| Title: |
Provably Efficient Long-Time Exponential Decompositions of Non-Markovian Gaussian Baths |
| Authors: |
Huang, Zhen; Ding, Zhiyan; Wang, Ke; Kaye, Jason; Li, Xiantao; Lin, Lin |
| Publication Year: |
2026 |
| Collection: |
ArXiv.org (Cornell University Library) |
| Subject Terms: |
Quantum Physics; Strongly Correlated Electrons; Mathematical Physics |
| Description: |
Gaussian baths are widely used to model non-Markovian environments, yet the cost of accurate simulation at long times remains poorly understood, especially when spectral densities exhibit nonanalytic behavior as in a range of realistic models. We rigorously bound the complexity of representing bath correlation functions on a time interval $[0,T]$ by sums of complex exponentials, as employed in recent variants of pseudomode and hierarchical equations of motion methods. These bounds make explicit the dependence on the maximal simulation time $T$, inverse temperature $β$, and the type and strength of singularities in an effective spectral density. For a broad class of spectral densities, the required number of exponentials is bounded independently of $T$, achieving time-uniform complexity. The $T$-dependence emerges only as polylogarithmic factors for spectral densities with strong singularities, such as step discontinuities and inverse power-law divergences. The temperature dependence is mild for bosonic environments and disappears entirely for fermionic environments. Thus, the true bottleneck for long-time simulation is not the simulation duration itself, but rather the presence of sharp nonanalytic features in the bath spectrum. Our results are instructive both for long-time simulation of non-Markovian open quantum systems, as well as for Markovian embeddings of classical generalized Langevin equations with memory kernels. |
| Document Type: |
text |
| Language: |
unknown |
| Relation: |
http://arxiv.org/abs/2603.25708 |
| Availability: |
http://arxiv.org/abs/2603.25708 |
| Accession Number: |
edsbas.D33C5308 |
| Database: |
BASE |