Quantum Brownian motion with non-Gaussian noises: Fluctuation-Dissipation Relation and nonlinear Langevin equation
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Quantum Physics arXiv:2602.10421 (quant-ph) [Submitted on 11 Feb 2026] Title:Quantum Brownian motion with non-Gaussian noises: Fluctuation-Dissipation Relation and nonlinear Langevin equation Authors:Hing-Tong Cho, Bei-Lok Hu View a PDF of the paper titled Quantum Brownian motion with non-Gaussian noises: Fluctuation-Dissipation Relation and nonlinear Langevin equation, by Hing-Tong Cho and Bei-Lok Hu View PDF HTML (experimental) Abstract:Building upon the work of Hu, Paz, and Zhang [1,2] on open quantum systems we consider the quantum Brownian motion (QBM) model with one oscillator (position variable $x$) as the system, {\it nonlinearly} coupled to an environment of $N$ harmonic oscillators (with mass $m_n$, natural frequency $\omega_n$, position $q_n$ and momentum $p_n$ variables) in the form $\sum_{n}\left(v_{n1}(x)q_{n}^{k}+v_{n2}(x)p_{n}^{l}\right)$ where $k, l$ are integers (the present work only considers the $k=l=2$ cases). The vertex functions $v_{n1}, v_{n2} $ are of the form $v_{n1}=\lambda C_{n1} f(x), v_{n2}(x)=-\lambda\,C_{n2}m_{n}^{-2}\omega_{n}^{-2}f(x)$ where $C_{n1,2}$ are the coupling constants with the $n$th oscillator, $f(x)$ is any arbitrary function of $x$, and $\lambda$ is a dimensionless constant. Employing the closed-time-path formalism the influence action $S_{IF}$ is calculated using a perturbative expansion in $\lambda$. It is possible to identify the terms in $S_{IF}$ quadratic or higher in $\Delta(s)\equiv f(x_{+}(s))-f(x_{-}(s))$ to constitute the noise kernel, while terms linear in $\Delta$ to that of the dissipation kernel. The non-Gaussian noise kernel gives rise to non-zero three-point correlation function of the corresponding stochastic force. The pathway presented here should be useful for the exploration of \textit{non-Gaussian properties of systems nonlinearly coupled with their environments}; examples in early universe cosmology and in quantum optomechanics (QOM) are mentioned. A modified fluctuation-dissipation relation (FDR) is also established, which ensures the consistency of the model and the accuracy of results even at higher perturbative orders. Another result of significance is the derivation of a nonlinear Langevin equation which is expected to be useful for many open quantum system applications. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th) Cite as: arXiv:2602.10421 [quant-ph] (or arXiv:2602.10421v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.10421 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Hing Tong Cho [view email] [v1] Wed, 11 Feb 2026 02:03:26 UTC (21 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Brownian motion with non-Gaussian noises: Fluctuation-Dissipation Relation and nonlinear Langevin equation, by Hing-Tong Cho and Bei-Lok HuView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: cond-mat cond-mat.stat-mech hep-th References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)