We obtain for the attractive Dirac δ-function potential in two-dimensional quantum mechanics a renormalized formulation that avoids reference to a cutoff and running coupling constant. Dimensional transmutation is carried out before attempting to solve the system, and leads to an interesting eigenvalue problem in N −2 degrees of freedom (in the center of momentum frame) when there are N particl...

Formulation of quantum Hall dynamics using von Neumann lattice of guiding center coordinates is presented. A topological invariant expression of the Hall conductance is given and a new mean field theory of the fractional Hall effect based on flux condensation is proposed. Because our mean field Hamiltonian has the same form as Hofstadter Hamiltonian, it is possible to understand characteristic ...

A generating function, expressed as a power series in the particle Larmor radius, is used to relate an arbitrary set of magnetic field line coordinates to particle canonical variables. A systematic procedure is described for successively choosing the generating function at each order in the Larmor radius so that the transformed particle Hamiltonian is independent of the Larmor phase angle. The ...

We derive and analyze several low dimensional Hamiltonian normal forms describing system symmetry breaking in ideal hydrodynamics. The equations depend on two parameters (e,2), where e is the strength of a system symmetry breaking perturbation and 2 is a detuning parameter. In many cases the resulting equations are completely integrable and have an interesting Hamiltonian structure. Our work is...

In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...

We revisit the HD molecular ion by starting from a definition of the nonrelativistic adiabatic Hamiltonian that recovers the isotopic splitting. The Hamiltonian is written in prolate spheroidal coordinates with the origin at the nuclear center of mass. This prescription for the adiabatic Hamiltonian implicitly contains the symmetrybreaking effects arising from the mass difference between the pr...

In this research we described the effective Hamiltonian theory and applied this theory to the calculation of current-current (Q1,2) and QCD penguin (Q3,…,6) c quark decay rates. We calculated the decay rates of semileptonic and hadronic of charm quark in the effective Hamiltonian theory. We investigated the decay rates of D meson decays according to Spectator Quark Model (SQM) for the calculati...

We present a simple and direct derivation of the SLLOD equations of motion for molecular simulations of general homogeneous flows. We show that these equations of motion (1) generate the correct particle trajectories, (2) conserve the total thermal momentum without requiring the center of mass to be located at the origin, and (3) exactly generate the required energy dissipation. These equations...

We consider the coupled Maxwell{Lorentz equations for a single charge with a rigid charge distribution subject to slowly varying external potentials. In the adiabatic limit, to lowest order, the motion of the charge is governed by an eeective Hamiltonian. In the next order we obtain, as a small correction, the radiation reaction containing q {terms. This equation has a stable center manifold an...

A mixed mean-field/BCS phase with an energy gap at high T c Abstract We construct a pair potential which in a scaling limit leads to a Hamiltonian that generates co-existing mean-field and superconducting phases. Depending on the relative values of the coupling constants, the superconducting phase may exist at arbitrarily high temperatures. ⋆ Work supported in part by " Fonds zur Förderung der ...