相关论文: Random maps in physical systems
In this work, it is introduced a new function based on the non-trivial zeros of the Riemann-zeta function. Such function shows an interesting behavior: when the argument of the function grows, it changes from a pseudo-random behavior to a…
We consider a recursive device that is based on a Mach-Zehnder interferometer and linear optical elements which allow self-feedback through multiple internal reflection of radiation between two parallel arrays of opposite faced mirrors. By…
Given a prime $p$, we consider the dynamical system generated by repeated exponentiations modulo $p$, that is, by the map $u \mapsto f_g(u)$, where $f_g(u) \equiv g^u \pmod p$ and $0 \le f_g(u) \le p-1$. This map is in particular used in a…
For every fixed graph $H$ and every fixed $0 < \alpha < 1$, we show that if a graph $G$ has the property that all subsets of size $\alpha n$ contain the ``correct'' number of copies of $H$ one would expect to find in the random graph…
We study the dynamics of a piecewise map defined on the set of three pairwise nonparallel, nonconcurrent lines in $\mathbb{R}^2$. The geometric map of study may be analogized to the billiard map with a different reflection rule so that each…
We describe a curious dynamical system that results in sequences of real numbers in $[0,1]$ with seemingly remarkable properties. Let the function $f:\mathbb{T} \rightarrow \mathbb{R}$ satisfy $\hat{f}(k) \geq c|k|^{-2}$ and define a…
A Chen generating series, along a path and with respect to $m$ differential forms,is a noncommutative series on $m$ letters and with coefficients which are holomorphic functionsover a simply connected manifold in other words a series with…
Sequences are often conveniently encoded in the form of a generating function depending on a formal variable. This note presents two observations that allow one to draw conclusions about the generated sequence from the generating function.…
We study automatic sequences and automatic systems generated by general constant length (nonprimitive) substitutions. While an automatic system is typically uncountable, the set of automatic sequences is countable, implying that most…
The phenomenon of sequential vibrational resonance existed in a multistable system that is excited by both high- and low-frequency signals is reported. By the method of direct separation of motions, the theoretical investigation on…
This paper presents a simple model that mimics quantum mechanics (QM) results without using complex wavefunctions or non-localities. The proposed model only uses integer-valued quantities and arithmetic operations, in particular assuming a…
A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as…
A physical random number generator based on the intrinsic randomness of quantum mechanics is described. The random events are realized by the choice of single photons between the two outputs of a beamsplitter. We present a simple device,…
Polymorphic circuits are a special kind of circuits which possess multiple build-in functions, and these functions are activated by environment parameters, like temperature, light and VDD. The behavior of a polymorphic circuit can be…
We show that the Circular Orthogonal Ensemble of random matrices arises naturally from a family of random polynomials. This sheds light on the appearance of random matrix statistics in the zeros of the Riemann zeta-function.
Nonlinear optical media that are normally dispersive, support a new type of localized (nondiffractive and nondispersive) wavepackets that are X-shaped in space and time and have slower than exponential decay. High-intensity X-waves, unlike…
The $n$th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of $n$ in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration…
We show that one may interpret physical reality as random fields in space-time. These have a probability given by the expectation of a coherent state projection operator, called the Q-function. The resulting dynamical evolution includes…
Consider a polynomial of large degree n whose coefficients are independent, identically distributed, nondegenerate random variables having zero mean and finite moments of all orders. We show that such a polynomial has exactly k real zeros…
For nice functions, invariant means over integral currents (certain generalized surfaces), can be uniquely defined.