Related papers: When are vector fields Hamiltonian?
It is shown that a given non-autonomous system of two first-order ordinary differential equations can be expressed in Hamiltonian form. The derivation presented here allow us to obtain previously known results such as the infinite number of…
The modeling framework of port-Hamiltonian systems is systematically extended to constrained dynamical systems (descriptor systems, differential-algebraic equations). A new algebraically and geometrically defined system structure is…
Several important dynamical systems are in $\mathbb{R}^2$, defined by the pair of differential equations $(x',y')=(f(x,y),g(x,y))$. A question of fundamental importance is how such systems might behave quantum mechanically. In developing…
We introduce two numerical conjugacy invariants for dynamical systems -- the complexity and weak complexity indices -- which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants can be seen as "slow…
Paper is devoted to maintaining the simple objective: We want to provide Hamiltonian canonical form for autonomous dynamical system reducible to even-dimensional one. Along the road we construct new class of conserved quantities, called…
General statistical ensembles in the Hamiltonian formulation of hybrid quantum-classical systems are analyzed. It is argued that arbitrary probability densities on the hybrid phase space must be considered as the class of possible…
The Camassa-Holm shallow water equation is known to be Hamiltonian with respect to two compatible Poisson brackets. A set of conjugate variables is constructed for both brackets using spectral theory.
The quantum harmonic oscillator is one of the most fundamental objects in physics. We consider the case where it is extended to an arbitrary number modes and includes all possible terms that are bilinear in the annihilation and creation…
Hamiltonian systems with linearly dependent constraints (irregular systems), are classified according to their behavior in the vicinity of the constraint surface. For these systems, the standard Dirac procedure is not directly applicable.…
Single-valuedness of the eigenfunctions of the quantised Hitchin Hamiltonians is proposed as a natural quantisation condition. Separation of Variables can be used to relate the classification of eigenstates to the classification of…
Quantization of a damped harmonic oscillator leads to so called Bateman's dual system. The corresponding Bateman's Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond…
On a manifold equipped with a bivector field, we introduce for every Hamiltonian a Lagrangian on paths valued in the cotangent space whose stationary points projects onto Hamiltonian vector fields. We show that the remaining components of…
First, we review the notion of a Poisson structure on a noncommutative algebra due to Block-Getzler and Xu and introduce a notion of a Hamiltonian vector field on a noncommutative Poisson algebra. Then we describe a Poisson structure on a…
We have previously shown how to construct a deformation quantization of any locally compact space on which a vector group acts. Within this framework we show here that, for a natural class of Hamiltonians, the quantum evolutions will have…
Easy steps through essential Hamiltonian dynamics are outlined, from necessary definitions of Poisson brackets and canonical transformations, to a quick proof that Hamiltonian evolution is made by canonical transformations, the quickest…
In systems where one coordinate undergoes periodic oscillation, the net displacement in any other coordinate over a single period is shown to be given by differentiation of the action integral associated with the oscillating coordinate.…
We study the entanglement Hamiltonian for finite intervals in infinite quantum chains for two different free-particle systems: coupled harmonic oscillators and fermionic hopping models with dimerization. Working in the ground state, the…
Based on two dissipative models, universal asymptotic behavior of flow equations for Hamiltonians is found and discussed. Universal asymptotic behavior only depends on fundamental bath properties but not on initial system parameters, and…
Dirac formalism of Hamiltonian constraint systems is studied for the noncommutative Abelian Proca field. It is shown that the system of constraints are of second class in agreement with the fact that the Proca field is not guage invariant.…
We consider scenarios where the dynamics of a quantum system are partially determined by prior local measurements of some interacting environmental degrees of freedom. The resulting effective system dynamics are described by a disordered…