The full control of high-dimensional quantum systems is discussed, particularly under the condition in which artificial access is severely restricted. Minimising the interaction with environment through control probes would be of use to maintain the quantum coherence. The mathematical background and physical examples are reviewed for the problems of control and system identification of many-body systems.
Strongly correlated materials such as Mott-insulators are important research target in terms of superconductivity. However, continuous doping at low temperature is still difficult due to the lack of appropriate technique. Recently, a photo-induced electric double layer is shown to generate strong electric-field-effect at molecular interface, resulting in a superconducting transition in an organic Mott-insulator. This method paves the way to complete the electronic phase diagram around a two-dimensional Mott-insulator as a function of temperature, band filling, and band width.
When we do not use or do not know a regularization that preserves a preferred symmetry, the construction of the Noether current composite operator corresponding to that symmetry is quite non-trivial. Such a situation occurs for the construction of the energy–momentum tensor in lattice gauge theory, because the lattice structure explicitly breaks the translational invariance. In this article, I explain a completely new approach to this problem on the basis of the gradient flow, a certain deformation of the gauge theory along a fictitious time according to diffusion-type equations.
What will happen when the 3D periodic crystal (bulk) is truncated? The surface may form the unique atomic and electronic structure quite different from its bulk. However, without such significant reconstruction, the truncation of the periodicity itself can play an important role for the two-dimensional electronic structure in the surface and subsurface region. To elucidate such sub-surface electronic structure, the origin of the two-dimensional surface states localized in subsurface regions of the Ge (111) substrate has been studied by angle-resolved photoelectron spectroscopy (ARPES) and density-functional-theory calculations. From the Ge (111) surfaces covered with various elements, we found the common 2D electronic states closely related to the bulk Ge bands nearby; the heavy-hole, light-hole, and spin-orbit split-off bands. These subsurface states originate from the bulk bands that are perturbed due to the truncation of the three-dimensional periodicity at the surface, which could be regarded as precursor electronic states to topological surface states that is, in most cases, also derived from the bulk bands.