From Classical to Quantum Kinetics

James W. Dufty, David B. Boercker

Ian P. Hamilton, Ricardo Antonio Mosna, Luigi Delle Site

Mitsuo Shimoji

Vir B. Bulchandani, Xiangyu Cao, Joel E. Moore

Abstract 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.

Ricardo Antonio Mosna, Ian P. Hamilton, Luigi Delle Site

We propose an approach to quantum–classical correspondence based on a deformation of the momentum and kinetic operators of quantum mechanics. Making use of the factorization method, we construct classical versions of the momentum and kinetic operators which, in addition to the standard quantum expressions, contain terms that are functionals of the N -particle density. We show that this implementation of quantum–classical correspondence is related to Witten's deformation of the exterior derivative and Laplacian, introduced in the context of supersymmetric quantum mechanics. The corresponding deformed action is also shown to be related to the Fisher information. Finally, we briefly consider the possible relevance of our approach to the construction of kinetic-energy density functionals.

Fedir T. Vasko, O. É. Raichev