Integrability of the Russian doll BCS model

We show that integrability of the BCS model extends beyond Richardson's model (where all Cooper pair scatterings have equal coupling) to that of the Russian doll BCS model for which the couplings have a particular phase dependence that breaks time-reversal symmetry. This model is shown to be integrable using the quantum inverse scattering method, and the exact solution is obtained by means of the algebraic Bethe ansatz. The inverse problem of expressing local operators in terms of the global operators of the monodromy matrix is solved. This result is used to find a determinant formulation of a correlation function for fluctuations in the Cooper pair occupation numbers. These results are used to undertake exact numerical analysis for small systems at half-filling.

Confucianism and the idea of equality

It is often supposed that Confucianism is opposed to the idea of equality insofar as the key ideals to which it is committed, such as meritocracy and li , are incompatible with equality. Sympathetic commentators typically defend Confucianism by saying that (a) the Confucian person is not a free-standing individual but a social being embedded in a social structure with different and unequal roles, and (b) social inequality has to be traded in for other values. This paper argues that in advocating meritocracy, Confucianism does not abandon the idea of equality. Indeed, invoking Aristotle's account of equality in the Nicomachean Ethics , it can be argued that the unequal distribution of rights and benefits reflects one aspect of equality, namely the vertical aspect, or the unequal treatment of unequals.