Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 52, Issue 33, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/ab2cf0
Keywords
Toda lattice; kinetic theory; Bethe ansatz; Lax matrix
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Funding
- DARPA DRINQS program
- ERC synergy Grant UQUAM
- DOE grant [DE-SC0019380]
- Center for Novel Pathways to Quantum Coherence in Materials, an Energy Frontier Research Center - US Department of Energy, Office of Science, Basic Energy Sciences
- Simons Investigatorship
- U.S. Department of Energy (DOE) [DE-SC0019380] Funding Source: U.S. Department of Energy (DOE)
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We consider the kinetic theory of the quantum and classical Toda lattice models. A kinetic equation of Bethe-Boltzmann type is derived for the distribution function of conserved quasiparticles. Near the classical limit, we show that the kinetic theory depends smoothly on Planck's constant, and explicitly characterise the leading quantum corrections to classical behaviour. The classical kinetic theory is compared with direct numerical simulations and shows excellent agreement. Finally, we connect the Bethe-Boltzmann approach with the classical inverse scattering method, by identifying conserved quasiparticles with the spectrum of the Lax matrix.
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