Fate of classical solitons in one-dimensional quantum systems.
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 quasiparticles and quasiholes. We discuss in detail two exactly solvable models exhibiting such crossover, the Lieb-Liniger model of bosons with weak contact repulsion and the quantum Toda model, and 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.
- Research Organization:
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Sponsoring Organization:
- USDOE Office of Science - Office of Basic Energy Sciences - Materials Sciences and Engineering Division; National Science Foundation (NSF)
- DOE Contract Number:
- AC02-06CH11357
- OSTI ID:
- 1237488
- Journal Information:
- Physical Review, B: Condensed Matter, Vol. 92, Issue 19; ISSN 0163-1829
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
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