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This research investigates how transient dynamics in driven non-Hermitian systems, such as the Kitaev chain, amplify memory and exhibit unique regularity near exceptional points. The study demonstrates that finite-time propagators remain analytic even when quasiparticle gaps close, providing critical insights into the stability of quantum evolution under broken-spectrum conditions. These findings advance the theoretical understanding of non-Hermitian fermionic dynamics relevant to future quantum computing architectures.
Amplified Memory and Finite-Time Regularity in Driven Non-Hermitian Systems
arXiv:2609.29137v1 Announce Type: cross Abstract: We study the roles of broken spectra and exceptional points in finite-time driven non-Hermitian fermionic dynamics. We compute the Nambu biorthogonal correlation matrix for this purpose. The imbalanced-pairing Kitaev chain serves as our concrete realization. Transient passage through a broken-spectrum region amplifies preparation memory. The effect survives when the final Hamiltonian returns to a real-spectrum regime. Negative imbalance forces spectral nonpositivity in the static endpoint state. We isolate the genuine drive history by subtracting out this baseline, leaving an excess that is strictly controlled by the accumulated imaginary-energy action and persists over the entire post-ramp time window. A connected longitudinal correlation mirrors this physics. Its slow-ramp growth tracks the corresponding doubled action. Unstable sectors instead continue amplifying post-ramp if the drive halts inside the broken-spectrum region. Exceptional points yield distinct physics. The finite-time propagator and subsystem correlation matrix remain entirely regular near an exceptional endpoint, even as the quasiparticle gap exhibits its characteristic square-root closing. This finite-time regularity reflects the analyticity of the matrix evolution in the endpoint parameter; a diagonalizable endpoint is strictly not required. A diverging long-time crossover eventually reveals the exceptional scale. We halt the drive exactly at the exceptional point to find that the correlation projector and the connected longitudinal correlation share an identical ballisti front. The subsystem saturation length establishes a distinct but comparable spatial scale. Memory and exceptional-endpoint scalings show no divergence across the tested negative-imbalance range. Memory scaling is fixed by the drive and remains insensitive to the specific choice of real-spectrum final endpoint.
Abstract:We study the roles of broken spectra and exceptional points in finite-time driven non-Hermitian fermionic dynamics. We compute the Nambu biorthogonal correlation matrix for this purpose. The imbalanced-pairing Kitaev chain serves as our concrete realization. Transient passage through a broken-spectrum region amplifies preparation memory. The effect survives when the final Hamiltonian returns to a real-spectrum regime. Negative imbalance forces spectral nonpositivity in the static endpoint state. We isolate the genuine drive history by subtracting out this baseline, leaving an excess that is strictly controlled by the accumulated imaginary-energy action and persists over the entire post-ramp time window. A connected longitudinal correlation mirrors this physics. Its slow-ramp growth tracks the corresponding doubled action. Unstable sectors instead continue amplifying post-ramp if the drive halts inside the broken-spectrum region. Exceptional points yield distinct physics. The finite-time propagator and subsystem correlation matrix remain entirely regular near an exceptional endpoint, even as the quasiparticle gap exhibits its characteristic square-root closing. This finite-time regularity reflects the analyticity of the matrix evolution in the endpoint parameter; a diagonalizable endpoint is strictly not required. A diverging long-time crossover eventually reveals the exceptional scale. We halt the drive exactly at the exceptional point to find that the correlation projector and the connected longitudinal correlation share an identical ballisti front. The subsystem saturation length establishes a distinct but comparable spatial scale. Memory and exceptional-endpoint scalings show no divergence across the tested negative-imbalance range. Memory scaling is fixed by the drive and remains insensitive to the specific choice of real-spectrum final endpoint.
Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
arXiv:2609.29137 [cond-mat.stat-mech]
(or arXiv:2609.29137v1 [cond-mat.stat-mech] for this version)
https://doi.org/10.48550/arXiv.2609.29137 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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