Mathematical aspects of the Digital Annealer's simulated annealing algorithm

The Digital Annealer is a CMOS hardware designed by Fujitsu Laboratories for high-speed solving of Quadratic Unconstrained Binary Optimization (QUBO) problems that could be difficult to solve by means of existing general-purpose computers. In this paper, we present a mathematical description of the first-generation Digital Annealer's Algorithm from the Markov chain theory perspective, establish a relationship between its stationary distribution with the Gibbs-Boltzmann distribution, and provide a necessary and sufficient condition on its cooling schedule that ensures asymptotic convergence to the ground states

First-principles calculation of electronic density of states and Seebeck coefficient in transition-metal-doped Si-Ge alloys

High $ZT$ value and large Seebeck coefficient have been reported in the nanostructured Fe-doped Si-Ge alloys. In this work, the large Seebeck coefficient in Fe-doped Si-Ge systems is qualitatively reproduced from the computed electronic density of states, where a hybrid functional, HSE06, is used for an exchange-correlation functional, as well as a special quasi-random structure (SQS) for a disordered atomic configuration. Furthermore, by replacing Fe with other transition metals, such as Mn, Co, Ni, Cu, Zn, and Au, a better dopant that produces a larger Seebeck coefficient in Si-Ge alloy systems is explored.Comment: 6 page