We study the quantum dynamics of soliton-like domain walls in anisotropic spin-1/2 chains in the presence of magnetic fields. In the absence of fields, domain walls form a Bloch band of delocalized quantum states while a static field applied along the easy axis localizes them into Wannier wave packets and causes them to execute Bloch oscillations, i.e. the domain walls oscillate along the chain...

Let μ $$ \mu be a finite Borel measure on [ 0,1 ) \left[0,1\right) . In this paper, we consider the generalized integral type Hilbert operator I α + 1 ( f z = ∫ 0 t − d > {\mathcal{I}}_{\mu_{\alpha +1}}(f)(z)={\int}_0^1\frac{f(t)}{{\left(1- tz\right)}^{\alpha +1}} d\mu (t)\kern0.30em \left(\alpha >-1\right). ...

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...

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...