra

Non-hermiticity presents a vast newly opened territory that harbors new physics and applications such as lasing and sensing. However, only non-Hermitian systems with real eigenenergies are stable, and great efforts have been devoted in…

Other Condensed Matter · Physics 2022-10-25 Russell Yang , Jun Wei Tan , Tommy Tai , Jin Ming Koh , Linhu Li , Stefano Longhi , Ching Hua Lee

The quantum-field model described by non-Hermitian, but a ${\cal PT}$-symmetric Hamiltonian is considered. It is shown by the algebraic way that the limiting of the physical mass value $m \leq m_{max}= {m_1}^2/2m_2$ takes place for the case…

Mathematical Physics · Physics 2012-07-24 V. N. Rodionov

A discrete $N-$point Runge-Kutta version $H^{(N)}({\lambda})$ of one of the simplest non-Hermitian square-well Hamiltonians with real spectrum is studied. A complete set of its possible hermitizations (i.e., of the eligible metrics…

Mathematical Physics · Physics 2010-01-04 Miloslav Znojil

The Feshbach-type reduction of the Hilbert space to the physically most relevant "model" subspace is suggested as a means of a formal unification of the standard quantum mechanics with its recently proposed PT symmetric modification. The…

Quantum Physics · Physics 2015-06-26 Miloslav Znojil