2017/03/13 by Jürg Fröhlich, Antti Knowles, Fröhlich, Jürg +5 · 2 citations
Mathematics · Physics and Astronomy · #35Q40 #35Q55 #60G60 #81V70 #82B10 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Probability (math.PR) #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.1703.04465
openalex publication_date 2017/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a microscopic derivation of time-dependent correlation functions of\nthe 1D cubic nonlinear Schr "odinger equation (NLS) from many-body quantum\ntheory. The starting point of our proof is our previous work on the\ntime-independent problem and work of the second author on the corresponding\nproblem on a finite lattice. An important new obstacle in our analysis is the\nneed to work with a cutoff in the number of particles, which breaks the\nGaussian structure of the free quantum field and prevents the use of the Wick\ntheorem. We overcome it by the means of complex analytic methods. Our methods\napply to the nonlocal NLS with bounded convolution potential. In the periodic\nsetting, we also consider the local NLS, arising from short-range interactions\nin the many-body setting. To that end, we need the dispersion of the NLS in the\nform of periodic Strichartz estimates in Xs,b spaces.\n