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Ken Umeno

Publications and source records attributed to Ken Umeno.

51 records · Page 3Linked to original sources
arXiv2012

Correlational properties of two-dimensional solvable chaos on the unit circle

This article investigates correlational properties of two-dimensional chaotic maps on the unit circle. We give analytical forms of higher-order covariances. We derive the characteristic function of their simultaneous and lagged ergodic densities. We found that these characteristic functions are described by three types of two-dimensional Bessel functions. Higher-order covariances between x and y and those between y and y show non-positive values. Asymmetric features between cosine and sine functions are elucidated.

nlin.CD↗
arXiv2009

A Class of Self-Trapped and Self-Focusing Wave Functions in Madelung Fluid Picture of A Single Free Particle Quantum System

Using the Madelung fluid picture of Schrödinger equation for a single free particle moving in one spatial dimension, we shall specify a class of wave functions whose quantum probability density is being trapped by the quantum potential it itself generates. The global convexity of the quantum potential generated by the initial self-trapped wave function will then be shown to further localize the quantum probability density through a self-generated focusing equation for a finite interval of time.

quant-ph↗
arXiv2009

Madelung Fluid Model for The Most Likely Wave Function of a Single Free Particle in Two Dimensional Space with a Given Average Energy

We consider spatially two dimensional Madelung fluid whose irrotational motion reduces into the Schrödinger equation for a single free particle. In this respect, we regard the former as a direct generalization of the latter, allowing a rotational quantum flow. We then ask for the most likely wave function possessing a given average energy by maximizing the Shannon information entropy over the quantum probability density. We show that there exists a class of solutions in which the wave function is self-trapped, rotationally symmetric, spatially localized with finite support, and spinning around its center, yet stationary. The stationarity comes from the balance between the attractive quantum force field of a trapping quantum potential generated by quantum probability density and the repulsive centrifugal force of a rotating velocity vector field. We further show that there is a limiting case where the wave function is non-spinning and yet still stationary. This special state turns out to be the lowest stationary state of the ordinary Schrödinger equation for a particle in a cylindrical tube classical potential.

quant-ph↗
arXiv2004

Randomness Evaluation and Hardware Implementation of Nonadditive CA-Based Stream Cipher

We shall review the cellular automaton(CA)-based pseudorandom-number generators (PRNGs), and show that one of these PRNGs can generate high-quality random numbers which can pass all of the statistical tests provided by the National Institute of Standards and Technology (NIST). A CA is suitable for hardware implementation. We demonstrate that the CA-based stream cipher, which is implemented in the field-programmable gate arrays (FPGA), has a high encryption speed in a real-time video encryption and decryption system.

nlin.CD↗
arXiv2004

Corrections of the NIST Statistical Test Suite for Randomness

It is well known that the NIST statistical test suite was used for the evaluation of AES candidate algorithms. We have found that the test setting of Discrete Fourier Transform test and Lempel-Ziv test of this test suite are wrong. We give four corrections of mistakes in the test settings. This suggests that re-evaluation of the test results should be needed.

nlin.CD↗
arXiv1999

Improvement of SNR with Chaotic Spreading Sequences for CDMA

We show that chaotic spreading sequences generated by ergodic mappings of Chebyshev orthogonal polynomials have better correlation properties for CDMA(code division multiple access) than the optimal binary sequences (Gold sequences) in the sense of ensemble average.

chao-dyn↗
arXiv1999

Chaotic Monte Carlo computation: a dynamical effect of random-number generations

It is shown that superefficient Monte Carlo computations can be carried out by using chaotic dynamical systems as non-uniform random-number generators. Here superefficiency means that the expectation value of the square of the error decreases to 0 as 1/N^{2} with N successive observations for N-> infinity, whereas the conventional Monte Carlo simulation gives the square of the error in the order 1/N. The order of N in the error convergence speed of superefficient Monte Carlo computations does not depend on the dimensionality of the problems. By deriving a necessary and sufficient condition for the superefficiency, it is shown that such high-performance Monte Carlo simulations can be carried out only if there exists a strong correlation of chaotic dynamical variables.

chao-dyn↗
arXiv1998

Exactly solvable chaos and addition theorems of elliptic functions

A unified view is given to recent developments about a systematic method of constructing rational mappings as ergodic transformations with non-uniform invariant measures on the unit interval I=[0,1]. All of the rational ergodic mappings of I with explicit non-uniform invariant densities can be obtained by addition theorems of elliptic functions. It is shown here that the class of the rational ergodic mappings I->I are essentially same as the permutable rational functions obtained by J. F. Ritt.

chao-dyn↗
arXiv1998

Superposition of chaotic process with convergence to Levy's stable law

We construct a family of chaotic dynamical systems with explicit broad distributions, which always violate the central limit theorem. In particular, we show that the superposition of many statistically independent, identically distributed random variables obeying such chaotic process converge in density to Levy's stable laws in a full range of the index parameters. The theory related to the connection between deterministic chaos and non-Gaussian distributions gives us a systematic view of the purely mechanical generation of Levy's stable laws.

chao-dyn↗
arXiv1997

Complex step-size dependences in tracking a simple two-body dynamics

In molecular simulations, one of the most difficult points is to track the real dynamics of many-body systems from the first principle. The present study shows that step-size dependences have an unexpected effect on simulation results, even when we use the standard high-precision numerical integrators to apply to a simple system with a two-body interaction. The validity of our analysis is checked by the theory of adiabatic approximations.

chao-dyn↗
arXiv1997

Method of constructing exactly solvable chaos

We present a new systematic method of constructing rational mappings as ergordic transformations with nonuniform invariant measures on the unit interval [0,1]. As a result, we obtain a two-parameter family of rational mappings that have a special property in that their invariant measures can be explicitly written in terms of algebraic functions of parameters and a dynamical variable. Furthermore, it is shown here that this family is the most generalized class of rational mappings possessing the property of exactly solvable chaos on the unit interval, including the Ulam=Neumann map y=4x(1-x). Based on the present method, we can produce a series of rational mappings resembling the asymmetric shape of the experimentally obtained first return maps of the Beloussof-Zhabotinski chemical reaction, and we can match some rational functions with other experimentally obtained first return maps in a systematic manner.

chao-dyn↗
arXiv1996

Integrability and Computability in Simulating Quantum Systems

An impossibility theorem on approximately simulating quantum non-integrable Hamiltonian systems is presented here. This result shows that there is a trade-off between the unitary property and the energy expectation conservation law in time-descretization of quantum non-integrable systems, whose classical counterpart is Ge-Marsden's impossibility result about simulating classically non-integrable Hamiltonian systems using integration schemes preserving symplectic (Lie-Poisson) property.

quant-ph↗
arXiv1996

Parallel Computation Using Generalized Models of Exactly Solvable Chaos

How chaos is useful in the brain information processing is greatly unknown. Here, we show that the statistical property of chaos such as invariant measures naturally organized under a great number of iterations of chaotic mappings can be used for some complex computations, while the precise information of initial conditions which vanishes in the course of iterations deos not matter for this kind of computations. The key observation of the present study is that computation using ergordicity of dynamical systems can be thought of as massively parallel Monte Carlo simulations. Here, to avoid difficulty in elucidating the ergordicity of dynamical systems, we propose computational schemes using the generalized class of one-dimensional chaos with explicit invariant measures. The validity of our results which connect chaos with parallel computation is checked by the precision computations of some transcendental numbers like π.

chao-dyn↗
arXiv1996

Non-perturbative non-integrability of non-homogeneous nonlinear lattices induced by non-resonance hypothesis

We prove the non-integrability (non-existence of additional analytic conserved quantities other than Hamiltonian) for Fermi-Pasta-Ulam (FPU) lattices by virtue of Lyapunov-Kovalevskaya- -Ziglin-Yoshida's monodromy method about the variational equations. The key to this analysis is that the normal variational equations along a certain solution happen to be in a type of Lamé equations. We also introduce the classification problem towards non-homogeneous nonlinear lattices including FPU lattices using non-integrability preserving transformation.

solv-int↗