Toda solitons as Fermi-quasiparticles

Franz G. Mertens, Manfred Hader

Franz G. Mertens, H. Büttner

Alberto Brollo

Two working Mathematica Notebooks. istTBA.nb provides the solution of the coupled soliton-radiation TBA equations. fluidTBA.nb provides the solution in terms of fluid excitations, i.e. quasiparticles. The two notebooks are self-contained, commented, and easy to run.

Igor Lyuksyutov, Антон Григорович Наумовець, V. L. Pokrovsky

M Hader, Franz G. Mertens

A linear chain with exponential plus linear interactions (Toda lattice) can be mapped by the Bethe ansatz to a Fermi gas. The thermodynamics is treated by analogy to the delta-function Bose gas (Yang and Yang). Analytical solutions are given for the strongly anharmonic regime and low temperatures; the general case is treated numerically. For the case of weak anharmonicity the specific heats are compared with earlier approximate calculations. The anharmonic part of the specific heat is shown to be not very different from the corresponding classical result which can be interpreted as the specific heat of an ideal gas of solitons. For the quantum case the soliton-gas picture needs further investigation.

Seema Chahal, Alberto Brollo, Indranil Mukherjee +3 more

Many-body integrable systems can be understood as a gas of quasiparticles. They propagate ballistically and drive large-scale transport. However, with the exception of the hard rods system, no tools have been available to numerically track such quasiparticles. Focusing on the Toda fluid, whose integrability relies on the availability of a Lax pair, we present a numerical scheme to track quasiparticle trajectories as determined by the time-dependent eigenvectors of the Lax matrix. Simulating the Toda fluid in thermal equilibrium, this tracking scheme is used to numerical confirm Brownian motion of a quasiparticle. Simulated is also the motion of a tagged particle. Our numerical results for the diffusion constant matches with a novel TBA prediction. We believe our numerical scheme can be extended to other classical many-particle models possessing a Lax matrix.