Diagonalization of System plus Environment Hamiltonians

Diagonalization of Hamiltonians, uncertainty matrices and Robertson inequality

The problem of diagonalization of Hamiltonians of N -dimensional boson systems by means of time-dependent canonical transformations (CT) is considered, the case of quadratic Hamiltonians being treated in greater detail. The unitary generator of time-dependent CT which can transform any Hamiltonian to that of a system of uncoupled stationary oscillators is constructed. The close relationship bet...

Universal correlations for deterministic plus random Hamiltonians.

We consider the (smoothed) average correlation between the density of energy levels of a disordered system, in which the Hamiltonian is equal to the sum of a deterministic H0 and of a random potential φ. Remarkably, this correlation function may be explicitly determined in the limit of large matrices, for any unperturbed H0 and for a class of probability distribution P (φ) of the random potenti...

Fast iterative diagonalization of nonlocal pseudopotential Hamiltonians using the fast Fourier transformation.

Maximally Efficient Symmetry Group Founded Diagonalization of Biophysical and Quantum Chemical Hamiltonians

We show that modified Wigner projector technique and generalized Bloch theorem approach yield maximally efficient diagonalization of the Hamiltonian of the large symmetrical systems. For the sake of illustration, we perform a case study of the simplified DNA molecule model and solve the energy eigenproblem analytically by using the unit symmetry cell (symcell) and the corresponding low-dimensio...

Block-Diagonalization of the Symmetric First-Order Coupled-Mode System

We consider the Hamiltonian first-order coupled-mode system that occurs in nonlinear optics, photonics, and atomic physics. Spectral stability of gap solitons is determined by eigenvalues of the linearized coupled-mode system, which is equivalent to a four-by-four Dirac system with sign-indefinite metric. In the special class of symmetric nonlinear potentials, we construct a block-diagonal repr...