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Related papers: Pseudospectra in non-Hermitian quantum mechanics

200 papers

Spectra of the second derivative operators corresponding to the special PT-symmetric point interactions are studied. The results are partly the completion of those obtained in [1]. The particular PT-symmetric point interactions causing…

Mathematical Physics · Physics 2009-06-02 Petr Siegl

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

It is know that PT-symmetric models have real spectra provided the symmetry is not spontaneously broken. Even pseudo-hermitian models have real spectra, which enlarge the the class of non-hermitian models possessing real spectra. We however…

High Energy Physics - Theory · Physics 2008-11-18 Pulak Ranjan Giri

Aim of this paper is to show the possible significance, and usefulness, of various non-selfadjoint operators for suitable Observables in non relativistic and relativistic quantum mechanics, and in quantum electrodynamics. More specifically,…

Quantum Physics · Physics 2010-05-10 Erasmo Recami , Vladislav S. Olkhovsky , Sergei P. Maydanyuk

We develop relativistic non-Hermitian quantum theory and its application to neutrino physics in a strong magnetic field. It is well known, that one of the fundamental postulates of quantum theory is the requirement of Hermiticity of…

High Energy Physics - Phenomenology · Physics 2016-03-25 V. N. Rodionov

Non-Hermitian models with real eigenenergies are highly desirable for their stability. Yet, most of the currently known ones are constrained by symmetries such as PT-symmetry, which is incompatible with realizing some of the most exotic…

Mesoscale and Nanoscale Physics · Physics 2022-07-13 Boxue Zhang , Qingya Li , Xiao Zhang , Ching Hua Lee

This paper explores quantum field theories with pseudo-Hermitian Hamiltonians, where PT-symmetric Hamiltonians serve as a special case. In specific regimes, these pseudo-Hermitian Hamiltonians have real eigenspectra, orthogonal eigenstates,…

High Energy Physics - Theory · Physics 2024-04-04 Esra Sablevice , Peter Millington

A non-Hermitian operator with a real spectrum and a complete set of eigenvectors may serve as the Hamiltonian operator for a unitary quantum system provided that one makes an appropriate choice for the defining inner product of the physical…

Quantum Physics · Physics 2009-11-13 Ali Mostafazadeh

The Heisenberg picture for non-Hermitian but $\eta$-pseudo-Hermitian Hamiltonian systems is suggested. If a non-Hermitian but $\eta$-pseudo-Hermitian Hamiltonian leads to real second order equations of motion, though their first order…

Quantum Physics · Physics 2016-04-14 Yan-Gang Miao , Zhen-Ming Xu

We propose that the real spectrum and the orthogonality of the states for several known complex potentials of both types, PT-symmetric and non-PT-symmetric can be understood in terms of currently proposed $\eta$-pseudo-Hermiticity…

Quantum Physics · Physics 2009-11-07 Zafar Ahmed

We find that a broken PT-symmetry operator when interacts with suitable Hermitian operator, new system becomes completely un-broken PT symmetry. Further on varying the contribution of Hermiticity one can delay or control the broken…

Quantum Physics · Physics 2020-04-14 Biswanath Rath

We examine the properties and consequences of pseudo-supersymmetry for quantum systems admitting a pseudo-Hermitian Hamiltonian. We explore the Witten index of pseudo-supersymmetry and show that every pair of diagonalizable (not necessarily…

Mathematical Physics · Physics 2008-11-26 Ali Mostafazadeh

. We study the statistical properties of the eigenvalues of non-Hermitian operators assoicated with the dissipative complex systems. By considering the Gaussian ensembles of such operators, a hierarchical relation between the correlators is…

Statistical Mechanics · Physics 2024-12-11 Pragya Shukla

Based on some results on reparmetrisation of time in Hamiltonian path integral formalism, a pseudo time formulation of operator formalism of quantum mechanics is presented. Relation of reparametrisation of time in quantum with super…

High Energy Physics - Theory · Physics 2016-04-21 A. K. Kapoor

We show that non-Hermitian engineering can play a positive role in quantum systems. This is in contrast to the widely accepted notion that optical losses are a foe that must be eliminated or, at least, minimized. We take advantage of the…

Quantum Physics · Physics 2019-12-19 Nicolás Quesada , Eugene Adjei , Ramy El-Ganainy , Agata M. Brańczyk

Criteria are formulated both for the existence and for the non-existence of complex eigenvalues for a class of non self-adjoint operators in Hilbert space invarariant under a particular discrete symmetry. Applications to the PT-symmetric…

Mathematical Physics · Physics 2009-11-10 Emanuela Caliceti , Sandro Graffi , Johannes Sjoestrand

For a class of non-selfadjoint semiclassical operators in dimension one, we get a complete asymptotic description of all eigenvalues near a critical value of the leading symbol of the operator on the boundary of the pseudospectrum.

Spectral Theory · Mathematics 2007-05-23 Michael Hitrik

We study a two-dimensional exactly solvable non-Hermitian $PT-$non-symmetric quantum model with real spectrum, which is not amenable to separation of variables, by supersymmetrical methods. Here we focus attention on the property of…

High Energy Physics - Theory · Physics 2008-11-26 F. Cannata , M. V. Ioffe , D. N. Nishnianidze

Recently, the ``Bootstrap" technique was applied in Quantum Mechanics to solve the eigenspectra of Hermitian Hamiltonians and extended to non-Hermitian PT-symmetric systems. However, its application has been limited to real spectra. In this…

High Energy Physics - Theory · Physics 2024-09-12 Sakil Khan , Harsh Rathod

We provide a careful analysis of the generating functional in the path integral formulation of pseudo-Hermitian and in particular PT-symmetric quantum mechanics and show how the metric operator enters the expression for the generating…

Quantum Physics · Physics 2009-11-13 Ali Mostafazadeh