Related papers: Symmetry actuated closed-loop Hamiltonian systems
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…
When a condensed-matter system is subjected to external electromagnetic fields, the gauge-invariant formulation of physical operators must explicitly incorporate the gauge-field contribution. However, in the context of spin-orbit coupling…
We propose and analyze a new dynamical system with a closed-loop control law in a Hilbert space $\mathcal{H}$, aiming to shed light on the acceleration phenomenon for \textit{monotone inclusion} problems, which unifies a broad class of…
We present the reaction-coordinate polaron-transform (RCPT) framework for generating effective Hamiltonian models to treat nonequilibrium open quantum systems at strong coupling with their surroundings. Our approach, which is based on two…
An odd-symplectic form is a closed and maximally non-degenerate $2$-form on a compact odd-dimensional manifold. It describes the dynamics of an autonomous Hamiltonian system on a regular energy level. It is called Zoll if the induced…
We develop a Poisson Hamiltonian formulation of Pontryagin dynamics for optimal control of mechanical systems on Lie groupoids. The reduced dynamics is formulated intrinsically on the dual Lie algebroid endowed with its canonical linear…
In this paper a new supersymmetric extension of conformal mechanics is put forward. The beauty of this extension is that all variables have a clear geometrical meaning and the super-Hamiltonian turns out to be the Lie-derivative of the…
Atmospheric systems incorporating thermal dynamics must be stable with respect to both energy and entropy. While energy conservation can be enforced via the preservation of the skew-symmetric structure of the Hamiltonian form of the…
It is well known that the allowed wavefunctions for an $N$-electron system should be antisymmetric with respect to the permutation of any pair of electron labels. On the other hand, the Hamiltonian for such system is invariant under any…
A Hamiltonian formulation is given for the gravitational dynamics of two spinning compact bodies to next-to-leading order ($G/c^4$ and $G^2/c^4$) in the spin-orbit interaction. We use a novel approach (valid to linear order in the spins),…
We explore a particular approach to the analysis of dynamical and geometrical properties of autonomous, Pfaffian non-holonomic systems in classical mechanics. The method is based on the construction of a certain auxiliary constrained…
A finite spin system invariant under a symmetry group G is a very illustrative example of the finite group action on a set of mappings f:X->Y. In the case of spin systems X is a set of spin carriers and Y contains 2s+1 z-components -s<=m<=s…
In this paper, we show how to use canonical perturbation theory for dissipative dynamical systems capable of showing limit cycle oscillations. Thus, our work surmounts the hitherto perceived barrier for canonical perturbation theory that it…
A case can be made that the utility of quasi-linear systems of conservation laws as physical models is largely limited to Euler system models of fluid flow, at least in higher dimensions. Qualified corroboration of this conjecture is…
We show that trapped ions can be used to simulate a highly symmetrical Hamiltonian with eingenstates naturally protected against local sources of decoherence. This Hamiltonian involves long range coupling between particles and provides a…
Noether's Theorem yields conservation laws for a Lagrangian with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation laws.…
Any quantum system with a non-trivial Hamiltonian is able to simulate any other Hamiltonian evolution provided that a sufficiently large group of unitary control operations is available. We show that there exist finite groups with this…
Within the post Newtonian framework the fully reduced Hamiltonian (i.e., with eliminated spin supplementary condition) for the next-to-leading order spin-squared dynamics of general compact binaries is presented. The Hamiltonian is…
Recently, the Hamiltonian Control Theory was used in [Boreux et al.] to increase the dynamic aperture of a ring particle accelerator having a localized thin sextupole magnet. In this letter, these results are extended by proving that a…
A new symmetry for Newtonian Dynamics is analyzed, this corresponds to going to an accelerated frame, which introduces a constant gravitational field into the system and subsequently. We consider the addition of a linear contribution to the…