We report that the prefactor for the migration of neutral indium has been successfully determined
via an ab-initio calculation in combination with classical rate theory for the first time.
Our theoretical approach starts with a search for the saddle points of indium in the transition
state from the initial state to final state by using a climbing image nudged elastic band (CINEB)
method, which enables us to extract the migration energy, 0.79 eV, for indium. Thereafter, we
obtain the prefactor of neutral indium by calculating the effective frequencies in the initial and the
final states by using a dynamical matrix method.

This paper is concerned with the space of all compact adjoint operators from dual spaces of Banach spaces into dual spaces of Banach spaces and approximation properties. For some topology on the space of all bounded linear operators from separable dual spaces of Banach spaces into dual spaces of Banach spaces, it is shown that if a bounded linear operator is approximated by a net of compact adjoint operators, then the operator can be approximated by a sequence of compact adjoint operators whose operator norms are less than or equal to the operator norm of the operator. Also we obtain applications of the theory and, in particular, apply the theory to approximation properties.

We study the formation of five-dimensional string solutions including the Gregory-Laflamme (GL) black string, the Kaluza-Klein (KK) bubble, and the geometry with a naked singularity from the gravitational collapse. The interior solutions of five-dimensional Einstein equations describe collapsing non-isotropic matter clouds. It is shown that the matter cloud always forms the GL black string solution while the KK bubble solution cannot be formed. The numerical study seems to suggest that the collapsing matter forms the geometries with timelike naked curvature singularities, which should be taken cautiously as the general relativity is not reliable in the strong curvature regime.

We study the formation of black strings from a gravitational collapse of cylindrical dust clouds in the three-dimensional low-energy string theory. New junction conditions for the dilaton as well as two junction conditions for metrics and extrinsic curvatures between both regions of the clouds are presented. As a result, it is found that the collapsing dust cloud always collapses to a black string within a finite collapse time, and then a curvature singularity formed at origin is cloaked by an event horizon. Moreover, it is also shown that the collapse process can form a naked singularity within finite time, regardless of the choice of initial data.

The entropy for two-dimensional black holes is obtained through the entropy function with the condition that the geometry approaches an AdS₂ spacetime in the near horizon limit. It is shown that the entropy is universal and proportional to the value of the dilaton field at the event horizon as expected. We find this universal behavior holds even after the inclusion of higher derivative terms, only modifying the proportional constant. More specifically, a variety of models of the dilaton gravity in two dimensions are considered, in which it is shown that the universal entropy coincides with the well-known results in the previous literatures.

The Schrödinger equation of the mesoscopic capacitance coupled circuit with an arbitrary power source is solved by means of two step unitary transformation. The original Hamiltonian transformed to a very simple form by unitary operators so that it can be easily treated. We derived the exact full wave functions in Fock state. By making use of these wave functions and introducing the Lewis--Riesenfeld invariant operator, the thermal state have been constructed. The fluctuations of charges and currents are evaluated in thermal state. For T→ 0, the uncertainty products between charges and currents in thermal state recovers exactly to that of Fock state with n, m=0.