One of the most basic applications of quantum mechanics is the study of a two body system with a spherically symmetric interaction. This problem is characterized simply by giving the mass of each particle as well as the inter-particle potential V (r) which is a function of the inter-particle separation only. This problem can be reduced in a straightforward way to a simpler one particle problem ...

We have proposed, in our previous papers[1, 2], a method to characterize integrable discrete soliton equations. In this paper we generalize the method further and obtain a q-difference Toda equation, from which we can derive various q-difference soliton equations by reductions.

The quantum hadrodynamics are studied by using non-perturbative renormalization group equations. Approximate discrete γ5-symmetry is studied. It is shown that the contributions of one-loop diagrams are important for effective potential. A relation between the local-potential approximation and the usual Hartree approximation is discussed. The local-potential approximation includes contribution o...

We discuss nonanomalous R-symmetry in the supersymmetric grand unified theories. In particular, we explore anomaly-free solutions predicting the gravitino mass in the range of 10 eV∼m3/2 ∼ 1 TeV when the μ-parameter is fixed to be μ ≃ 1 TeV. In the minimal SU(5) GUT, we have shown that μ ≃ 1 TeV is obtained only if the gravitino is ultralight with mass m3/2 ∼ 10 eV. If extra fields 5⊕ 5 or 10⊕ ...

The most general form for symmetric modes of nonlinear discrete-symmetry systems with nonlinearity depending on the modulus of the field is presented. Vortex solutions are demonstrated to behave as Bloch modes characterized by an angular Bloch momentum associated to a periodic variable, periodicity being fixed by the order of discrete point-symmetry of the system. The concept of angular Bloch m...

We investigate the occurrence of a phase transition, characterized by the spontaneous breaking of a discrete symmetry, in a driven-dissipative Bose-Hubbard lattice in the presence of two-photon coherent driving. The driving term does not lift the original U(1) symmetry completely and a discrete Z2 symmetry is left. When driving the bottom of the Bose-Hubbard band, a mean-field analysis of the s...