Quantum graphs and microwave networks as narrow band filters for quantum and microwave devices

We investigate properties of the transmission amplitude of quantum graphs and microwave networks composed of regular polygons such as triangles and squares. We show that for the graphs composed of regular polygons with the edges of the length $l$ the transmission amplitude displays a band of transmission suppression with some narrow peaks of full transmission. The peaks are distributed symmetrically with respect to the symmetry axis $kl=\pi$, where $k$ is the wave vector. For microwave networks the transmission peak amplitudes are reduced and their symmetry is broken due to the influence of internal absorption. We demonstrate that for the graphs composed of the same polygons but separated by the edges of length $l' < l$ the transmission spectrum is generally not symmetric according to the axis $kl'=\pi$. We also show that graphs composed of regular polygons of different size with the edges being irrational numbers are not fully chaotic and their level spacing distribution and the spectral rigidity are well described by the Berry-Robnik distributions. Moreover, the transmission spectrum of such a graph displays peaks which are very close to $1$. Furthermore, the microwave networks are investigated in the time-domain using short Gaussian pulses. In this case the delay-time distributions, though very sensitive to the internal structure of the networks, show the sequences of transmitted peaks with the amplitudes much smaller than the input one. The analyzed properties of the graphs and networks suggest that they can be effectively used to manipulate quantum and wave transport

A Class Of Measurable Dynamical Systems For Chaotic Cryptography

Teori kaos merupakan teori yang merangkumi semua aspek sains. Kini, dalam dunia hari ini, ia turut merangkumi semua aspek matematik, fizik, biologi, kewangan, komputer dan juga muzik. Sebagai suatu daripada aplikasi teori ini, keselamatan komunikasi mula dikaji seawal 1990-an. Daya tarikan utama teori ini digunakan sebagai asas untuk membangunkan kriptosistem adalah disebabkan sifat intrinsiknya, antaranya: kepekaannya terhadap keadaan awal dan parameter kawalan, perlakuan seakan-akan rawak, ergodisiti dan sifat campurannya, yang mempunyai hubungan erat dengan keperluan kriptografi. Sifat teori ini yang paling penting adalah ergodisiti dan campuran, yang boleh dihubungkan dengan dua sifat kriptografi asas, iaitu kekeliruan (“confusion”) dan pembauran (“diffusion”). Bagi membuktikan ergodisiti dan kekuatan campuran, cukup dengan hanya menunjukkan bahawa sistem memperoleh ukuran takvarian dan entropi Kolmogorov-Sinai (K-S) daripada sudut pandangan sistem dinamik. Chaos theory is a blanketing theory that covers all aspects of science, hence, it shows up everywhere in the world today: mathematics, physics, biology, finance, computer and even music. As an application of chaos theory, secure communications have been studied since the early 1990s. The attractiveness of using chaos as the basis for developing cryptosystem is mainly due to the intrinsic nature of chaos such as the sensitivity to the initial condition and control parameter, random-like behaviors, ergodicity and mixing property, which have tight relationships with the requirements of cryptography. The most important features of chaos are ergodicity and mixing, which can be connected with two basic cryptographic properties; confusion and diffusion. To prove ergodicity and strength of the mixing, it’s enough to show that the system possess an invariant measure and Kolmogorov-Sinai (K-S) entropy from dynamical systems point of view

Quantum Chaotic Cryptography : A New Approach

Sejak 1990-an, sistem rawak dinamik digunakan secara meluas untuk mereka bentuk strategi baru bagi menyulitkan maklumat dalam bidang analog dan digital. Kini, banyak kriptosistem yang berasaskan rawak digital dicadangkan dan sebilangan daripada mereka dikriptanalisis. Since 1990s chaotic dynamical systems have been widely used to design new strategies to encrypt information in analog and digital areas. Recently, many digital chaos-based cryptosystems are proposed and a number of them have been cryptanalyzed

Distributions of the Wigner reaction matrix for microwave networks with symplectic symmetry in the presence of absorption

We report on experimental studies of the distribution of the reflection coefficients, and the imaginary and real parts of Wigner's reaction (K) matrix employing open microwave networks with symplectic symmetry and varying size of absorption. The results are compared to analytical predictions derived for the single-channel scattering case within the framework of random matrix theory (RMT). Furthermore, we performed Monte Carlo simulations based on the Heidelberg approach for the scattering (S) and K matrix of open quantum-chaotic systems and the two-point correlation function of the S-matrix elements. The analytical results and the Monte Carlo simulations depend on the size of absorption. To verify them, we performed experiments with microwave networks for various absorption strengths. We show that deviations from RMT predictions observed in the spectral properties of the corresponding closed quantum graph, and attributed to the presence of nonuniversal short periodic orbits, does not have any visible effects on the distributions of the reflection coefficients and the K and S matrices associated with the corresponding open quantum graph

Applications of tripled chaotic maps in cryptography

Security of information has become a major issue during the last decades. New algorithms based on chaotic maps were suggested for protection of different types of multimedia data, especially digital images and videos in this period. However, many of them fundamentally were flawed by a lack of robustness and security. For getting higher security and higher complexity, in the current paper, we introduce a new kind of symmetric key block cipher algorithm that is based on \emph{tripled chaotic maps}. In this algorithm, the utilization of two coupling parameters, as well as the increased complexity of the cryptosystem, make a contribution to the development of cryptosystem with higher security. In order to increase the security of the proposed algorithm, the size of key space and the computational complexity of the coupling parameters should be increased as well. Both the theoretical and experimental results state that the proposed algorithm has many capabilities such as acceptable speed and complexity in the algorithm due to the existence of two coupling parameter and high security. Note that the ciphertext has a flat distribution and has the same size as the plaintext. Therefore, it is suitable for practical use in secure communications.Comment: 21 pages, 10 figure

Notes on Dynamics of an External Cavity Semiconductor Lasers

Dynamics of external cavity semiconductor lasers is known to be a complex and uncontrollable phenomenon. Due to the lack of experimental studies on the nature of the external cavity semiconductor lasers, there is a need to theoretically clarify laser dynamics. The stability of laser dynamics in the present paper, is analyzed through plotting the Lyapunov exponent spectra, bifurcation diagrams, phase portrait and electric field intensity time series. The analysis is preformed with respect to applied feedback phase $C_p$, feedback strength $\eta$ and the pump current of the laser. The main argument of the paper is to show that the laser dynamics can not be accounted for through simply a bifurcation diagram and single-control parameter. The comparison of the obtained results provides a very detailed picture of the qualitative changes in laser dynamics.Comment: 7 pages, 34 figure

Controlling Chaos in Damped and Driven Morse Oscillator via Slave-Master Feedback

The dynamical behavior of the Morse oscillator is investigated primarily by means of the Lyapunov exponent and bifurcation diagrams. Then, the problem of controlling chaos for this oscillator is studied using a new method introduced by Behnia and Akhshani, which is based on the construction of slave-master feedback. In the control model based on slave-master feedback, the oscillator as the slave system is coupled with a dynamical system as the master, so its implementation becomes quite simple and similar statements can be made for the high dimensional cases. The validity of this method is verified by numerical simulations. The obtained results show the effectiveness of the proposed control model

The Generalized Euler Characteristics of the Graphs Split at Vertices

We show that there is a relationship between the generalized Euler characteristic Eo(|VDo|) of the original graph that was split at vertices into two disconnected subgraphs i=1,2 and their generalized Euler characteristics Ei(|VDi|). Here, |VDo| and |VDi| denote the numbers of vertices with the Dirichlet boundary conditions in the graphs. The theoretical results are experimentally verified using microwave networks that simulate quantum graphs. We demonstrate that the evaluation of the generalized Euler characteristics Eo(|VDo|) and Ei(|VDi|) allow us to determine the number of vertices where the two subgraphs were initially connected