Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Annales Henri Poincaré

On Unitarity of the Scattering Operator in Non-Hermitian Quantum Mechanics

Roman Gennadievich Novikov, Iskander Asanovich Taimanov

Published Feb 5, 2024• 6 citations
Publisher
DOI
10.1007/s00023-024-01414-5

Related papers

Reciprocity and unitarity in scattering from a non-Hermitian complex PT-symmetric potential

Zafar Ahmed

arXiv:1207.6896•Physics Letters A•Feb 20, 2013•30 citations

New scattering features in non-Hermitian space fractional quantum mechanics

Mohammad Hasan, Bhabani Prasad Mandal

arXiv:1712.09727•Annals of Physics•Aug 1, 2018•18 citations

A remark on the unitarity property of the scattering operator

T. Kato, Shige Toshi Kuroda

Il Nuovo Cimento•Dec 1, 1959•21 citations

Biorthogonal scattering and generalized unitarity in non-Hermitian systems

Jung-Wan Ryu, Henning Schomerus, Hee Chul Park

We investigate the two-port scattering process in non-Hermitian dimer models via quantum measurements using external leads. We focus on two exemplary dimer models that preserve parity-time symmetry via spatial gain-loss balance and exhibit non-reciprocity due to directional hopping. The scattering matrix is constructed using the biorthogonality of the left and right scattering states of the Hamiltonian, allowing us to calculate the reflection and transmission probabilities. Our analysis compares the reflection and transmission coefficients derived from the left, right, and combined scattering states, revealing that, unlike in Hermitian systems, the non-Hermitian scattering process does not adhere to unitarity when considering only the right scattering states. Furthermore, non-Hermitian scattering can enhance the reflection and transmission probabilities, with distinct physical contributions arising independently from complex eigenvalues and the non-orthogonality of eigenstates. Our results clarify how biorthogonality restores generalized unitarity and identify distinct physical origins of enhanced transport in PT-symmetric and non-reciprocal dimers, providing new insights into quantum transport in non-Hermitian systems.

cond-mat.mes-hallCross-listedarXiv:2602.06349•Feb 9, 2026•0 citations

Pseudo-Hermitian QFT: relativistic scattering and symmetry structure

Ruifeng Leng, Cheng-Yang Lee, Siyi Zhou

Unitarity is a cornerstone of quantum theory, ensuring the conservation of probability and information. Although non-Hermitian Hamiltonians are typically associated with open or dissipative systems, pseudo-Hermitian quantum mechanics shows that real spectra and unitary evolution can still emerge through a suitably defined inner product. Motivated by this insight, we extend the pseudo-Hermitian framework to relativistic quantum field theory and construct a consistent formulation of scattering processes. A novel structural feature of this theory is the presence of distinct metric operators for the in and out sectors, connected through a nontrivial metric projector that guarantees global probability conservation under pseudo-unitary time evolution. We further develop a general symmetry formalism, showing that each symmetry generally corresponds to two pseudo-unitary operators associated with the in and out metrics, respectively. Within this framework, the scattering matrix admits a perturbative expansion through the Dyson series and remains Lorentz invariant and unitary, remarkably in complete agreement with the conventional Hermitian case. The fundamental CPT theorem is also shown to hold. Our results provide a rigorous foundation for interacting pseudo-Hermitian quantum field theories and open new directions for exploring their possible physical implications beyond the standard Hermitian paradigm.

arXiv:2510.27404•Oct 31, 2025•0 citations

Non-Hermitian Operators in Quantum Physics

Hynek Bíla

•May 11, 2009•9 citations
We investigate the two-port scattering process in non-Hermitian dimer models via quantum measurements using external leads. We focus on two exemplary dimer models that preserve parity-time symmetry via spatial gain-loss balance and exhibit non-reciprocity due to directional hopping. The scattering matrix is constructed using the biorthogonality of the left and right scattering states of the Hamiltonian, allowing us to calculate the reflection and transmission probabilities. Our analysis compares the reflection and transmission coefficients derived from the left, right, and combined scattering states, revealing that, unlike in Hermitian systems, the non-Hermitian scattering process does not adhere to unitarity when considering only the right scattering states. Furthermore, non-Hermitian scattering can enhance the reflection and transmission probabilities, with distinct physical contributions arising independently from complex eigenvalues and the non-orthogonality of eigenstates. Our results clarify how biorthogonality restores generalized unitarity and identify distinct physical origins of enhanced transport in PT-symmetric and non-reciprocal dimers, providing new insights into quantum transport in non-Hermitian systems.
Unitarity is a cornerstone of quantum theory, ensuring the conservation of probability and information. Although non-Hermitian Hamiltonians are typically associated with open or dissipative systems, pseudo-Hermitian quantum mechanics shows that real spectra and unitary evolution can still emerge through a suitably defined inner product. Motivated by this insight, we extend the pseudo-Hermitian framework to relativistic quantum field theory and construct a consistent formulation of scattering processes. A novel structural feature of this theory is the presence of distinct metric operators for the in and out sectors, connected through a nontrivial metric projector that guarantees global probability conservation under pseudo-unitary time evolution. We further develop a general symmetry formalism, showing that each symmetry generally corresponds to two pseudo-unitary operators associated with the in and out metrics, respectively. Within this framework, the scattering matrix admits a perturbative expansion through the Dyson series and remains Lorentz invariant and unitary, remarkably in complete agreement with the conventional Hermitian case. The fundamental CPT theorem is also shown to hold. Our results provide a rigorous foundation for interacting pseudo-Hermitian quantum field theories and open new directions for exploring their possible physical implications beyond the standard Hermitian paradigm.