The collisions of two vertical Bloch lines are studied numerically. It is found that soliton like properties of the Bloch lines are obtained for a nonzero damping constant if the power input is large enough to balance the effect of dissipation. In the strict sense solitons are obtained in nondissipative nonlinear systems [I]. On the other hand, most solid state physical systems are dissipative....

By using the concept of the weak subordination, we examine the stability a class of analytic functions in the unit disk is said to be stable if it is closed under weak subordination for a class of admissible functions in complex Banach spaces. The stability of analytic functions in the following classes is discussed: Bloch class, little Bloch class, hyperbolic little Bloch class, extend Bloch c...

A novel Bloch band based level set method is proposed for computing the semiclassical limit of Schrödinger equations in periodic media. For the underlying equation subject to a highly oscillatory initial data, a hybrid of the WKB approximation and homogenization leads to the Bloch eigenvalue problem and an associated HamiltonJacobi system for the phase in each Bloch band, with the Bloch eigenva...

In this paper boundedness and compactness of generalized composition oper-ators from logarithmic Bloch type spaces to Q_K type spaces are investigated.

A Bloch ion has periodic symmetry and is distributed in space in a lattice array form. Its spatial density distribution is neutralized within each unit cell by a metal's electrons. The wave function repeats coherently modulo a Bravais lattice vector. Paired Bloch deuterons partitioned over a sufficiently large number of unit cells become superposed and coherently mixed by coordinate exchange. A...

In the framework of the theory of an electron in a periodic potential, we reconsider the longstanding problem of the existence of smooth and periodic quasi-Bloch functions, which is shown to be equivalent to the triviality of the Bloch bundle. By exploiting the time-reversal symmetry of the Hamiltonian and some bundle-theoretic methods, we show that the problem has a positive answer in any dime...

When the Bloch vectors are perpendicularly oriented, the level surfaces of quantum discord of non-X state are formed by three ”tubes” along orthogonal directions. The level surfaces shrink when the Bloch vectors are increased while they expand when the quantum discord are increased. For different Bloch vectors, the tube along one direction may disappear while tubes along other directions may st...