Related papers: Antibracket as the Hamiltonian Structure of a clas…
For linear bose field theories, I show that if a classical Hamiltonian function is strictly positive, then there is a canonical transformation making the evolution orthogonal. This structure theorem is used to analyze the corresponding…
We investigate various types of symmetries and their mutual relationships in Hamiltonian systems defined on manifolds with different geometric structures: symplectic, cosymplectic, contact and cocontact. In each case we pay special…
The quantum mechanical brachistochrone system with PT-symmetric Hamiltonian is Naimark dilated and reinterpreted as subsystem of a Hermitian system in a higher-dimensional Hilbert space. This opens a way to a direct experimental…
We consider evolution equations of the Lotka-Volterra type, and elucidate especially their formulation as canonical Hamiltonian systems. The general conditions under which these equations admit several conserved quantities…
In this paper, time-independent Hamiltonian systems are investigated via a Lie-group/algebra formalism. The (unknown) solution linked with the Hamiltonian is considered to be a Lie-group transformation of the initial data, where the group…
A canonical Hamiltonian formalism is derived for a class of Ermakov systems specified by several different frequency functions. This class of systems comprises all known cases of Hamiltonian Ermakov systems and can always be reduced to…
This paper presents a "historical" formalism for dynamical systems, in its Hamiltonian version (Lagrangian version was presented in a previous paper). It is universal, in the sense that it applies equally well to time dynamics and to field…
This paper is focused on the development of the notions of canonical and canonoid transformations within the framework of Hamiltonian Mechanics on locally conformal symplectic manifolds. Both, time-independent and time-dependent dynamics…
We study strongly isochronous Hamiltonians that generate periodic time evolution with the same basic period for a dense set of initial values. We explain that all such Hamiltonians are maximally superintegrable, and show that if the system…
Topological constraints play a key role in the self-organizing processes that create structures in macro systems. In fact, if all possible degrees of freedom are actualized on equal footing without constraint, the state of "equipartition"…
For a linear non-Hermitian system, I demonstrate that a Hamiltonian can be constructed such that the non-Hermitian equations can be expressed exactly in the form of Hamilton's canonical equations. This is first shown for discrete systems…
We present a general framework for finding the time-optimal evolution and the optimal Hamiltonian for a quantum system with a given set of initial and final states. Our formulation is based on the variational principle and is analogous to…
Using the notion of a contravariant derivative, we give some algebraic and geometric characterizations of Poisson algebras associated to the infinitesimal data of Poisson submanifolds. We show that such a class of Poisson algebras provides…
In this paper, we discuss time evolution and adiabatic approximation in $PT$-symmetric quantum mechanics. we give the time evolving equation for a class of $PT$-symmetric Hamiltonians and some conditions of the adiabatic approximation for…
A generalization of the Hamilton-Jacobi theory to arbitrary dynamical systems, including non-Hamiltonian ones, is considered. The generalized Hamilton-Jacobi theory is constructed as a theory of ensemble of identical systems moving in the…
We construct integrable Hamiltonian systems on $G/K$, where $G$ is a quasitriangular Poisson Lie group and $K$ is a Lie subgroup arising as the fixed point set of a group automorphism $\sigma$ of $G$ satisfying the classical reflection…
The classical invariants of a Hamiltonian system are expected to be derivable from the respective quantum spectrum. In fact, semiclassical expressions relate periodic orbits with eigenfunctions and eigenenergies of classical chaotic…
The Hamiltonian structure of the guiding-center Vlasov-Maxwell equations is presented in terms of a Hamiltonian functional and a guiding-center Vlasov-Maxwell bracket. The bracket, which is shown to satisfy the Jacobi identity exactly, is…
In this note we clarify the relation between extended world-sheet supersymmetry and generalized complex structure. The analysis is based on the phase space description of a wide class of sigma models. We point out the natural isomorphism…
We construct a modification of the Poisson bracket which is suitable for a canonical analysis of space-time noncommutative field theories. We show that this bracket satisfies the Jacobi identities and generates equations of motion. In this…