hardy-space analyticity 1kramers-kronig relations 1memory kernel 1non-unitary exchange statistics 1open quantum systems 1paraparticles 1
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quant-ph2026
Paraparticles intrinsically exhibit Hardy-space breakdown
Kejun Liu
The paper shows that particles with non‑unitary exchange statistics (paraparticles) inherently violate the Hardy‑space analyticity required for Kramers–Kronig relations in the memo…
quant-ph2026
Operator-Valued Hardy Spaces and Kramers--Kronig Relations for Non-Markovian Quantum Memory Kernels
Kejun Liu
Retarded support, upper-half-plane holomorphy, and Hardy boundary control are distinct properties of a memory kernel. We give sufficient conditions linking them for the Nakajima--Z…
quant-ph2026
Dispersion Relations Across the Unitarity Boundary
Kejun Liu
Kramers-Kronig (KK) relations rest on a binary premise: a response function is either analytic in the upper half-plane or it is not. We show that a single reduced-state transform o…