In this paper a Hamiltonian analogue of the well-known meandering transition from rotating waves to modulated rotating and modulated travelling waves in systems with the Euclidean symmetry of the plane is presented. In non-Hamiltonian systems, for example in spiral wave dynamics, this transition is a Hopf bifurcation in a corotating frame, as external parameters are varied, and modulated travel...

It may be possible to derive a constituent approximation for bound states in QCD using hamiltonian light-front field theory. Cutoffs that violate explicit gauge invariance and Lorentz covariance must be employed. A similarity renormalization group and coupling coherence are used to compute the effective hamiltonian as an expansion in powers of the canonical QCD running coupling constant. At sec...

The renormalization of the effective QCD-Hamiltonian theory for the quarkantiquark channel is performed in terms of a renormalized or fixed-point Hamiltonian that leads to subtracted dynamical equations. The fixed pointHamiltonian brings the renormalization conditions as well as the counterterms that render the theory finite. The approach is renormalization group invariant. The parameters of th...

We present an new system of ordinary differential equations with affine Weyl group symmetry of type E (1) 6 . This system is expressed as a Hamiltonian system of sixth order with a coupled Painlevé VI Hamiltonian. Introduction The Painlevé equations PJ (J = I, . . . ,VI) are ordinary differential equations of second order. It is known that these PJ admit the following affine Weyl group symmetri...

We present an new system of ordinary differential equations with affine Weyl group symmetry of type E (1) 6 . This system is expressed as a Hamiltonian system of sixth order with a coupled Painlevé VI Hamiltonian. 2000 Mathematics Subject Classification: 34M55, 17B80, 37K10. Introduction The Painlevé equations PJ (J = I, . . . ,VI) are ordinary differential equations of second order. It is know...

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 property and present a sufficient condition in terms of group characters. We give examples of such groups in dimension 2 and 3. Furthermore, we show that it is p...

It it known that to get the usual Hamiltonian formulation of lattice Yang-Mills theory in the temporal gauge A 0 = 0 one should place on every link the cotangent bundle of a Lie group. The cotangent bundle may be considered as a limiting case of a so called Heisenberg double of a Lie group which is one of the basic objects in the theory of Lie-Poisson and quantum groups. It is shown in the pape...

The general form of the operators commuting with the ground representation (appearing in many physical problems within single particle approximation) of the group is found. With help of the modified group projector technique, this result is applied to the system of identical particles with spin independent interaction, to derive the Dirac-Heisenberg hamiltonian and its effective space for arbit...