The Quantum Ising model is an exactly solvable model of quantum phase transition. This Letter gives an exact solution when the system is driven through the critical point at a finite rate. The evolution goes through a series of Landau-Zener level anticrossings when pairs of quasiparticles with opposite pseudomomenta get excited with a probability depending on the transition rate. The average de...

Numerical analysis of renormalon technique in quantum mechanics. Abstract We mimic infrared renormalons of QCD by resumming a Born series for s-wave scattering within an exactly solvable model of quantum mechanics. Numerical estimates show that traditional technique based on introduction of nonperturbative power corrections fails to determine the low-energy mass scale of the model analogous to ...

We show that dynamical symmetry methods can be applied to Hamiltonians with periodic potentials. We construct dynamical symmetry Hamiltonians for the Scarf potential and its extensions using representations of su(1, 1) and so(2, 2). Energy bands and gaps are readily understood in terms of representation theory. We compute the transfer matrices and dispersion relations for these systems, and fin...

We examine a class of problems which seeks to find tree-structured networks which minimize the maximum cost among a subset of nodes in a graph. The cost metric is characterized by a series of parameters which can represent distance, flow volume, and delivery deadlines. Derived through variations in problem parameters, we present 17 different problems and discuss their worst-case complexity. Fou...

The inverse p-median problem with variable edge lengths on graphs is to modify the edge lengths at minimum total cost with respect to given modification bounds such that a prespecified set of p vertices becomes a pmedian with respect to the new edge lengths. The problem is shown to be strongly NP-hard on general graphs and weakly NP-hard on series-parallel graphs. Therefore, the special case on...

This paper presents procedures for constructing numerically solvable discretizations of multistage stochastic programs that epi-converge to the original problem as the discretizations are made finer. Epi-convergence implies, in particular, that the cluster points of the first-stage solutions of the discretized problems are optimal first-stage solutions of the original problem. The discretizatio...

A robust fuzzy controller is designed to stabilize a class of solvable nonlinear descriptor systems with time-varying delay. First, a new modeling and control method for nonlinear descriptor systems is presented with a fuzzy descriptor model. A sufficient condition for the existence of the fuzzy controller is given in terms of a series of LMIs. Then, a less conservative fuzzy controller design ...

What dynamics govern a time series representing the appearance of words in social media data? In this paper, we investigate an elementary dynamics, from which word-dependent special effects are segregated, such as breaking news, increasing (or decreasing) concerns, or seasonality. To elucidate this problem, we investigated approximately three billion Japanese blog articles over a period of six ...

According to Skolem’s conjecture, if an exponential Diophantine equation is not solvable, then it solvable modulo appropriately chosen modulus. Besides several concrete equations, the conjecture has only been proved for rather special cases. In