An algebraic semi-classical approach to Bloch electrons in a magnetic field

Spectrum of 2D Bloch electrons in a periodic magnetic field : algebraic approach

Quantum Group, Bethe Ansatz and Bloch Electrons in a Magnetic Field

The wave functions for two dimensional Bloch electrons in a uniform magnetic field at the mid-band points are studied with the help of the algebraic structure of the quantum group Uq(sl2). A linear combination of its generators gives the Hamiltonian. We obtain analytical and numerical solutions for the wave functions by solving the Bethe Ansatz equations, proposed by Wiegmann and Zabrodin on th...

From Compact U ( 1 ) Maxwell Chern - Simons to Azbel - Hofstadter : Testing Magnetic Monopoles and Gravity to ∼ 10 − 17 m on a Nearby Laboratory

It is built a map between the Topological Quantum Field Theory (TQFT) 3D compact U(1) gauge Maxwell Chern-Simons and the non-relativistic quantum mechanics (semi-classical) Azbel-Hofstadter model of Bloch-electrons. The U q (sl 2) quantum group of magnetic translations in the Azbel-Hofstadter model is interpreted as discretized gauge transformations on the TQFT. The monopole confining and monop...

Asymptotic Analysis of the Quantum Dynamics in Crystals: The Bloch-Wigner Transform, Bloch Dynamics and Berry Phase

We study the semi-classical limit of the Schrödinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play ...

Analytical investigation of the practical range and deflection of megavoltage electron beam in the water phantom with the presence of magnetic field

Introduction: Integrated radiation therapy - MRI systems are capable of delivering high doses to the target tissues near sensitive organs and achieve better therapeutic results; however, the Applied magnetic fields for imaging, can influence the charged path, change the penetration depth and deflect the particles, laterally, leading to dose distribution variations. Therefore, i...