We study the quantum dynamics of opened three-level su(1, 1) bosonic model. The effective non-Hermitian Hamiltonians describing system Lindblad equation in short time limit are constructed. obtained exactly solvable by Algebraic Bethe Ansatz. This approach allows representing biorthogonal and nonorthogonal bases system. analyze expectation values a number particles zero mode represent it determ...

In [1], Beylkin et al. introduced a wavelet-based algorithm that approximates integral or matrix operators of a certain type by highly sparse matrices, as the basis for efficient approximate calculations. The wavelets best suited for achieving the highest possible compression with this algorithm are Daubechies wavelets, while Coiflets lead to a faster decomposition algorithm at slightly lesser ...

We use generating functions to express orthogonality relations in the form of q-beta integrals. The integrand of such a q-beta integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials of Szegő and leads naturally to the Al-Salam-Chihara p...