Tests of alpha-, beta-, and electron capture decays for randomness

Silverman, Mark P.; Strange, Wayne; Silverman, Chris; Lipscombe, Trevor Davis

doi:10.1016/s0375-9601(99)00668-4

Cited by 24 publications

(14 citation statements)

References 8 publications

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“…However, in each case the theoretical consequences of relation (1) were validated experimentally and shown to be in accord with currently known laws of physics [19] [20].…”

Section: Introduction: Two Approaches To Brownian Motionsupporting

confidence: 53%

Brownian Motion of Decaying Particles: Transition Probability, Computer Simulation, and First-Passage Times

Silverman¹

2017

JMP

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Recent developments in the measurement of radioactive gases in passive diffusion motivate the analysis of Brownian motion of decaying particles, a subject that has received little previous attention. This paper reports the derivation and solution of equations comparable to the Fokker-Planck and Langevin equations for one-dimensional diffusion and decay of unstable particles. In marked contrast to the case of stable particles, the two equations are not equivalent, but provide different information regarding the same stochastic process. The differences arise because Brownian motion with particle decay is not a continuous process. The discontinuity is readily apparent in the computer-simulated trajectories of the Langevin equation that incorporate both a Wiener process for displacement fluctuations and a Bernoulli process for random decay. This paper also reports the derivation of the mean time of first passage of the decaying particle to absorbing boundaries. Here, too, particle decay can lead to an outcome markedly different from that for stable particles. In particular, the first-passage time of the decaying particle is always finite, whereas the time for a stable particle to reach a single absorbing boundary is theoretically infinite due to the heavy tail of the inverse Gaussian density. The methodology developed in this paper should prove useful in the investigation of radioactive gases, aerosols of radioactive atoms, dust particles to which adhere radioactive ions, as well as diffusing gases and liquids of unstable molecules.

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“…However, in each case the theoretical consequences of relation (1) were validated experimentally and shown to be in accord with currently known laws of physics [19] [20].…”

Section: Introduction: Two Approaches To Brownian Motionsupporting

confidence: 53%

Brownian Motion of Decaying Particles: Transition Probability, Computer Simulation, and First-Passage Times

Silverman¹

2017

JMP

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“…The times are independent from previous results and the number of pulses that arrive in a fixed time period follows a Poisson distribution. The exact rate depends on many factors, but it can be determined experimentally and we can be satisfied that the pulses arrive at independent times (Silverman et al, 1999). The probability of finding m pulses in an observation period of T seconds is P m (T ) = (λT ) m m!…”

Section: A the First Quantum Random Number Generatorsmentioning

confidence: 99%

Quantum random number generators

2017

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Random numbers are a fundamental resource in science and engineering with important applications in simulation and cryptography. The inherent randomness at the core of quantum mechanics makes quantum systems a perfect source of entropy. Quantum random number generation is one of the most mature quantum technologies with many alternative generation methods. We discuss the different technologies in quantum random number generation from the early devices based on radioactive decay to the multiple ways to use the quantum states of light to gather entropy from a quantum origin. We also discuss randomness extraction and amplification and the notable possibility of generating trusted random numbers even with untrusted hardware using device independent generation protocols.

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“…It is worth mentioning that methods for generating random numbers can be broadly divided into two main approaches: True Random Number Generators (TRNGs) and Pseudo-Random Number Generators (PRNGs). On the one hand, TRNGs rely on physical sources such as throwing a dice or flipping a coin to more sophisticated processes such as radius material decay [45,49], thermal noise in resistors [8], atmospheric noise [17,14], lava lamps [36] and quantum physics [43,52]. However, there are certain challenges in terms of implementation, including additional special equipment and circuitries (often requiring either cooling or high voltages), limited speed, restricted rates of production, e.g 16 Mbps [20], and degradation of the statistical properties when implemented at a hardware and software level [11].…”

Section: Introductionmentioning

confidence: 99%

Improving the pseudo-randomness properties of chaotic maps using deep-zoom

Machicao

Bruno

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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A generalized method is proposed to compose new orbits from a given chaotic map. The method provides an approach to examine discrete-time chaotic maps in a "deep-zoom" manner by using k-digits to the right from the decimal separator of a given point from the underlying chaotic map. Interesting phenomena have been identified. Rapid randomization was observed, i.e., chaotic patterns tend to become indistinguishable when compared to the original orbits of the underlying chaotic map. Our results were presented using different graphical analyses (i.e., time-evolution, bifurcation diagram, Lyapunov exponent, Poincaré diagram, and frequency distribution). Moreover, taking advantage of this randomization improvement, we propose a Pseudo-Random Number Generator (PRNG) based on the k-logistic map. The pseudo-random qualities of the proposed PRNG passed both tests successfully, i.e., DIEHARD and NIST, and were comparable with other traditional PRNGs such as the Mersenne Twister. The results suggest that simple maps such as the logistic map can be considered as good PRNG methods.

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Tests of alpha-, beta-, and electron capture decays for randomness

Cited by 24 publications

References 8 publications

Brownian Motion of Decaying Particles: Transition Probability, Computer Simulation, and First-Passage Times

Brownian Motion of Decaying Particles: Transition Probability, Computer Simulation, and First-Passage Times

Quantum random number generators

Improving the pseudo-randomness properties of chaotic maps using deep-zoom

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