Causality in PT-symmetric systems carries a topological charge at exceptional points, causing a pole migration that produces a Lorentzian residual in Kramers-Kronig relations whose magnitude scales as |gamma - gamma_c|^(-1.08).
How acausal equations emerge from causal dynamics
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abstract
We construct a causal and covariantly stable kinetic model whose spectrum at real wavenumbers $k$ reproduces any rest-frame stable dissipative dispersion relation $\omega(k)$ via suitable initialization of the microscopic degrees of freedom. Macroscopic observables can therefore obey arbitrary linear evolution equations (including forms that would be acausal if taken as fundamental), while the underlying dynamics remains causal, and all apparent propagation is encoded in the initial data. This provides an explicit counterexample to the idea that microscopic causality alone constrains the analytic form of dispersion relations at real $k$. In particular, bounds on transport coefficients based solely on the analytic structure of $\omega(k)$, such as the hydrohedron bounds, require additional assumptions about the region in the complex $k$-plane where $\omega(k)$ corresponds to physical modes.
fields
quant-ph 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
The Nakajima-Zwanzig memory kernel belongs to the operator-valued Hardy space and obeys Kramers-Kronig relations under a real-axis spectral hypothesis, while effective kernels can show upper-half-plane poles from uncancelled zeros in the state transform.
citing papers explorer
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Topological Charge of Causality at a PT-Symmetric Exceptional Point
Causality in PT-symmetric systems carries a topological charge at exceptional points, causing a pole migration that produces a Lorentzian residual in Kramers-Kronig relations whose magnitude scales as |gamma - gamma_c|^(-1.08).
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Kramers-Kronig Relations and Causality in Non-Markovian Open Quantum Dynamics: Kernel, State, and Effective Kernel
The Nakajima-Zwanzig memory kernel belongs to the operator-valued Hardy space and obeys Kramers-Kronig relations under a real-axis spectral hypothesis, while effective kernels can show upper-half-plane poles from uncancelled zeros in the state transform.