We review the Krein-Gel'fand-Lidskii theory of strong stability of Hamiltonian and symplectic matrices in order to nd a quantitative measure of the strong stability. As a result, formulas for the 2-norm distance from a strongly stable Hamiltonian or symplectic matrix to the set of unstable matrices are derived. 1 Deenition and simple properties of symplectic and Hamiltonian matrices Throughout ...

We present an explicit computation of matrix elements of the hamiltonian constraint operator in non-perturbative quantum gravity. In particular, we consider the euclidean term of Thiemann’s version of the constraint and compute its action on trivalent states, for all its natural orderings. The calculation is performed using graphical techniques from the recoupling theory of colored knots and li...

The smallness of the variation rate of the hamiltonian matrix elements compared to the (square of the) energy spectrum gap is usually believed to be the key parameter for a quantum adiabatic evolution. However it is only perturbatively valid for scaled timed hamiltonian and resonance processes as well as off resonance possible constructive Stückelberg interference effects violate this usual con...

On the basis of the collective field method, we analyze the Calogero– Sutherland model (CSM) and the Selberg–Aomoto integral, which defines, in particular case, the partition function of the matrix models. Vertex operator realizations for some of the eigenstates (the Jack polynomials) of the CSM Hamiltonian are obtained. We derive Virasoro constraint for the generalized matrix models and indica...

The investigation of the recently described generalized transformation theory which leads to a non-Hamiltonian description of dynamics is pursued. The concept of generalized unitary transformations of superoperators is introduced and a specific class of transformations studied. For nondissipative systems it is equivalent to the usual unitary transformations that diagonalize the Hamiltonian. The...

A linear set of ordinary differential equations with a matrix depending on a set of adiabatically varying parameters is considered. Its asymptotic solutions are constructed to an arbitrary accuracy in the adiabaticity parameter «. By extending the phase space of the system not only with the space of parameters, like in the theory of Berry’s phase, but also with the space of their derivatives, i...

Various trace minimization principles have interplayed with numerical computations for the standard eigenvalue and generalized problems in general, as well important applied including linear response problem from electronic structure calculation symplectic of positive definite matrices that play roles classical Hamiltonian dynamics, quantum mechanics, information, among others. In this paper, K...