An Exact Operator Formulation of Statistical Quasiparticle Theory for Nonlinear System-Bath Coupling
Abstract
We develop an operator formulation of statistical quasiparticle theory for open quantum systems with nonlinear system-bath coupling, extending beyond the linear coupling setting of the standard Gaussian influence functional formulation. For Gaussian baths, the statistical quasiparticles, termed dissipatons, are explicitly constructed as collective operators in the thermofield bath space. Our construction provides a microscopic operator basis for the dissipaton algebra and generates hierarchical equations of motion directly from the Liouville equation. Nonlinear interactions are incorporated through a recursive generalized Wick's theorem, enabling automatic generation of hierarchical equations for polynomial couplings. The resulting framework connects explicit bath operator representations to nonperturbative, non-Markovian dynamics and unifies the treatment of linear and nonlinear system-bath interactions.
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BibTeX
@misc{su2026exact,
title = {{An Exact Operator Formulation of Statistical Quasiparticle Theory for Nonlinear System-Bath Coupling}},
author = {Yu Su and Yao Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24603},
eprint = {2609.24603},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24603},
}
RIS
TY - UNPB
TI - An Exact Operator Formulation of Statistical Quasiparticle Theory for Nonlinear System-Bath Coupling
AU - Yu Su
AU - Yao Wang
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24603
UR - https://arxiv.org/abs/2609.24603
AB - We develop an operator formulation of statistical quasiparticle theory for open quantum systems with nonlinear system-bath coupling, extending beyond the linear coupling setting of the standard Gaussian influence functional formulation. For Gaussian baths, the statistical quasiparticles, termed dissipatons, are explicitly constructed as collective operators in the thermofield bath space. Our construction provides a microscopic operator basis for the dissipaton algebra and generates hierarchical equations of motion directly from the Liouville equation. Nonlinear interactions are incorporated through a recursive generalized Wick's theorem, enabling automatic generation of hierarchical equations for polynomial couplings. The resulting framework connects explicit bath operator representations to nonperturbative, non-Markovian dynamics and unifies the treatment of linear and nonlinear system-bath interactions.
ER -