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Register a new userTowards a Non-equilibrium Bethe ansatz for the Kondo Model
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Authors
Eldad Bettelheim
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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 situations. 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.
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We find the statistical weight of excitations at long times following a quench in the Kondo problem. The weights computed are directly related to the overlap between initial and final states that are, respectively, states close to the Kondo ground state and states close to the normal metal ground state. The overlap is computed making use of the Slavnov approach, whereby a functional representation method is adopted, in order to obtain definite expressions.
We extend the exact periodic Bethe Ansatz solution for one-dimensional bosons and fermions with delta-interaction and arbitrary internal degrees of freedom to the case of hard wall boundary conditions. We give an analysis of the ground state properties of fermionic systems with two internal degrees of freedom, including expansions of the ground state energy in the weak and strong coupling limits in the repulsive and attractive regimes.
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