In this article we present some results concerning natural dissipative perturbations of 3d Hamiltonian systems. Given a Hamiltonian system ẋ = PdH, and a Casimir function S, we construct a symmetric covariant tensor g, so that the modified (so-called “metriplectic”) system ẋ = PdH + gdS satisfies the following conditions: dH is a null vector for g, and dS(gdS) ≤ 0. Along solutions to a dynamica...

This work is devoted to a force control strategy of a class of standard mechanical systems in the port-Hamiltonian framework. First, a coordinate transformation is applied to equivalently describe the original port-Hamiltonian system in a port-Hamiltonian form which has a constant mass-inertia matrix in the Hamiltonian. Then, we show how to derive an extended port-Hamiltonian system with struct...

We derive a model Hamiltonian whose ground state expectation value of any two-body operator coincides with that obtained with the Jastrow correlated wave function of the many-body Fermi system. Using this Hamiltonian we show that the variational principle can be extended to treat systems with dynamical mesons, even if in this case the concept of wave function looses its meaning.

The bi-Hamiltonian structure of certain multi-component integrable systems, generalizations of the dispersionless Toda hierarchy, is studied for systems derived from a rational Lax function. One consequence of having a rational rather than a polynomial Lax functions is that the corresponding bi-Hamiltonian structures are degenerate, i.e. the metric which defines the Hamiltonian structure has va...

The characteristic function of the work performed by an external time-dependent force on a Hamiltonian quantum system is identified with the time-ordered correlation function of the exponentiated system's Hamiltonian. A similar expression is obtained for the averaged exponential work which is related to the free energy difference of equilibrium systems by the Jarzynski work theorem.

in this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite hamiltonian group. the coverings with three proper subgroups and the principal series of such a group are also counted. finally, we give a complete description of the lattice of characteristic subgroups of a finite h...