We review here particular aspects of the connection between Laplacian growth problems and classical integrable systems. In addition, we put forth a possible relation between quantum integrable systems and Laplacian growth problems. Such a connection,
if confirmed, has the potential to allow for a theoretical prediction of the fractal properties of Laplacian growth clusters, through the representation theory of conformal field theory.
We give integral equations for the generating function of the cummulants of the work done in a quench for the Kondo model in the thermodynamic limit. Our approach is based on an extension of the thermodynamic Bethe ansatz to non-equilibrium situation
s. This extension is made possible by use of a large $N$ expansion of the overlap between Bethe states. In particular, we make use of the Slavnov determinant formula for such overlaps, passing to a function-space representation of the Slavnov matrix . We leave the analysis of the resulting integral equations to future work.
We present a derivation of a previously announced result for matrix elements between exact eigenstates of the pairing Hamiltnonian. Our results, which generalize the well known BCS (Bardeen-Cooper-Schrieffer) expressions for what is known as coherenc
e factors, are derived based on the Slavnov formula for overlaps between Bethe-ansatz states, thus making use of the known connection between the exact diagonalization of the BCS Hamiltonian, due to Richardson, and the algebraic Bethe ansatz. The resulting formula has a compact form after a suitable parameterization of the Energy plane. Although we apply our method here to the pairing Hamiltonian, it may be adjusted to study what is termed the Sutherland limit for exactly solvable models, namely where a macroscopic number of rapidities form a large string.
