Related papers: Pseudorandomness and Dynamics of Fermat Quotients
We show that the use of the main characteristics of the circle map leads naturally to establish a few statements on primes and pseudoprimes. In this way a Fermat's theorem on primes and some interesting properties of pseudoprimes are…
Dynamic properties of fermionic systems, like contollability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory. Observing the parity superselection rule, we treat the fully…
We review novel results and investigate actions and transformations of groups and semigroups on (quantum) spaces, present dynamical systems and zeta functions arising from these spaces, actions and transformations, discuss their stochastic…
We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating…
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
In this paper we study the monomial dynamical systems of dimension one over finite fields from the viewpoints of arithmetic and graph theory. We give formulas for the number of periodic points with period r and cycles with length r. Then we…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
Pseudogap is a ubiquitous phenomenon in strongly correlated systems such as high-$T_{\rm c}$ superconductors, ultracold atoms and nuclear physics. While pairing fluctuations inducing the pseudogap are known to be enhanced in low-dimensional…
Statistical properties of Fermionic Molecular Dynamics are studied. It is shown that, although the centroids of the single--particle wave--packets follow classical trajectories in the case of a harmonic oscillator potential, the equilibrium…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
We investigate the probability distribution of the quantum fluctuations of thermodynamic functions of finite, ballistic, phase-coherent Fermi gases. Depending on the chaotic or integrable nature of the underlying classical dynamics, on the…
In this paper we review some general properties of probability distributions which exibit a singular behavior. After introducing the matter with several examples based on various models of statistical mechanics, we discuss, with the help of…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
Pseudorandmness plays an important role in number theory, complexity theory and cryptography. Our aim is to use models of arithmetic to explain pseudorandomness by randomness. To this end we construct a set of models $\cal M$, a common…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
We study random dynamical systems on the real line, considering each dynamical system together with the one generated by the inverse maps. We show that there is a duality between forward and inverse behaviour for such systems, splitting…
The properties of a fictitious, fermionic, many-body system based on the complex zeros of the Riemann zeta function are studied. The imaginary part of the zeros are interpreted as mean-field single-particle energies, and one fills them up…
Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties…
We discuss the role of pseudo-fermions in the analysis of some two-dimensional models, recently introduced in connection with non self-adjoint hamiltonians. Among other aspects, we discuss the appearance of exceptional points in connection…