Imaginary magnetic fields induce exceptional points in neutral meson mass spectra computed via hadronic effective Lagrangian and constituent quark models, separating real and complex eigenvalue regimes.
Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
10 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of pseudo-Hermitian Hamiltonians, and argue that the basic structure responsible for the particular spectral properties of these Hamiltonians is their pseudo-Hermiticity. We explore the basic properties of general pseudo-Hermitian Hamiltonians, develop pseudo-supersymmetric quantum mechanics, and study some concrete examples, namely the Hamiltonian of the two-component Wheeler-DeWitt equation for the FRW-models coupled to a real massive scalar field and a class of pseudo-Hermitian Hamiltonians with a real spectrum.
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For any diagonalisable non-Hermitian H with real spectrum, the biorthogonal Gibbs functional satisfies positivity of ω_bi(A†A) for all A if and only if H is quasi-Hermitian.
A pseudo-unitary quasiperiodic quantum walk model exhibits a novel mobility edge sharply dividing metallic and insulating phases plus a second transition unique to discrete time, with PT-symmetry breaking quantified by spectral winding number.
Exact WKB analysis produces median-summed spectra and an algebraic equation for the exceptional point of PT-symmetry breaking in the inverted triple-well system.
Short-time real-time pseudo entropy obeys S_A(t,0)=S_A(0)-it ⟨K_A(H−⟨H⟩)⟩ + O(t²), with imaginary response from symmetrized covariance of H and K_A.
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
Analytic continuation produces a PT-invariant CFT state reproducing the Bunch-Davies Wightman function for dS, but entanglement entropy captures only real central charge, motivating a timelike geodesic-integrated dual for OPE block correlators and conformal defects from dS/CFT symmetry.
A density matrix approach to non-Hermitian two-flavor neutrino oscillations shows steady-state probabilities not necessarily 1/2, indicating non-Markovian behavior.
In a BRST-symmetric theory with non-Hermitian fermion mass matrix, the one-loop contribution to the φ†φ two-point function becomes real for real external momentum after removing the i factor from the e^{iS} normalization, due to conjugate pole pairing.
Lecture notes on defining scalar QFTs and assigning geometric structure to the space of possible theories.
citing papers explorer
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Hadronic exceptional points
Imaginary magnetic fields induce exceptional points in neutral meson mass spectra computed via hadronic effective Lagrangian and constituent quark models, separating real and complex eigenvalue regimes.
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Kubo-Martin-Schwinger conditions for non-Hermitian systems
For any diagonalisable non-Hermitian H with real spectrum, the biorthogonal Gibbs functional satisfies positivity of ω_bi(A†A) for all A if and only if H is quasi-Hermitian.
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Mobility edges in pseudo-unitary quasiperiodic quantum walks
A pseudo-unitary quasiperiodic quantum walk model exhibits a novel mobility edge sharply dividing metallic and insulating phases plus a second transition unique to discrete time, with PT-symmetry breaking quantified by spectral winding number.
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Exact WKB analysis of inverted triple-well: resonance, PT-symmetry breaking, and resurgence
Exact WKB analysis produces median-summed spectra and an algebraic equation for the exceptional point of PT-symmetry breaking in the inverted triple-well system.
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Real-time pseudo entropy and modular-Hamiltonian correlations
Short-time real-time pseudo entropy obeys S_A(t,0)=S_A(0)-it ⟨K_A(H−⟨H⟩)⟩ + O(t²), with imaginary response from symmetrized covariance of H and K_A.
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Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
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CFT Dual for Timelike Geodesic in Lorentzian dS
Analytic continuation produces a PT-invariant CFT state reproducing the Bunch-Davies Wightman function for dS, but entanglement entropy captures only real central charge, motivating a timelike geodesic-integrated dual for OPE block correlators and conformal defects from dS/CFT symmetry.
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Two flavor neutrino oscillations in presence of non-Hermitian dynamics
A density matrix approach to non-Hermitian two-flavor neutrino oscillations shows steady-state probabilities not necessarily 1/2, indicating non-Markovian behavior.
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Pathways to Real Composite Operators from Non-Hermitian Fermions
In a BRST-symmetric theory with non-Hermitian fermion mass matrix, the one-loop contribution to the φ†φ two-point function becomes real for real external momentum after removing the i factor from the e^{iS} normalization, due to conjugate pole pairing.
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Scalar Quantum Fields: Theory Space and its Geometry
Lecture notes on defining scalar QFTs and assigning geometric structure to the space of possible theories.