9 papers
Metric completion of the Bender--Brody--Müller Hamiltonian: dilation spectrum and missing eigenstates
Kejun Liu
The Bender--Brody--Müller (BBM) Hamiltonian was proposed as a non-Hermitian Hilbert--Pólya operator. We analyze the Hilbert completion induced, on the standard half-line core…
A real-space exceptional ring mediates an eigenframe-charge transition in a non-Hermitian skyrmion
Kejun Liu
The integer topological charge of a skyrmion is the standard example of topological protection. We ask what happens to that protection when the local generator is made non-Hermitia…
Paraparticles intrinsically exhibit Hardy-space breakdown
Kejun Liu
The memory kernel of an open quantum system obeys Kramers--Kronig (KK) relations if and only if its Laplace transform is analytic in the upper half-plane -- a property known as Har…
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…
Exceptional Points as Manifestations of Analyticity Breakdown in the 't Hooft Model
Kejun Liu
We use the exactly-solvable t Hooft model of 1+1D large-N_c QCD as a rigorous laboratory for the breakdown of analyticity of a causal response function, the meson two-point functio…
The Predictive-Causal Gap: An Impossibility Theorem and Large-Scale Neural Evidence
Kejun Liu
We report a systematic failure mode in predictive representation learning. Across 2695 neural network configurations trained to predict linear-Gaussian dynamics, the optimal encode…
Algebraic Spectral Curves of Two-Channel Operator Pencils with Power-Law Response
Kejun Liu
A finite matrix can acquire a nontrivial algebraic spectral curve when its entries contain a multivalued response. We study this mechanism for a two-channel pencil with scalar resp…
Chemical Medium-Range Order Enables Stoichiometric Rigidity
Kejun Liu
Maxwell counting predicts an isostatic threshold at for covalent network glasses, but which structural correlations actually produce rigidity near this poi…
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…