We provide a general method for constructing bosonic Bogoliubov transformations that diagonalize class of quadratic Hamiltonians. These Hamiltonians describe the pair interaction models. are constructed algebraically, and resulting become second quantizations explicit one-particle Moreover, an formula ground state energies is given. Our systematically diagonalizes various models quantum field t...

In this paper, we consider a family of Jacobi-type algorithms for simultaneous orthogonal diagonalization problem of symmetric tensors. For the Jacobi-based algorithm of [SIAM J. Matrix Anal. Appl., 2(34):651–672, 2013], we prove its global convergence for simultaneous orthogonal diagonalization of symmetric matrices and 3rd-order tensors. We also propose a new Jacobi-based algorithm in the gen...

We suggest that low-lying eigenvalues of realistic quantum many-body hamiltonians, given, as in the nuclear shell model, by large matrices, can be calculated, instead of the full diagonalization, by the diagonalization of small truncated matrices with the exponential extrapolation of the results. We show numerical data confirming this conjecture. We argue that the exponential convergence in an ...

We consider the problem of convolutive blind signal separation through the optimization of contrast functions. In this work, we show that some links between contrasts and joint diagonalization criteria can be exhibited in the convolutive case. This allows to devise a constructive algorithm performing MIMO blind equalization, with the help of a joint approximate diagonalization of a set of matri...

A class of simple Jacobi-type algorithms for non-orthogonal matrix joint diagonalization based on the LU or QR factorization is introduced. By appropriate parametrization of the underlying manifolds, i.e. using triangular and orthogonal Jacobi matrices we replace a high dimensional minimization problem by a sequence of simple one dimensional minimization problems. In addition, a new scale-invar...

Abstract—The diagonalization of a conventional multiple-input multiple-output (MIMO) channel into parallel and independent subchannels via singular value decomposition (SVD) is a fundamental strategy that allows the MIMO channel capacity to be achieved using scalar channel codes. This letter establishes a similar channel diagonalization result for the uplink and the downlink of a cloud radio ac...

We present numerical studies of fermion and boson models with random all-to-all interactions (the SYK models). The high temperature expansion and exact diagonalization of the N -site fermion model are used to compute the entropy density: our results are consistent with the numerical solution of N =1 saddle point equations, and the presence of a non-zero entropy density in the limit of vanishing...