Melosh rotation: source of the proton's missing spin

It is shown that the observed small value of the integrated spin structure function for protons could be naturally understood within the naive quark model by considering the effect from Melosh rotation. The key to this problem lies in the fact that the deep inelastic process probes the light-cone quarks rather than the instant-form quarks, and that the spin of the proton is the sum of the Melosh rotated light-cone spin of the individual quarks rather than simply the sum of the light-cone spin of the quarks directly.Comment: 5 latex page

Collapse and revival oscillations as a probe for the tunneling amplitude in an ultra-cold Bose gas

We present a theoretical study of the quantum corrections to the revival time due to finite tunneling in the collapse and revival of matter wave interference after a quantum quench. We study hard-core bosons in a superlattice potential and the Bose-Hubbard model by means of exact numerical approaches and mean-field theory. We consider systems without and with a trapping potential present. We show that the quantum corrections to the revival time can be used to accurately determine the value of the hopping parameter in experiments with ultracold bosons in optical lattices.Comment: 10 pages, 12 figures, typos in section 3A correcte

Non-Abelian Discrete Symmetries and Neutrino Masses: Two Examples

Two recent examples of non-Abelian discrete symmetries (S_3 and A_4) in understanding neutrino masses and mixing are discussed.Comment: 16 pages, no figure, invited contribution to NJP focus issue on neutrino

Extension of Hereditary Symmetry Operators

Two models of candidates for hereditary symmetry operators are proposed and thus many nonlinear systems of evolution equations possessing infinitely many commutative symmetries may be generated. Some concrete structures of hereditary symmetry operators are carefully analyzed on the base of the resulting general conditions and several corresponding nonlinear systems are explicitly given out as illustrative examples.Comment: 13 pages, LaTe

A refined invariant subspace method and applications to evolution equations

The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear system of dissipative equations was analyzed to shed light on the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differential equations and their corresponding exact solutions with generalized separated variables.Comment: 16 page

A Class of Coupled KdV systems and Their Bi-Hamiltonian Formulations

A Hamiltonian pair with arbitrary constants is proposed and thus a sort of hereditary operators is resulted. All the corresponding systems of evolution equations possess local bi-Hamiltonian formulation and a special choice of the systems leads to the KdV hierarchy. Illustrative examples are given.Comment: 8 pages, late