2015/07/31 by M. Pustilnik, K. A. Matveev, К. А. Матвеев
Mathematics · Physics and Astronomy · #Boson #Classical limit #Cold Atom Physics and Bose-Einstein Condensates #Crossover #Korteweg–de Vries equation #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear system #Phonon #Physics #Quantum #Quantum mechanics #Quantum system #Quantum, superfluid, helium dynamics #Strong Light-Matter Interactions #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.92.195146
published as Phys. Rev. B 92, 195146 (2015)
openalex publication_date 2015/11/23 · arxiv created 2015/11/24 · arxiv updated 2015/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We study one-dimensional quantum systems near the classical limit described by the Korteweg--de Vries (KdV) equation. The excitations near this limit are the well-known solitons and phonons. The classical description breaks down at long wavelengths, where quantum effects become dominant. Focusing on the spectra of the elementary excitations, we describe analytically the entire classical-to-quantum crossover. We show that the ultimate quantum fate of the classical KdV excitations is to become fermionic particles and holes. We discuss in detail two exactly solvable models exhibiting such crossover, namely the Lieb-Liniger model of bosons with weak contact repulsion and the quantum Toda model. We argue that the results obtained for these models are universally applicable to all quantum one-dimensional systems with a well-defined classical limit described by the KdV equation.