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The time evolution of a closed quantum system is connected to its Hamiltonian through Schroedinger's equation. The ability to estimate the Hamiltonian is critical to our understanding of quantum systems, and allows optimization of control.…
This note is devoted to inverse spectral problems for canonical Hamiltonian systems on the half-line. An approach to inverse spectral problems based on the use of truncated Toeplitz operators has been especially effective in the case when…
A sixth order quadrupole boson Hamiltonian is treated through a time dependent variational principle approach choosing as trial function a coherent state with respect to zeroth $b^{\dagger}_0$ and second $b^{\dagger}_2+b^{\dagger}_{-2}$…
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
One of the main open problems in the qualitative theory of real planar differential systems is the study of limit cycles. In this article, we present an algorithmic approach for detecting how many limit cycles can bifurcate from the…
We derive a Hamiltonian for the external and internal dynamics of an electromagnetically bound, charged two-particle system in external electromagnetic and gravitational fields, including leading-order relativistic corrections. We apply…
The equations of classical spin-orbit motion can be extended to a Hamiltonian system in 9-dimensional phase space by introducing a coupled spin-orbit Poisson bracket and a Hamiltonian function. After this extension and by establishing…
We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed system presents a…
For any given spacetime the choice of time coordinate is undetermined. A particular choice is the absolute time associated with a preferred vector field. Using the absolute time Hamilton's equations are $- (\delta H_{c})/(\delta…
Quasicrystals are long-range ordered, yet not periodic, and thereby present a fascinating challenge for condensed matter physics, as one cannot resort to the usual toolbox based on Bloch's theorem. Here, we present a numerical method for…
In this paper we consider a class of planar autonomous systems having an isolated limit cycle x_0 of smallest period T>0 such that the associated linearized system around it has only one characteristic multiplier with absolute value 1. We…
For a wide class of Hamiltonians, a novel method to obtain lower and upper bounds for the lowest energy is presented. Unlike perturbative or variational techniques, this method does not involve the computation of any integral (a…
We derive a Hamiltonian for an extended spinning test body in a curved background spacetime, to quadratic order in the spin, in terms of three-dimensional position, momentum, and spin variables having canonical Poisson brackets. This…
We consider Arnoldi like processes to obtain symplectic subspaces for Hamiltonian systems. Large systems are locally approximated by ones living in low dimensional subspaces; we especially consider Krylov subspaces and some extensions. This…
As periodic orbit theory works badly on computing the observable averages of dynamical systems with intermittency, we propose a scheme to cooperate with cycle expansion and perturbation theory so that we can deal with intermittent systems…
The dynamics of classical and quantum systems which are driven by a high frequency ($\omega$) field is investigated. For classical systems the motion is separated into a slow part and a fast part. The motion for the slow part is computed…
We extend a Gaussian model for the internal electrical potential of a two-dimensional Coulomb gas by a non-Gaussian measure term, which singles out the physically relevant configurations of the potential. The resulting Hamiltonian,…
Index theory revealed its outstanding role in the study of periodic orbits of Hamiltonian systems and the dynamical consequences of this theory are enormous. Although the index theory in the periodic case is well-established, very few…
We analyze a new class of time-periodic nonreciprocal dynamics in interacting chaotic classical spin systems, whose equations of motion are conservative (phase-space-volume-preserving) yet possess no symplectic structure. As a result, the…
The present paper is a review of counterexamples to the ``Hamiltonian Seifert conjecture'' or, more generally, of examples of Hamiltonian systems having no periodic orbits on a compact energy level. We begin with the discussion of the…