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.
The physics of exceptional points
6 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
A short resume is given about the nature of exceptional points (EPs) followed by discussions about their ubiquitous occurrence in a great variety of physical problems. EPs feature in classical as well as in quantum mechanical problems. They are associated with symmetry breaking for ${\cal PT}$-symmetric Hamiltonians, where a great number of experiments have been performed in particular in optics, and to an increasing extent in atomic and molecular physics. EPs are involved in quantum phase transition and quantum chaos, they produce dramatic effects in multichannel scattering, specific time dependence and more. In nuclear physics they are associated with instabilities and continuum problems. Being spectral singularities they also affect approximation schemes.
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The compositeness of near-threshold eigenstates with Coulomb plus short-range forces is determined solely by the Coulomb scattering length, effective range, and Bohr radius, with the Coulomb interaction qualitatively altering threshold behavior and internal structure compared to short-range cases.
Critical unstable qubits exhibit indefinite anharmonic oscillations and coherence-decoherence cycles in a co-decaying frame, with first-time explicit geometric constructions for pure and mixed state trajectories on the Bloch sphere.
The paper introduces a general framework extending piecewise-deterministic unravelings to arbitrary trace-nonpreserving master equations requiring only positivity and Hermiticity of the dynamics.
A density matrix approach to non-Hermitian two-flavor neutrino oscillations shows steady-state probabilities not necessarily 1/2, indicating non-Markovian behavior.
citing papers explorer
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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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Compositeness of near-threshold eigenstates with Coulomb plus short-range interactions
The compositeness of near-threshold eigenstates with Coulomb plus short-range forces is determined solely by the Coulomb scattering length, effective range, and Bohr radius, with the Coulomb interaction qualitatively altering threshold behavior and internal structure compared to short-range cases.
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Trajectories of Critical Unstable Qubits in and on the Bloch Sphere
Critical unstable qubits exhibit indefinite anharmonic oscillations and coherence-decoherence cycles in a co-decaying frame, with first-time explicit geometric constructions for pure and mixed state trajectories on the Bloch sphere.
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Stochastic unravelings for Heisenberg picture and trace-nonpreserving dynamics
The paper introduces a general framework extending piecewise-deterministic unravelings to arbitrary trace-nonpreserving master equations requiring only positivity and Hermiticity of the dynamics.
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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.
- Black hole spectroscopy: from theory to experiment