Valuations of Mortality-Linked Structured Notes

Analytical solutions for a boundary-driven XY chain

“…Note that, once the problem is brought into a L × L matrix of bordered 2−Toeplitz form, it may also be possible to find other further analytical solutions to Eqs. (76, 77), as well as the expressions for the eigenvectors, by referring to, for example, references [20][21][22][23].…”

“…P is a tridiagonal bordered Toeplitz matrix, and g is an anti-symmetric tridiagonal Toeplitz matrix. In the isotropic case of γ = 0, P is block diagonal withP andP * on its diagonal,P has shown to be analytically diagonalizable in [20][21][22], something which we exploited in [19].…”

“…In our previous work [19], we showed that for number conserving quadratic systems (be them bosonic, fermionic or made of spins), finding that the rapidities (eigenvalues of the Lindbladian) and the decay modes could be reduced to the problem of diagonalizing an L×L matrix which could be of special form, i.e. a bordered Toeplitz matrix, which has known analytical solutions [20][21][22]. This allowed us to find explicit analytical solutions.…”