A detailed study of an S = 1 2 spin ladder model is given. The ladder consists of plaquettes formed by nearest neighbor rungs with all possible SU(2)-invariant interactions. For properly chosen coupling constants, the model is shown to be integrable in the sense that the quantum Yang-Baxter equation holds and one has an infinite number of conserved quantities. The R-matrix and L-operator associated with the model Hamiltonian are given in a limiting case. It is shown that after a simple transformation, the model can be solved via a Bethe ansatz. The phase diagram of the ground state is exactly derived using the Bethe ansatz equation.
Abstract. We study by methods of nonstandard analysis second order differential operators with zero order coefficients which are too singular to be defined by standard functions. In particular we study perturbations of the Laplacian in R1 given by potentials of the form X2j S(x -xj). We also study Sturm-Liouville problems with zero order coefficients given by measures and prove that they satisfy the same oscillation theorems as the regular Sturm-Liouville problems.
In this paper adapting to p-adic case some methods of real valued Gibbs measures on Cayley trees we construct several p-adic distributions on the set Zp of p-adic integers. Moreover, we give conditions under which these p-adic distributions become p-adic measures (i.e. bounded distributions). Mathematics Subject Classifications (2010). 46S10, 82B26, 12J12 (primary); 60K35 (secondary)
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