Coarse-Grained Picture for Controlling Quantum Chaos

We propose a coarse-grained picture to analyze control problems for quantum chaos systems. Using optimal control theory, we first show that almost perfect control is achieved for random matrix systems and a quantum kicked rotor. Second, under the assumption that the controlled dynamics is well described by a Rabi-type oscillaion between unperturbed states, we derive an analytic expression for the optimal field. Finally we numerically confirm that the analytic field can steer an initial state to a target state in random matrix systems.Comment: REVTeX4 with graphicx package, 11 pages, 10 figures; replaced fig.1(a) and 2(a

Asymptotic Distribution of Multilevel Channel Polarization for a Certain Class of Erasure Channels

This study examines multilevel channel polarization for a certain class of erasure channels that the input alphabet size is an arbitrary composite number. We derive limiting proportions of partially noiseless channels for such a class. The results of this study are proved by an argument of convergent sequences, inspired by Alsan and Telatar's simple proof of polarization, and without martingale convergence theorems for polarization process.Comment: 31 pages; 1 figure; 1 table; a short version of this paper has been submitted to the 2018 IEEE International Symposium on Information Theory (ISIT2018

Common property resource and private capital accumulation with random jump

In [6], Long and Katayama presented a model of exploitation of a common property resource, when agents can also invest in private and productive capital. They considered the case where the resource extracted from a common pool is non-renewable. In this paper, we try to extend their result to the case where the common pool is under uncertainty in the sense that it could have a sudden increase or decrease in the process of extraction and moreover we shall calculate the exhaustion probability.common property resource, private capital accumulation, pure jump process, exhaustion probability, HJB (Hamilton-Jacobi-Bellman) equation

Countably Infinite Multilevel Source Polarization for Non-Stationary Erasure Distributions

Polar transforms are central operations in the study of polar codes. This paper examines polar transforms for non-stationary memoryless sources on possibly infinite source alphabets. This is the first attempt of source polarization analysis over infinite alphabets. The source alphabet is defined to be a Polish group, and we handle the Ar{\i}kan-style two-by-two polar transform based on the group. Defining erasure distributions based on the normal subgroup structure, we give recursive formulas of the polar transform for our proposed erasure distributions. As a result, the recursive formulas lead to concrete examples of multilevel source polarization with countably infinite levels when the group is locally cyclic. We derive this result via elementary techniques in lattice theory.Comment: 12 pages, 1 figure, a short version has been accepted by the 2019 IEEE International Symposium on Information Theory (ISIT2019