Resonance-Protected Pointer States: Stationary-Phase Analysis of Entanglement in an Environment-Coupled Two-Spin System
Abstract
In this manuscript, we analyze the dynamics of a model in which two spin-1/2 systems are each coupled noncommutingly to a static environmental field and to a self-Hamiltonian, while also being mutually coupled through a σy(1)σy(2) interaction. By constructing an exact solution that exploits parity symmetry, and by applying the stationary-phase approximation (the saddle-point method) in the continuum limit of the environmental field, we show that coherence associated with the ordinary isolated stationary point decays as t−1, whereas, under the resonance condition at which the local effective fields of the two spins cancel each other, only the coherence between a pair of maximally entangled, Bell-type states- the eigenbasis of the inter-system coupling-survives, decaying via the anomalously slow power law t−1/2. Through a comparison with the pointer-basis theory of W. H. Zurek and coworkers (the 1981 and 2005 models), we further reveal a mechanism not reducible to local coupling: in this system, the pointer observable is determined not by the individual system-environment couplings but by a statistical resonance condition between the two environments.
Related
- Predicting Entanglement Spectra of Gapless Symmetry-Protected Topological States in One Dimension
- A General Master Equation for Two Accelerated Detectors: Stationary States and Entanglement
- Entanglement dynamics of accelerated atoms with environment-induced interactions
- Crossovers between Time-Bin and Energy-Time Entanglement in Homodyned Resonance Fluorescence
- Entanglement and parametric resonance in coupled oscillator systems
BibTeX
@misc{urasaki2026resonanceprotected,
title = {{Resonance-Protected Pointer States: Stationary-Phase Analysis of Entanglement in an Environment-Coupled Two-Spin System}},
author = {Kentaro Urasaki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18641},
eprint = {2609.18641},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18641},
}
RIS
TY - UNPB
TI - Resonance-Protected Pointer States: Stationary-Phase Analysis of Entanglement in an Environment-Coupled Two-Spin System
AU - Kentaro Urasaki
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.18641
UR - https://arxiv.org/abs/2609.18641
AB - In this manuscript, we analyze the dynamics of a model in which two spin-1/2 systems are each coupled noncommutingly to a static environmental field and to a self-Hamiltonian, while also being mutually coupled through a σ_y^(1)σ_y^(2) interaction. By constructing an exact solution that exploits parity symmetry, and by applying the stationary-phase approximation (the saddle-point method) in the continuum limit of the environmental field, we show that coherence associated with the ordinary isolated stationary point decays as t^−1, whereas, under the resonance condition at which the local effective fields of the two spins cancel each other, only the coherence between a pair of maximally entangled, Bell-type states- the eigenbasis of the inter-system coupling-survives, decaying via the anomalously slow power law t^−1/2. Through a comparison with the pointer-basis theory of W. H. Zurek and coworkers (the 1981 and 2005 models), we further reveal a mechanism not reducible to local coupling: in this system, the pointer observable is determined not by the individual system-environment couplings but by a statistical resonance condition between the two environments.
ER -