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Proofs of Two Conjectures Related to the Thermodynamic Bethe Ansatz

Craig A. Tracy, Harold Widom

Abstract

We prove that the solution to a pair of nonlinear integral equations arising in the thermodynamic Bethe Ansatz can be expressed in terms of the resolvent kernel of the linear integral operator with kernel exp(-u(theta)-u(theta'))/cosh[(1/2)(theta-theta')]

Proofs of Two Conjectures Related to the Thermodynamic Bethe Ansatz

Abstract

We prove that the solution to a pair of nonlinear integral equations arising in the thermodynamic Bethe Ansatz can be expressed in terms of the resolvent kernel of the linear integral operator with kernel exp(-u(theta)-u(theta'))/cosh[(1/2)(theta-theta')]

Paper Structure

This paper contains 90 equations.