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

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11379/499490
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