Quantization and Mirror Reduction Do Not Commute in Hamiltonian Embeddings of Nonreciprocal Dynamics
Abstract
Hamiltonian embeddings can represent dissipative nonreciprocal classical dynamics exactly on invariant manifolds of enlarged reciprocal systems. We show that canonical quantization of such an embedding need not commute with reduction to the target dynamics. For the mirror construction recently introduced for pairwise nonreciprocal interactions, the invariant manifold is Lagrangian. Exact quantum enforcement of the mirror condition therefore removes the dynamical sector rather than producing a quantum analogue of the reduced flow. If the constraint is imposed only semiclassically, contraction of the target dynamics generates inverse-transpose expansion in the conjugate mirror directions. Quantum uncertainty then gives ln D≥Ξ(t)+nln[π/(σε)], where Ξ=−ln|det M| is the accumulated contraction and D the torus Hilbert-space dimension. Exact finite-dimensional Weyl evolution of one- and two-degree-of-freedom nonreciprocal models confirms the resulting logarithmic correspondence time, including its predicted change when the initial localization scales with ℏ. Thus the classical embedding is exact, but its direct canonical quantization is a singular semiclassical construction.
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BibTeX
@misc{sarmah2026quantization,
title = {{Quantization and Mirror Reduction Do Not Commute in Hamiltonian Embeddings of Nonreciprocal Dynamics}},
author = {Gaurav Sarmah and Ramakrishna Podila},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28494},
eprint = {2609.28494},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28494},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Quantization and Mirror Reduction Do Not Commute in Hamiltonian Embeddings of Nonreciprocal Dynamics
AU - Gaurav Sarmah
AU - Ramakrishna Podila
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.28494
UR - https://arxiv.org/abs/2609.28494
AB - Hamiltonian embeddings can represent dissipative nonreciprocal classical dynamics exactly on invariant manifolds of enlarged reciprocal systems. We show that canonical quantization of such an embedding need not commute with reduction to the target dynamics. For the mirror construction recently introduced for pairwise nonreciprocal interactions, the invariant manifold is Lagrangian. Exact quantum enforcement of the mirror condition therefore removes the dynamical sector rather than producing a quantum analogue of the reduced flow. If the constraint is imposed only semiclassically, contraction of the target dynamics generates inverse-transpose expansion in the conjugate mirror directions. Quantum uncertainty then gives ln D≥Ξ(t)+nln[π/(σε)], where Ξ=−ln|det M| is the accumulated contraction and D the torus Hilbert-space dimension. Exact finite-dimensional Weyl evolution of one- and two-degree-of-freedom nonreciprocal models confirms the resulting logarithmic correspondence time, including its predicted change when the initial localization scales with ℏ. Thus the classical embedding is exact, but its direct canonical quantization is a singular semiclassical construction.
ER -