Semiclassical theory of transport

Quantum Physics [Submitted on 14 Apr 2026] Semiclassical theory of transport Marcel Novaes We discuss the semiclassical approximation to transport problems in quantum chaotic systems. The figures of merit are moments of the transmission matrix and of the time delay matrix. After reviewing a few results obtained by treating these matrices are random matrices, we show how expressions for their elements in terms of sums over trajectories lead to diagrammatic formulations that correspond to perturbative calculations. This semiclassical approach agrees with random matrix theory when it should, and allows further elements to be incorporated, like tunnel barriers, superconductors, absorption effects. We also discuss how this approach can be encoded in matrix integrals, resulting in a powerful and versatile theory that is amenable to algebraic solutions. Comments: Chapter for the Quantum Chaos volume in 'Comprehensive Quantum Mechanics', to be published by Elsevier (Main editor: R.B. Mann; volume editors: S. Gnutzmann and K. {Ż}yczkowski) Subjects: Quantum Physics (quant-ph); Chaotic Dynamics (nlin.CD) Cite as: arXiv:2604.13193 [quant-ph]   (or arXiv:2604.13193v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.13193 Focus to learn more Submission history From: Marcel Novaes [view email] [v1] Tue, 14 Apr 2026 18:16:32 UTC (70 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: nlin nlin.CD References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)