We derive a systematic and recursive approach to local conservation laws and the Hamiltonian formalism for the Ablowitz–Ladik (AL) hierarchy. Our methods rely on a recursive approach to the AL hierarchy using Laurent polynomials and on asymptotic expansions of the Green’s function of the AL Lax operator, a five-diagonal finite difference operator.

In this paper we discuss the concept of cosymmetries and co–recursion operators for difference equations and present a co–recursion operator for the Viallet equation. We also discover a new type of factorisation for the recursion operators of difference equations. This factorisation enables us to give an elegant proof that the recursion operator given in arXiv:1004.5346 is indeed a recursion op...

The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the existence of a positivedefinite inner product that renders the Hamiltonian self-adjoint. Unlike for a time-independent Hamiltonian, this does not imply the uni...

In this paper a generalization of Weyl quantization which maps a dynamical operator in a function space to a dynamical superoperator in an operator space is suggested. Quantization of dynamical operator, which cannot be represented as Poisson bracket with some function, is considered. The usual Weyl quantization of observables can be derived as a specific case of suggested quantization if dynam...

For a spin subjected to an adiabatically changing magnetic field, the " solid angle result " as embodied by a rotation operator is the only non-trivial factor in the evolution operator. For a charged particle, the infinite degeneracy of the energy levels calls for a rigorous investigation. We find that in this case, it is the product of the rotation operator and a magnetic translation operator ...

For a spin subjected to an adiabatically changing magnetic field, the ”solid angle result” as embodied by a rotation operator is the only nontrivial factor in the quantum evolution operator. For a charged particle, the infinite degeneracy calls for a rigorous investigation. We find that in this case, it is the product of the rotation operator and a magnetic translation operator that enters into...

In the classical theory of Hamiltonian systems, great emphasis is placed on the introduction of canonical coordinates-the positions and conjugate momenta of classical mechanics. I Canonical coordinates serve to simplify many of the equations and transformations required in the study of finite-dimensional Hamiltonian systems. Most quantization procedures require that the Hamiltonian system be in...

The size consistency of multi-reference Møller-Plesset perturbation theory as a function of the structure of the zeroth-order Hamiltonian is studied. In calculations it is shown that the choice of projection operators to define the zeroth-order Hamiltonian is crucial. In essence whenever such a projection operator can be written as the sum of projection operators onto particular subspaces, cros...

PACS numbers: 11.10.Ef 02.30.Wd 02.30.Jr 03.40.Gc Abstract We propose a general scheme to construct multiple Lagrangians for completely integrable non-linear evolution equations that admit multi-Hamiltonian structure. The recursion operator plays a fundamental role in this construction. We use a conserved quantity higher/lower than the Hamiltonian in the potential part of the new Lagrangian and...

in this research we work with the effective hamiltonian and the quark model. we investigate the decay rates of matter-antimatter of quark. we describe the effective hamiltonian theory and apply this theory to the calculation of current-current ( ), qcd penguin ( ), magnetic dipole ( ) and electroweak penguin ( ) decay rates. the gluonic penguin structure of hadronic decays is studied through th...