We construct the Baxter operator and the corresponding Baxter equation for a quantum version of the Ablowitz-Ladik model. The result is achieved in two different ways: by using the well-known Bethe ansatz technique and by looking at the quantum analogue of the classical Backlund transformations. General results about integrable models governed by the same r-matrix algebra will be given. Baxter's equation comes out to be a q-difference equation involving both the trace and the quantum determinant of the monodromy matrix. The spectrality property of the classical Backlund transformations gives a trace formula representing the classical analogue of Baxter's equation. A q-integral representation of the Baxter operator is discussed.
A q-difference Baxter operator for the Ablowitz-Ladik chain
Zullo, Federico
2015-01-01
Abstract
We construct the Baxter operator and the corresponding Baxter equation for a quantum version of the Ablowitz-Ladik model. The result is achieved in two different ways: by using the well-known Bethe ansatz technique and by looking at the quantum analogue of the classical Backlund transformations. General results about integrable models governed by the same r-matrix algebra will be given. Baxter's equation comes out to be a q-difference equation involving both the trace and the quantum determinant of the monodromy matrix. The spectrality property of the classical Backlund transformations gives a trace formula representing the classical analogue of Baxter's equation. A q-integral representation of the Baxter operator is discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
