Related papers: A geometric approach to solve time dependent and d…
This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of…
Port-Hamiltonian systems provide an energy-based formulation with a model class that is closed under structure preserving interconnection. For continuous-time systems these interconnections are constructed by geometric objects called Dirac…
A new approach leading to the formulation of the Hamilton-Jacobi equation for field theories is investigated within the framework of jet-bundles and multi-symplectic manifolds. An algorithm associating classes of solutions to given sets of…
The abelian Chern-Simons system is treated as a constrained system using the Hamilton-Jacobi approach. The equations of motion are obtained as total differential equations in many variables. It is shown that their simultaneous solutions…
An ordinary unambiguous integral representation for the finite propagator of a quantum system is found by starting of a privileged skeletonization of the functional action in phase space, provided by the complete solution of the…
We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system, specifically in cases where the Hamiltonian is explicitly time-dependent. Using Nielsen's geometric formulation of circuit complexity, we…
General analytical solutions of the Quantum Hamilton Jacobi Equation for conservative one-dimensional or reducible motion are presented and discussed. The quantum Hamilton's characteristic function and its derivative, i.e. the quantum…
This paper tackles Hamiltonian chaos by means of elementary tools of Riemannian geometry. More precisely, a Hamiltonian flow is identified with a geodesic flow on configuration space-time endowed with a suitable metric due to Eisenhart.…
In this paper, we consider a time independent $C^2$ Hamiltonian, sa\-tisfying the usual hypothesis of the classical Calculus of Variations, on a non-compact connected manifold. Using the Lax-Oleinik semigroup, we give a proof of the…
The geometric formulation of the Hamilton-Jacobi theory enables us to generalize it to systems of higher-order ordinary differential equations. In this work we introduce the unified Lagrangian-Hamiltonian formalism for the geometric…
Keeping in view the ordering ambiguity that arises due to the presence of position-dependent effective mass in the kinetic energy term of the Hamiltonian, a general scheme for obtaining algebraic solutions of quantum mechanical systems with…
We study the practical scope of the $k$-contact Hamilton--De Donder--Weyl formalism as a geometric framework for dissipative field equations. In particular, our work focuses on canonical $k$-contact manifolds on $\bigoplus^k {\rm…
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture) that can be put into correspondence with the usual…
The dynamics of a spherically symmetric thin shell with arbitrary rest mass and surface tension interacting with a central black hole is studied. A careful investigation of all classical solutions reveals that the value of the radius of the…
One method to overcome the notorious problem of time in the quantisation of gravity is the identification of a physically preferred time parameter, a promising candidate being so-called `York time'. The dynamical equations for matter and…
D=2,N=2 generalized Wess-Zumino theory is investigated by the dimensional reduction from D=4,N=1 theory. For each solitonic configuration (i,j) the classical static solution is solved by the Hamilton-Jacobi method of equivalent…
Gauge invariance of systems whose Hamilton-Jacobi equation is separable is improved by adding surface terms to the action fuctional. The general form of these terms is given for some complete solutions of the Hamilton-Jacobi equation. The…
The asymptotic stability of a global solution satisfying Hamilton-Jacobi equations with jumps will be analyzed in dependence on the strong dissipativity of the jump control function and using orbits of the differentiable flows to describe…
In the case of two degree system the pairs of quadratic in momenta Hamiltonians commuting according the standard Poisson bracket are considered. The new many-parametrical families of such pairs are founded. The universal method of…
We establish existence and uniqueness of minimax solutions for a fairly general class of path-dependent Hamilton-Jacobi equations. In particular, the relevant Hamiltonians can contain the solution and they only need to be measurable with…