We propose a canonical tranformation approach to the effective interaction Weff between two holes, based on the three-band Hubbard model but ready to include extra interactions as well. An effective two-body Hamiltonian can in principle be obtained including any kind of virtual intermediate states. We derive the closed-form analytic expression of the effective interaction including 4-body virtu...

We consider the problem of sampling k-bandlimited graph signals, i.e., linear combinations of the first k graph Fourier modes. We know that a set of k nodes embedding all k-bandlimited signals always exists, thereby enabling their perfect reconstruction after sampling. Unfortunately, to exhibit such a set, one needs to partially diagonalize the graph Laplacian, which becomes prohibitive at larg...

Let p be a rational prime number. We refine Brauer’s elementary diagonalisation argument to show that any system of r homogeneous polynomials of degree d, with rational coefficients, possesses a non-trivial p-adic solution provided only that the number of variables in this system exceeds (rd) d 1 . This conclusion improves on earlier results of Leep and Schmidt, and of Schmidt. The methods exte...

In this paper we present a speech enhancement algorithm for noisy speech signal. A worldwide subspace approach is used for enhancement of speech corrupted by noise. The proposed approach is based on the instantaneous diagonalisation of the clean speech and noise covariance matrices. The system designed in this paper takes the PCA method as its basis and used a strong and accurate noise estimati...

The level spacing distribution is numerically calculated at the disorder-induced metal–insulator transition for dimensionality d = 4 by applying the Lanczos diagonalisation. The critical level statistics are shown to deviate stronger from the result of the random matrix theory compared to those of d = 3 and to become closer to the Poisson limit of uncorrelated spectra. Using the finite size sca...

We compute the representations (" nim-reps ") of the fusion algebra of sl(N) which determine the boundary conditions of sl(N) WZW theories twisted by the charge conjugation. This is done following two procedures, one of general validity, the other specific to the problem at hand. The problem is related to the classical problem of decomposition of the fundamental representations of sl(N) onto re...

We compute the representations (" nim-reps ") of the fusion algebra of sl(N) which determine the boundary conditions of sl(N) WZW theories twisted by the charge conjugation. This is done following two procedures, one of general validity, the other specific to the problem at hand. The problem is related to the classical problem of decomposition of the fundamental representations of sl(N) onto re...

The optical conductivity of charge carriers coupled to quantum phonons is studied in the framework of the one-dimensional spinless Holstein model. For one electron, variational diagonalisation yields exact results in the thermodynamic limit, whereas at finite carrier density analytical approximations based on previous work on single-particle spectral functions are obtained. Particular emphasis ...

DVR3D calculates rotationless (J = 0) vibrational energy levels and wavefunctions for triatomic systems using scattering (Jacobi) coordinates, or optionally unsymmetrised Radau coordinates, for a given potential energy surface. The program uses a discrete variable representation (DVR) based on Gauss—Legendre and Gauss—Laguerre quadrature for all 3 internal coordinates and thus yields a fully po...

We compute the representations (" nim-reps ") of the fusion algebra of sl(N) which determine the boundary conditions of sl(N) WZW theories twisted by the charge conjugation. This is done following two procedures, one of general validity, the other specific to the problem at hand. The problem is related to the classical problem of decomposition of the fundamental representations of sl(N) onto re...