Hamiltonian systems are a class of dynamical systems which can be characterised by preservation of a symplectic form. This allows to write down the equations of motion in terms of a single function, the Hamiltonian function. They were conceived in the 19th century to study physical systems varying from optics to frictionless mechanics in a unified way. This description turned out to be particul...

In this note, we apply canonical quantization to the selfdual particle system describing the motion of poles to a higher rank solution of the KP hierarchy, explicitly determining both the quantum Hamiltonian and the wave function. It is verified that the quantum Hamiltonian is trivially bispectral (that is, that the wave function can be taken to be symmetric) as predicted by a widely held hypot...

The frameworks of thermodynamic availability function and irreversible port Hamiltonian systems are used to derive passivity based control strategies for irreversible thermodynamic systems. An energy based availability function is defined using as generating function the internal energy. This is a variation with respect to previous works where the total entropy usually corresponds to the genera...

We consider the use of Lagrange manifolds to construct viscosity solutions of first order Hamiltonian-Jacobi equations. Recent work of several authors is indicated in which the essential underlying structure consists of a Lagrange manifold on which 1) the desired Hamiltonian function vanishes and 2) the canonical 1-form p·dx of classical mechanics has an integral S(x, p). We explore the proposi...

We propose an intensity-dependent pion-nucleon coupling Hamiltonian within a unitary multiparticle-production model of the Auerbach-Avin-Blankenbecler-Sugar (AABS) type in which the pion field is represented by the thermal-density matrix. Using this Hamiltonian, we explain the appearance of the negative-binomial (NB) distribution for pions and the well-known empirical relation, the so-called Wr...

This paper proposes a pseudo port Hamiltonian formulation of non isothermal Continuous Stirred Tank Reactor CSTR) model. This structured modeling shows how the opposite of the entropy can be used as Hamiltonian function and how the associated dissipation can be related to the irreversible entropy production due to chemical reaction. The IDAPBC approach based control is then applied to stabilize...

A Hilbert manifold structure is described for the phase space F of asymptotically flat initial data for the Einstein equations. The space of solutions of the constraint equations forms a Hilbert submanifold C ⊂ F . The ADM energy-momentum defines a function which is smooth on this submanifold, but which is not defined in general on all of F . The ADM Hamiltonian defines a smooth function on F w...

This paper proposes a thermodynamical pseudo Hamiltonian formulation of Continuous Stirred Tank Reactor model in which takes place some chemical reaction. This is done both in the isothermal and non isothermal cases. It is shown that the Gibbs free energy and the opposite of entropy can be chosen as Hamiltonian function respectively. For the non isothermal case, the so called Interconnection an...

We present a simple recipe to construct the Green’s function associated with a Hamiltonian of the form H = H0 + λ δ(x), where H0 is a Hamiltonian for which the associated Green’s function is known. We apply this result to the case in which H0 is the Hamiltonian of a free particle in D dimensions. Field theoretic concepts such as regularization, renormalization, dimensional transmutation and tri...

We introduce a new approach to highly correlated systems which generalizes the Fermi Hypernetted Chain and Correlated Basis Function techniques. While the latter approaches can only be applied to systems for which a non-relativistic wave function can be defined, the new approach is based on the variation of a trial hamiltonian within a path integral framework and thus can also be applied to rel...