Kei Inoue

Semiclassical properties and chaos degree for the quantum Baker’s map

We study the chaotic behavior and the quantum-classical correspondence for the Baker’s map. Correspondence between quantum and classical expectation values is investigated and it is numerically shown that it is lost at the logarithmic timescale. The quantum chaos degree is computed and it is demonstrated that it describes the chaotic features of the model. The correspondence between classical and quantum chaos degrees is considered.

APPLICATION OF CHAOS DEGREE TO SOME DYNAMICAL SYSTEMS

Abstract Chaos degree defined through two complexities in information dynamics is applied to some deterministic dynamical models. It is shown that this degree well describes the chaotic feature of the models.

Characterization of quantum teleportation processes by nonlinear quantum channel and quantum mutual entropy

Abstract The quantum mutual entropy was introduced by one of the present authors in 1983 as a quantum extension of the Shannon mutual information. It has been used for several studies such as quantum information transmission in optical communication and quantum irreversible processes. In this paper, a nonlinear channel for a quantum teleportation process is rigorously constructed and the quantum mutual entropy is applied to characterize the quantum teleportation processes of Bennett et al.

Operation of heat pump water heaters for restriction of photovoltaic reverse power flow

Japanese government plans to introduce photovoltaic (PV) systems 20-fold by 2020 compared to the 2005 level, and then grid-connected PV systems are expected to increase rapidly. At the same time, however, there is concern that a large scale PV systems introduction might bring an excess of supply when the electricity demand is low such as in spring or autumn in Japan. Meanwhile, heat pump water heaters (HPWHs) are highly efficient water heaters and have been introduced rapidly. If hot water is stored in the daytime using HPWHs, it will contribute to absorb economically a part of the excess of PV output. In this paper, we propose a use of residential HPWHs in the daytime as a means of PV reverse power flow restriction. And we evaluate how the difference of the actual demand patterns influences on PV reverse power flow restriction and HPWH power consumption.

Internal Noise Caused by the Memory

In modern brain research, an internal noise caused by the memory is represented by the output of EEG-measurement. However, based on classical models specialists in EEG-mapping cannot explain the observed properties of the internal noise. In this paper using the quantum models we consider the asymptotic behaviour of the internal noise caused by the memory.

On a Quantum Model of Brain Activities — Distribution of the Outcomes of EEG-Measurements and Random Point Fields

Considering models based on classical probability theory, states of signals in the brain should be identified with probability distributions of certain random point fields representing the configuration of excited neurons. Then the outcomes of EEG-measurements can be considered as random variables being certain functions of that random point field. In practice, specialists use certain statistical methods evaluating the outcomes of the sequence of these measurements. To make these statistical investigations precise, one should know the distribution of the stochastic process on the space of point configurations representing the time evolution of the configuration of excited neurons in the brain. Up to now that distribution is totally unknown. In this paper we consider time evolutions of random point fields as well as the distribution of the outcomes of EEG-measurements related to unitary evolutions of certain quantum states used in [4, 5, 10 – 14] in order to describe activities of the brain.

Approximative approaches to a stochastic partialdifferential equation by point systems

Abstract. Several scientific and technical problems can be described by a stochastic partial differential equation. The solution of the equation could be considered as the limit of a suitable discrete particle model. The existence of such a kind of approximation was discussed in [Serdica 13 (1987), 396–402]. In this paper we will consider a completely discrete particle model.

ON THE LOW-TEMPERATURE BEHAVIOR OF THE INFINITE-VOLUME IDEAL BOSE GAS

In Ref. 11 clustering representations of the position distribution of the ideal Bose gas were considered. In principle that gives rise to possibilities concerning simulations of the system of positions of the particles. But one has to take into account that in case of low temperature the clusters are very large and their origins are far from a fixed bounded volume. For that reason we will consider some estimations of the influence of these clusters on the behavior of the subsystem of particles located in a fixed bounded volume. All points in the fixed bounded volume come from a bigger volume which the estimation (5.2) in Theorem 5.2 gives on average. Several numerical simulations in dimension two are shown in Sec. 5.

On a combined quantum baker's map and its characterization by entropic chaos degree

Quantum Bakers map is a theoretical model that exhibits chaos in a quantum system. In this paper, we introduce a combined map by combining several quantum Bakers maps. Chaos of such a combined dynamics is studied by the entropic chaos degree.

ε-Entropy and Fractal Dimension of a State for a Gaussian Measure

Kolmogorov introduced the concept of ε-entropy to analyze information in classical continuous systems. The fractal dimension of a geometric set was introduced by Mandelbrot as a new criterion to analyze the geometric complexity of the set. The ε-entropy and the fractal dimension of a state in a general quantum system were introduced by one of the present authors (MO) in order to characterize chaotic properties of general states.In this paper, we show that ε-entropy of a state includes Kolmogorovs ε-entropy, and that the fractal dimension of a state describes fractal structure of Gaussian measures.