2017/08/31 by Yuan Fang, Fan Wu, Biao Wu
Mathematics · Physics and Astronomy · #Basis (linear algebra) #Basis function #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Function (biology) #Geometry #Mathematical analysis #Mathematics #Mechanical and Optical Resonators #Phase (matter) #Phase space #Physics #Point (geometry) #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Space (punctuation) #Wannier function #Wave function #quant-ph
paper · pdf · doi:10.1088/1742-5468/aaac54
published as J. Stat. Mech. (2018) 023113 · 6 figures
arxiv created 2017/11/22 · openalex publication_date 2018/02/27 · arxiv updated 2018/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A quantum phase space with Wannier basis is constructed: (i) classical phase space is divided into Planck cells; (ii) a complete set of Wannier functions are constructed with the combination of Kohn's method and Löwdin method such that each Wannier function is localized at a Planck cell. With these Wannier functions one can map a wave function unitarily onto phase space. Various examples are used to illustrate our method and compare it to Wigner function. The advantage of our method is that it can smooth out the oscillations in wave functions without losing any information and is potentially a better tool in studying quantum-classical correspondence. In addition, we point out that our method can be used for time-frequency analysis of signals.