6533b7defe1ef96bd12765a2

RESEARCH PRODUCT

Solitons ofq-deformed quantum lattices and the quantum soliton

N. M. BogoliubovJussi TimonenAndrei RybinR. K. BulloughG. G. Varzugin

subject

PhysicsQuantum dynamicsGeneral Physics and AstronomyStatistical and Nonlinear PhysicsQuantum channelQuantum chaosNonlinear Sciences::Exactly Solvable and Integrable SystemsQuantum processQuantum mechanicsQuantum operationMethod of quantum characteristicsQuantum algorithmQuantum dissipationMathematical Physics

description

We use the classical N-soliton solution of a q-deformed lattice, the Maxwell-Bloch (MB) lattice, which we reported recently (Rybin A V, Varzugin G G, Timonen J and Bullough R K Year 2001 J. Phys. A: Math. Gen. 34 157) in order, ultimately, to fully comprehend the `quantum soliton'. This object may be the source of a new information technology (Abram I 1999 Quantum solitons Phys. World 21-4). We suggested in Rybin et al 2001 that a natural quantum mechanical matrix element of the q-deformed quantum MB lattice becomes in a suitable limit the classical 1-soliton solution of the classical q-deformed MB lattice explicitly derived by a variant of the Darboux-Backlund method. The classical q-deformed MB lattice was introduced in Bogoliubov N M, Rybin A V, Bullough R K and Timonen J 1995 Phys. Rev. A 52 1487. In this short paper the quantum inverse method is viewed as a Darboux-Backlund transformation at quantum level, two q-deformed quantum lattices are introduced and solved, and relevant matrix elements are formally derived. Further investigation of the classical limits of these matrix elements must however be deferred until future work.

https://doi.org/10.1088/0305-4470/34/48/311