Experimental Demonstration of Coherent Control in Quantum Chaotic Systems
NASA Astrophysics Data System (ADS)
Bitter, M.; Milner, V.
2017-01-01
We experimentally demonstrate coherent control of a quantum system, whose dynamics is chaotic in the classical limit. Interaction of diatomic molecules with a periodic sequence of ultrashort laser pulses leads to the dynamical localization of the molecular angular momentum, a characteristic feature of the chaotic quantum kicked rotor. By changing the phases of the rotational states in the initially prepared coherent wave packet, we control the rotational distribution of the final localized state and its total energy. We demonstrate the anticipated sensitivity of control to the exact parameters of the kicking field, as well as its disappearance in the classical regime of excitation.
NASA Astrophysics Data System (ADS)
Tan, Ru-Chao; Lei, Tong; Zhao, Qing-Min; Gong, Li-Hua; Zhou, Zhi-Hong
2016-12-01
To improve the slow processing speed of the classical image encryption algorithms and enhance the security of the private color images, a new quantum color image encryption algorithm based on a hyper-chaotic system is proposed, in which the sequences generated by the Chen's hyper-chaotic system are scrambled and diffused with three components of the original color image. Sequentially, the quantum Fourier transform is exploited to fulfill the encryption. Numerical simulations show that the presented quantum color image encryption algorithm possesses large key space to resist illegal attacks, sensitive dependence on initial keys, uniform distribution of gray values for the encrypted image and weak correlation between two adjacent pixels in the cipher-image.
Huang, Yu; Guo, Feng; Li, Yongling; Liu, Yufeng
2015-01-01
Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO) is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm.
Quantum chaotic scattering in graphene systems in the absence of invariant classical dynamics.
Wang, Guang-Lei; Ying, Lei; Lai, Ying-Cheng; Grebogi, Celso
2013-05-01
Quantum chaotic scattering is referred to as the study of quantum behaviors of open Hamiltonian systems that exhibit transient chaos in the classical limit. Traditionally a central issue in this field is how the elements of the scattering matrix or their functions fluctuate as a system parameter, e.g., the electron Fermi energy, is changed. A tacit hypothesis underlying previous works was that the underlying classical phase-space structure remains invariant as the parameter varies, so semiclassical theory can be used to explain various phenomena in quantum chaotic scattering. There are, however, experimental situations where the corresponding classical chaotic dynamics can change characteristically with some physical parameter. Multiple-terminal quantum dots are one such example where, when a magnetic field is present, the classical chaotic-scattering dynamics can change between being nonhyperbolic and being hyperbolic as the Fermi energy is changed continuously. For such systems semiclassical theory is inadequate to account for the characteristics of conductance fluctuations with the Fermi energy. To develop a general framework for quantum chaotic scattering associated with variable classical dynamics, we use multi-terminal graphene quantum-dot systems as a prototypical model. We find that significant conductance fluctuations occur with the Fermi energy even for fixed magnetic field strength, and the characteristics of the fluctuation patterns depend on the energy. We propose and validate that the statistical behaviors of the conductance-fluctuation patterns can be understood by the complex eigenvalue spectrum of the generalized, complex Hamiltonian of the system which includes self-energies resulted from the interactions between the device and the semi-infinite leads. As the Fermi energy is increased, complex eigenvalues with extremely smaller imaginary parts emerge, leading to sharp resonances in the conductance.
Quantum synchronization of chaotic oscillator behaviors among coupled BEC-optomechanical systems
NASA Astrophysics Data System (ADS)
Li, Wenlin; Li, Chong; Song, Heshan
2017-03-01
We consider and theoretically analyze a Bose-Einstein condensate (BEC) trapped inside an optomechanical system consisting of single-mode optical cavity with a moving end mirror. The BEC is formally analogous to a mirror driven by radiation pressure with strong nonlinear coupling. Such a nonlinear enhancement can make the oscillator display chaotic behavior. By establishing proper oscillator couplings, we find that this chaotic motion can be synchronized with other oscillators, even an oscillator network. We also discuss the scheme feasibility by analyzing recent experiment parameters. Our results provide a promising platform for the quantum signal transmission and quantum logic control, and they are of potential applications in quantum information processing and quantum networks.
Husimi-Wehrl entropy in the quantum chaotic system -An efficient calculational method-
NASA Astrophysics Data System (ADS)
Tsukiji, Hidekazu; Iida, Hideaki; Kunihiro, Teiji; Ohnishi, Akira
2014-09-01
Early thermalization in heavy ion collisions still remains a theoretical challenge. It was suggested in the hydrodynamical analyses of the relativistic heavy-ion collisions at RHIC and later at LHC. There are many proposals for pinning down the underlying mechanism for it. Quantum fluctuations on top of the classical configurations (glasma) are found to induce instabilities. It may trigger the chaotic behavior of the gauge field and eventually give rise to entropy production. In this work, we investigate thermalization of glasma by using the Husimi-Wehrl entropy. Quasi-distribution function defined in phase space should be useful to describe possible chaotic behavior of a quantum system. We adopt the Husimi distribution function to discuss entropy production of quantum systems. Husimi function is a minimally coarse-grained Wigner function and semi-positive definite. As a first stage of the study, we calculate the Husimi-Wehrl (H-W) entropy of a quantum Yang-Mills system [Tsai, Muller (2012)] with two-degrees of freedom. We propose a Monte-Carlo method to numerically calculate the time evolution of the Husimi function and the H-W entropy. We also discuss an extension of the method to quantum field theories.
Zurek, W.H.; Pas, J.P. |
1995-08-01
Violation of correspondence principle may occur for very macroscopic byt isolated quantum systems on rather short timescales as illustrated by the case of Hyperion, the chaotically tumbling moon of Saturn, for which quantum and classical predictions are expected to diverge on a timescale of approximately 20 years. Motivated by Hyperion, we review salient features of ``quantum chaos`` and show that decoherence is the essential ingredient of the classical limit, as it enables one to solve the apparent paradox caused by the breakdown of the correspondence principle for classically chaotic systems.
NASA Astrophysics Data System (ADS)
Ramos, J. G. G. S.; Barbosa, A. L. R.; Carlson, B. V.; Frederico, T.; Hussein, M. S.
2016-01-01
We derive analytical expressions for the correlation functions of the electronic conductance fluctuations of an open quantum dot under several conditions. Both the variation of energy and that of an external parameter, such as an applied perpendicular or parallel magnetic fields, are considered in the general case of partial openness. These expressions are then used to obtain the ensemble-averaged density of maxima, a measure recently suggested to contain invaluable information concerning the correlation widths of chaotic systems. The correlation width is then calculated for the case of energy variation, and a significant deviation from the Weisskopf estimate is found in the case of two terminals. The results are extended to more than two terminals. All of our results are analytical. The use of these results in other fields, such as nuclei, where the system can only be studied through a variation of the energy, is then discussed.
Fractal dynamics in chaotic quantum transport.
Kotimäki, V; Räsänen, E; Hennig, H; Heller, E J
2013-08-01
Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis-a widely used method in time-series analysis-and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that in turn qualitatively agree with the previous experimental data.
The Loschmidt echo in classically chaotic systems: Quantum chaos, irreversibility and decoherence
NASA Astrophysics Data System (ADS)
Cucchietti, Fernando M.
2004-10-01
The Loschmidt echo (LE) is a measure of the sensitivity of quantum mechanics to perturbations in the evolution operator. It is defined as the overlap of two wave functions evolved from the same initial state but with slightly different Hamiltonians. Thus, it also serves as a quantification of irreversibility in quantum mechanics. In this thesis the LE is studied in systems that have a classical counterpart with dynamical instability, that is, classically chaotic. An analytical treatment that makes use of the semiclassical approximation is presented. It is shown that, under certain regime of the parameters, the LE decays exponentially. Furthermore, for strong enough perturbations, the decay rate is given by the Lyapunov exponent of the classical system. Some particularly interesting examples are given. The analytical results are supported by thorough numerical studies. In addition, some regimes not accessible to the theory are explored, showing that the LE and its Lyapunov regime present the same form of universality ascribed to classical chaos. In a sense, this is evidence that the LE is a robust temporal signature of chaos in the quantum realm. Finally, the relation between the LE and the quantum to classical transition is explored, in particular with the theory of decoherence. Using two different approaches, a semiclassical approximation to Wigner functions and a master equation for the LE, it is shown that the decoherence rate and the decay rate of the LE are equal. The relationship between these quantities results mutually beneficial, in terms of the broader resources of decoherence theory and of the possible experimental realization of the LE.
Synchronization of chaotic systems
Pecora, Louis M.; Carroll, Thomas L.
2015-09-15
We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.
Parametric number covariance in quantum chaotic spectra.
Vinayak; Kumar, Sandeep; Pandey, Akhilesh
2016-03-01
We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the covariance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal noninvariant cases. A local version of the parametric number variance introduced earlier is also investigated.
NASA Astrophysics Data System (ADS)
Yan, Sen-Lin
2007-11-01
A scheme of synchronized injection multi-quantum-well (MQW) laser system using optical coupling-feedback is presented for performing chaotic dual-directional secure communication. The performance characterization of chaos masking is investigated theoretically, the equation of synchronization demodulation is deduced and its root is also given. Chaos masking encoding with a rate of 5Gbit/s and a modulation frequency of 1GHz, chaos modulation with a rate of 0.2Gbit/s and a modulation frequency of 0.2 GHz and chaos shifting key with a rate of 0.2Gbit/s are numerically simulated, separately. The ratio of the signal to the absolute synchronous error and the time for achieving synchronous demodulation are analysed in detail. The results illustrate that the system has stronger privacy and good performances so that it can be applied in chaotic dual-directional high rate secure communications.
NASA Astrophysics Data System (ADS)
Aguilar-López, Ricardo; López-Pérez, Pablo A.; Lara-Cisneros, Gerardo; Femat, Ricardo
2016-09-01
In this paper, a robust nonlinear feedback control scheme with adaptive gain is proposed to control the chaotic behavior in a Bose-Einstein condensate (BEC). The control goal concerns the track or regulation purposes. The BEC system is represented as stochastic ordinary differential equations with measured output perturbed by Gaussian noise, which represents the nature of the quantum systems. The convergence of the BEC control law is analyzed under the frame of the Lyapunov stability theory. Numerical experiments show an adequate performance of the proposed methodology under the required conditions. The results are applicable when the shape of the condensate is sufficiently simple.
Will Quantum Cosmology Resurrect Chaotic Inflation Model?
NASA Astrophysics Data System (ADS)
Kim, Sang Pyo; Kim, Won
2016-07-01
The single field chaotic inflation model with a monomial power greater than one seems to be ruled out by the recent Planck and WMAP CMB data while Starobinsky model with a higher curvature term seems to be a viable model. Higher curvature terms being originated from quantum fluctuations, we revisit the quantum cosmology of the Wheeler-DeWitt equation for the chaotic inflation model. The semiclassical cosmology emerges from quantum cosmology with fluctuations of spacetimes and matter when the wave function is peaked around the semiclassical trajectory with quantum corrections a la the de Broglie-Bohm pilot theory.
Cascade Chaotic System With Applications.
Zhou, Yicong; Hua, Zhongyun; Pun, Chi-Man; Chen, C L Philip
2015-09-01
Chaotic maps are widely used in different applications. Motivated by the cascade structure in electronic circuits, this paper introduces a general chaotic framework called the cascade chaotic system (CCS). Using two 1-D chaotic maps as seed maps, CCS is able to generate a huge number of new chaotic maps. Examples and evaluations show the CCS's robustness. Compared with corresponding seed maps, newly generated chaotic maps are more unpredictable and have better chaotic performance, more parameters, and complex chaotic properties. To investigate applications of CCS, we introduce a pseudo-random number generator (PRNG) and a data encryption system using a chaotic map generated by CCS. Simulation and analysis demonstrate that the proposed PRNG has high quality of randomness and that the data encryption system is able to protect different types of data with a high-security level.
Quantum chaotic resonances from short periodic orbits.
Novaes, M; Pedrosa, J M; Wisniacki, D; Carlo, G G; Keating, J P
2009-09-01
We present an approach to calculating the quantum resonances and resonance wave functions of chaotic scattering systems, based on the construction of states localized on classical periodic orbits and adapted to the dynamics. Typically only a few such states are necessary for constructing a resonance. Using only short orbits (with periods up to the Ehrenfest time), we obtain approximations to the longest-living states, avoiding computation of the background of short living states. This makes our approach considerably more efficient than previous ones. The number of long-lived states produced within our formulation is in agreement with the fractal Weyl law conjectured recently in this setting. We confirm the accuracy of the approximations using the open quantum baker map as an example.
Conductance fluctuations in chaotic bilayer graphene quantum dots.
Bao, Rui; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2015-07-01
Previous studies of quantum chaotic scattering established a connection between classical dynamics and quantum transport properties: Integrable or mixed classical dynamics can lead to sharp conductance fluctuations but chaos is capable of smoothing out the conductance variations. Relativistic quantum transport through single-layer graphene systems, for which the quasiparticles are massless Dirac fermions, exhibits, due to scarring, this classical-quantum correspondence, but sharp conductance fluctuations persist to a certain extent even when the classical system is fully chaotic. There is an open issue regarding the effect of finite mass on relativistic quantum transport. To address this issue, we study quantum transport in chaotic bilayer graphene quantum dots for which the quasiparticles have a finite mass. An interesting phenomenon is that, when traveling along the classical ballistic orbit, the quasiparticle tends to hop back and forth between the two layers, exhibiting a Zitterbewegung-like effect. We find signatures of abrupt conductance variations, indicating that the mass has little effect on relativistic quantum transport. In solid-state electronic devices based on Dirac materials, sharp conductance fluctuations are thus expected, regardless of whether the quasiparticle is massless or massive and whether there is chaos in the classical limit.
Superpersistent currents and whispering gallery modes in relativistic quantum chaotic systems
Xu, Hongya; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2015-01-01
Persistent currents (PCs), one of the most intriguing manifestations of the Aharonov-Bohm (AB) effect, are known to vanish for Schrödinger particles in the presence of random scatterings, e.g., due to classical chaos. But would this still be the case for Dirac fermions? Addressing this question is of significant value due to the tremendous recent interest in two-dimensional Dirac materials. We investigate relativistic quantum AB rings threaded by a magnetic flux and find that PCs are extremely robust. Even for highly asymmetric rings that host fully developed classical chaos, the amplitudes of PCs are of the same order of magnitude as those for integrable rings, henceforth the term superpersistent currents (SPCs). A striking finding is that the SPCs can be attributed to a robust type of relativistic quantum states, i.e., Dirac whispering gallery modes (WGMs) that carry large angular momenta and travel along the boundaries. We propose an experimental scheme using topological insulators to observe and characterize Dirac WGMs and SPCs, and speculate that these features can potentially be the base for a new class of relativistic qubit systems. Our discovery of WGMs in relativistic quantum systems is remarkable because, although WGMs are common in photonic systems, they are relatively rare in electronic systems. PMID:25758591
Chaotic Behaviour in Quantum Dynamics.
1986-12-01
1.6 Relevance of Classical Analisys to the Problem of Microwave Ionization The other nonconservative system discussed in this report - the H-atom in...a microwave field - had never been sublected to quantum analisys , neither theoretical nor computational, up to the start of our program. Nevertheless...m, . A2) can tie expanded in a double Fourier series in the angle variables Xi, X2: (I,, A, ,klk2 Z= > (ni, n,, n) e i(0 K C) The coefficeuts z ,i can
Chaotic systems in optical communications
NASA Astrophysics Data System (ADS)
Siuzdak, J.
2016-09-01
Communications application of chaotic oscillations of lasers with optoelectronic feedback was discussed. The possibility of eavesdropping of the transmission was analyzed. It was proved that if the rogue party precisely knows parameters of the chaotic system it may recreate the entire signals solely by observation of the optical signal power causing security breach.
Quantum localization of chaotic eigenstates and the level spacing distribution
NASA Astrophysics Data System (ADS)
Batistić, Benjamin; Robnik, Marko
2013-11-01
The phenomenon of quantum localization in classically chaotic eigenstates is one of the main issues in quantum chaos (or wave chaos), and thus plays an important role in general quantum mechanics or even in general wave mechanics. In this work we propose two different localization measures characterizing the degree of quantum localization, and study their relation to another fundamental aspect of quantum chaos, namely the (energy) spectral statistics. Our approach and method is quite general, and we apply it to billiard systems. One of the signatures of the localization of chaotic eigenstates is a fractional power-law repulsion between the nearest energy levels in the sense that the probability density to find successive levels on a distance S goes like ∝Sβ for small S, where 0≤β≤1, and β=1 corresponds to completely extended states. We show that there is a clear functional relation between the exponent β and the two different localization measures. One is based on the information entropy and the other one on the correlation properties of the Husimi functions. We show that the two definitions are surprisingly linearly equivalent. The approach is applied in the case of a mixed-type billiard system [M. Robnik, J. Phys. A: Math. Gen.JPHAC50305-447010.1088/0305-4470/16/17/014 16, 3971 (1983)], in which the separation of regular and chaotic eigenstates is performed.
Chakraborty, Debdutta; Kar, Susmita; Chattaraj, Pratim Kumar
2015-12-21
The orbital free density functional theory and the single density equation approach are formally equivalent. An orbital free density based quantum dynamical strategy is used to study the quantum-classical correspondence in both weakly and strongly coupled van der Pol and Duffing oscillators in the presence of an external electric field in one dimension. The resulting quantum hydrodynamic equations of motion are solved through an implicit Euler type real space method involving a moving weighted least square technique. The Lagrangian framework used here allows the numerical grid points to follow the wave packet trajectory. The associated classical equations of motion are solved using a sixth order Runge-Kutta method and the Ehrenfest dynamics is followed through the solution of the time dependent Schrodinger equation using a time dependent Fourier Grid Hamiltonian technique. Various diagnostics reveal a close parallelism between classical regular as well as chaotic dynamics and that obtained from the Bohmian mechanics.
Decoherence induced by a chaotic enviroment: A quantum walker with a complex coin
Ermann, Leonardo; Paz, Juan Pablo; Saraceno, Marcos
2006-01-15
We study the differences between the processes of decoherence induced by chaotic and regular environments. For this we analyze a family of simple models that contain both regular and chaotic environments. In all cases the system of interest is a ''quantum walker,'' i.e., a quantum particle that can move on a lattice with a finite number of sites. The walker interacts with an environment which has a D-dimensional Hilbert space. The results we obtain suggest that regular and chaotic environments are not distinguishable from each other in a (short) time scale t*, which scales with the dimensionality of the environment as t*{proportional_to}log{sub 2}(D). However, chaotic environments continue to be effective over exponentially longer time scales while regular environments tend to reach saturation much sooner. We present both numerical and analytical results supporting this conclusion. The family of chaotic evolutions we consider includes the so-called quantum multibaker map as a particular case.
Andreev Conductance of a Chaotic Quantum Dot
NASA Astrophysics Data System (ADS)
Clerk, A. A.; Brouwer, P. W.; Ambegaokar, V.
2000-03-01
Using random matrix theory, we study the full magnetic field (B) and voltage (V) dependence of the Andreev conductance of a chaotic quantum dot coupled via point contacts to both a normal metal and a superconductor. We recover previous results in the zero and large B,V limits, but also observe interesting non-monotonic behaviour in the crossover regime. Our results demonstrate that the induced superconductivity effect previously seen in calculations of the density of states (J.A. Melsen, P.W. Brouwer, K.M. Frahm and C.W.J. Beenakker, Europhys. Lett., 35), 7 (1996). can also have a pronounced signature in the conductance; this may explain certain anomalous features observed in recent experiments on metallic normal-superconducting point contacts (P. Chalsani, S.K. Uphadyay, R.A. Buhrman, unpublished.).
Force Analysis of Qi Chaotic System
NASA Astrophysics Data System (ADS)
Qi, Guoyuan; Liang, Xiyin
2016-12-01
The Qi chaotic system is transformed into Kolmogorov type of system. The vector field of the Qi chaotic system is decomposed into four types of torques: inertial torque, internal torque, dissipation and external torque. Angular momentum representing the physical analogue of the state variables of the chaotic system is identified. The Casimir energy law relating to the orbital behavior is identified and the bound of Qi chaotic attractor is given. Five cases of study have been conducted to discover the insights and functions of different types of torques of the chaotic attractor and also the key factors of producing different types of modes of dynamics.
Chaotic transport in dynamical systems
NASA Astrophysics Data System (ADS)
Wiggins, Stephen
The subject of chaotic transport in dynamical systems is examined from the viewpoint of problems of phase space transport. The examples considered include uniform elliptical vortices in external linear time-dependent velocity fields; capture and passage through resonance in celestial mechanics; bubble dynamics in straining flows; and photodissociation of molecules. The discussion covers transport in two-dimensional maps; convective mixing and transport problems in fluid mechanics; transport in quasi-periodically forced systems; Markov models; and transport in k-degree-of-freedom Hamiltonian systems.
Information encoder/decoder using chaotic systems
Miller, S.L.; Miller, W.M.; McWhorter, P.J.
1997-10-21
The present invention discloses a chaotic system-based information encoder and decoder that operates according to a relationship defining a chaotic system. Encoder input signals modify the dynamics of the chaotic system comprising the encoder. The modifications result in chaotic, encoder output signals that contain the encoder input signals encoded within them. The encoder output signals are then capable of secure transmissions using conventional transmission techniques. A decoder receives the encoder output signals (i.e., decoder input signals) and inverts the dynamics of the encoding system to directly reconstruct the original encoder input signals. 32 figs.
Information encoder/decoder using chaotic systems
Miller, Samuel Lee; Miller, William Michael; McWhorter, Paul Jackson
1997-01-01
The present invention discloses a chaotic system-based information encoder and decoder that operates according to a relationship defining a chaotic system. Encoder input signals modify the dynamics of the chaotic system comprising the encoder. The modifications result in chaotic, encoder output signals that contain the encoder input signals encoded within them. The encoder output signals are then capable of secure transmissions using conventional transmission techniques. A decoder receives the encoder output signals (i.e., decoder input signals) and inverts the dynamics of the encoding system to directly reconstruct the original encoder input signals.
Chaotic evolution of the solar system
NASA Technical Reports Server (NTRS)
Sussman, Gerald J.; Wisdom, Jack
1992-01-01
The evolution of the entire planetary system has been numerically integrated for a time span of nearly 100 million years. This calculation confirms that the evolution of the solar system as a whole is chaotic, with a time scale of exponential divergence of about 4 million years. Additional numerical experiments indicate that the Jovian planet subsystem is chaotic, although some small variations in the model can yield quasi-periodic motion. The motion of Pluto is independently and robustly chaotic.
Anticorrelation for conductance fluctuations in chaotic quantum dots.
Barbosa, A L R; Hussein, M S; Ramos, J G G S
2013-07-01
We investigate the correlation functions of mesoscopic electronic transport in open chaotic quantum dots with finite tunnel barriers in the crossover between Wigner-Dyson ensembles. Using an analytical stub formalism, we show the emergence of a depletion and amplification of conductance fluctuations as a function of tunnel barriers for both parametric variations of electron energy and magnetoconductance fields. Furthermore, even for pure Dyson ensembles, correlation functions of conductance fluctuations in chaotic quantum dots can exhibit anticorrelation. Experimental support to our findings is pointed out.
Nonlinear Dynamics, Chaotic and Complex Systems
NASA Astrophysics Data System (ADS)
Infeld, E.; Zelazny, R.; Galkowski, A.
2011-04-01
Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet
Chaotic control and synchronization for system identification.
Carroll, T L
2004-04-01
Research into applications of synchronized chaotic systems assumes that it will be necessary to build many different drive-response pairs, but little is known in general about designing higher dimensional chaotic flows. In this paper, I do not add any design techniques, but I show that it is possible to create multiple drive-response pairs from one chaotic system by applying chaos control techniques to the drive and response systems. If one can design one chaotic system with the desired properties, then many drive-response pairs can be built from this system, so that it is not necessary to solve the design problem more than once. I show both numerical simulations and experimental work with chaotic circuits. I also test the response systems for ability to overcome noise or other interference.
Electric circuit networks equivalent to chaotic quantum billiards
Bulgakov, Evgeny N.; Maksimov, Dmitrii N.; Sadreev, Almas F.
2005-04-01
We consider two electric RLC resonance networks that are equivalent to quantum billiards. In a network of inductors grounded by capacitors, the eigenvalues of the quantum billiard correspond to the squared resonant frequencies. In a network of capacitors grounded by inductors, the eigenvalues of the billiard are given by the inverse of the squared resonant frequencies. In both cases, the local voltages play the role of the wave function of the quantum billiard. However, unlike for quantum billiards, there is a heat power because of the resistance of the inductors. In the equivalent chaotic billiards, we derive a distribution of the heat power which describes well the numerical statistics.
Synchronisation control of composite chaotic systems
NASA Astrophysics Data System (ADS)
Zha, Jindao; Li, Chunbiao; Song, Bing; Hu, Wen
2016-12-01
Synchronisation conditions are studied for composite chaotic systems with complex compound structure and the signum function based on the theorem of zero-solution stability for a class of linear time-varying systems with countable discontinuous points. The synchronisation controller and its gain range are deduced according to the stability theorem, where the gain of the controller can speed synchronisation. Numerical simulation further proves the control theory and the validity of the synchronisation controller. The proposed controller can be widely applied in those chaotic systems with switch functions or other hybrid chaotic systems.
The study of effects of small perturbations on chaotic systems
Grebogi, C. . Lab. for Plasma Research); Yorke, J.A. . Inst. for Physical Science and Technology)
1990-12-01
This report discusses the following topics on small perturbations on chaotic systems: controlling chaos; shadowing and noise reduction; chaotic scattering; random maps; magnetic dynamo; and aids transmission. (LSP)
NASA Astrophysics Data System (ADS)
Cros, Anne; Castillo Flores, Fernando; Le Gal, Patrice
2008-11-01
We present the experimental study of a collapsible tube conveying an ascending air flow. An extreme of the membrane tube is mounted on the air blower exit, while the other extreme is free. The flow velocity can be varied. For low speeds -- and tubes short enough -- the cylinder stands up (stable state). As the velocity is increased, the system presents sporadic turbulent fluctuations, when the tube bends and rises again. As the air speed is increased again, the intermittent events become more and more frequent. Films realized in front of the system permit to observe waves that propagate in the tube. We measure that these waves have a sonic speed, confirming previous results. Moreover, films taken from the top of the system allow a quantitative characterization of the transition to chaos. By processing the images, we can reduce the evolution of the system to two states: stable (when it is raised) and chaotic (when the tube fluctuates). The histograms of unstable / stable states are coherent with an intermittent transition in the theory of chaos.
Chaotic dynamics of controlled electric power systems
NASA Astrophysics Data System (ADS)
Kozlov, V. N.; Trosko, I. U.
2016-12-01
The conditions for appearance of chaotic dynamics of electromagnetic and electromechanical processes in energy systems described by the Park-Gorev bilinear differential equations with account for lags of coordinates and restrictions on control have been formulated. On the basis of classical equations, the parameters of synchronous generators and power lines, at which the chaotic dynamics of energy systems appears, have been found. The qualitative and quantitative characteristics of chaotic processes in energy associations of two types, based on the Hopf theorem, and methods of nonstationary linearization and decompositions are given. The properties of spectral characteristics of chaotic processes have been investigated, and the qualitative similarity of bilinear equations of power systems and Lorentz equations have been found. These results can be used for modernization of the systems of control of energy objects. The qualitative and quantitative characteristics for power energy systems as objects of control and for some laws of control with the feedback have been established.
Theory of chaos regularization of tunneling in chaotic quantum dots.
Lee, Ming-Jer; Antonsen, Thomas M; Ott, Edward; Pecora, Louis M
2012-11-01
Recent numerical experiments of Pecora et al. [Phys. Rev. E 83, 065201 (2011)] have investigated tunneling between two-dimensional symmetric double wells separated by a tunneling barrier. The wells were bounded by hard walls and by the potential barrier which was created by a step increase from the zero potential within a well to a uniform barrier potential within the barrier region, which is a situation potentially realizable in the context of quantum dots. Numerical results for the splitting of energy levels between symmetric and antisymmetric eigenstates were calculated. It was found that the splittings vary erratically from state to state, and the statistics of these variations were studied for different well shapes with the fluctuation levels being much less in chaotic wells than in comparable nonchaotic wells. Here we develop a quantitative theory for the statistics of the energy level splittings for chaotic wells. Our theory is based on the random plane wave hypothesis of Berry. While the fluctuation statistics are very different for chaotic and nonchaotic well dynamics, we show that the mean splittings of differently shaped wells, including integrable and chaotic wells, are the same if their well areas and barrier parameters are the same. We also consider the case of tunneling from a single well into a region with outgoing quantum waves.
Applied mathematics of chaotic systems
Jen, E.; Alber, M.; Camassa, R.; Choi, W.; Crutchfield, J.; Holm, D.; Kovacic, G.; Marsden, J.
1996-07-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The objectives of the project were to develop new mathematical techniques for describing chaotic systems and for reexpressing them in forms that can be solved analytically and computationally. The authors focused on global bifurcation analysis of rigid body motion in an ideal incompressible fluid and on an analytical technique for the exact solution of nonlinear cellular automata. For rigid-body motion, they investigated a new completely integrable partial differential equation (PDE) representing model motion of fronts in nematic crystals and studied perturbations of the integrable PDE. For cellular automata with multiple domain structures, the work has included: (1) identification of the associated set of conserved quantities for each type of domain; (2) use of the conserved quantities to construct isomorphism between the nonlinear system and a linear template; and (3) use of exact solvability methods to characterize detailed structure of equilibrium states and to derive bounds for maximal transience times.
Pseudo random number generator based on quantum chaotic map
NASA Astrophysics Data System (ADS)
Akhshani, A.; Akhavan, A.; Mobaraki, A.; Lim, S.-C.; Hassan, Z.
2014-01-01
For many years dissipative quantum maps were widely used as informative models of quantum chaos. In this paper, a new scheme for generating good pseudo-random numbers (PRNG), based on quantum logistic map is proposed. Note that the PRNG merely relies on the equations used in the quantum chaotic map. The algorithm is not complex, which does not impose high requirement on computer hardware and thus computation speed is fast. In order to face the challenge of using the proposed PRNG in quantum cryptography and other practical applications, the proposed PRNG is subjected to statistical tests using well-known test suites such as NIST, DIEHARD, ENT and TestU01. The results of the statistical tests were promising, as the proposed PRNG successfully passed all these tests. Moreover, the degree of non-periodicity of the chaotic sequences of the quantum map is investigated through the Scale index technique. The obtained result shows that, the sequence is more non-periodic. From these results it can be concluded that, the new scheme can generate a high percentage of usable pseudo-random numbers for simulation and other applications in scientific computing.
Synchronization between uncertain nonidentical networks with quantum chaotic behavior
NASA Astrophysics Data System (ADS)
Li, Wenlin; Li, Chong; Song, Heshan
2016-11-01
Synchronization between uncertain nonidentical networks with quantum chaotic behavior is researched. The identification laws of unknown parameters in state equations of network nodes, the adaptive laws of configuration matrix elements and outer coupling strengths are determined based on Lyapunov theorem. The conditions of realizing synchronization between uncertain nonidentical networks are discussed and obtained. Further, Jaynes-Cummings model in physics are taken as the nodes of two networks and simulation results show that the synchronization performance between networks is very stable.
Multiple channel secure communication using chaotic system encoding
Miller, S.L.
1996-12-31
fA new method to encrypt signals using chaotic systems has been developed that offers benefits over conventional chaotic encryption methods. The method simultaneously encodes multiple plaintext streams using a chaotic system; a key is required to extract the plaintext from the chaotic cipertext. A working prototype demonstrates feasibility of the method by simultaneously encoding and decoding multiple audio signals using electrical circuits.
Ontic and epistemic descriptions of chaotic systems
NASA Astrophysics Data System (ADS)
Atmanspacher, Harald
2000-05-01
Traditional philosophical discourse draws a distinction between ontology and epistemology and generally enforces this distinction by keeping the two subject areas separated and unrelated. In addition, the relationship between the two areas is of central importance to physics and philosophy of physics. For instance, all kinds of measurement-related problems force us to consider both our knowledge of the states and observables of a system (epistemic perspective) and its states and observables independent of such knowledge (ontic perspective). This applies to quantum systems in particular. In this contribution we present an example which shows the importance of distinguishing between ontic and epistemic levels of description even for classical systems. Corresponding conceptions of ontic and epistemic states and their evolution will be introduced and discussed with respect to aspects of stability and information flow. These aspects show why the ontic/epistemic distinction is particularly important for systems exhibiting deterministic chaos. Moreover, this distinction provides some understanding of the relationships between determinism, causation, predictability, randomness, and stochasticity in chaotic systems.
An adaptive strategy for controlling chaotic system.
Cao, Yi-Jia; Hang, Hong-Xian
2003-01-01
This paper presents an adaptive strategy for controlling chaotic systems. By employing the phase space reconstruction technique in nonlinear dynamical systems theory, the proposed strategy transforms the nonlinear system into canonical form, and employs a nonlinear observer to estimate the uncertainties and disturbances of the nonlinear system, and then establishes a state-error-like feedback law. The developed control scheme allows chaos control in spite of modeling errors and parametric variations. The effectiveness of the proposed approach has been demonstrated through its applications to two well-known chaotic systems: Duffing oscillator and Rössler chaos.
Controlled transitions between cupolets of chaotic systems
Morena, Matthew A.; Short, Kevin M.; Cooke, Erica E.
2014-01-01
We present an efficient control scheme that stabilizes the unstable periodic orbits of a chaotic system. The resulting orbits are known as cupolets and collectively provide an important skeleton for the dynamical system. Cupolets exhibit the interesting property that a given sequence of controls will uniquely identify a cupolet, regardless of the system's initial state. This makes it possible to transition between cupolets, and thus unstable periodic orbits, simply by switching control sequences. We demonstrate that although these transitions require minimal controls, they may also involve significant chaotic transients unless carefully controlled. As a result, we present an effective technique that relies on Dijkstra's shortest path algorithm from algebraic graph theory to minimize the transients and also to induce certainty into the control of nonlinear systems, effectively providing an efficient algorithm for the steering and targeting of chaotic systems. PMID:24697373
Controlled transitions between cupolets of chaotic systems
Morena, Matthew A. Short, Kevin M.; Cooke, Erica E.
2014-03-15
We present an efficient control scheme that stabilizes the unstable periodic orbits of a chaotic system. The resulting orbits are known as cupolets and collectively provide an important skeleton for the dynamical system. Cupolets exhibit the interesting property that a given sequence of controls will uniquely identify a cupolet, regardless of the system's initial state. This makes it possible to transition between cupolets, and thus unstable periodic orbits, simply by switching control sequences. We demonstrate that although these transitions require minimal controls, they may also involve significant chaotic transients unless carefully controlled. As a result, we present an effective technique that relies on Dijkstra's shortest path algorithm from algebraic graph theory to minimize the transients and also to induce certainty into the control of nonlinear systems, effectively providing an efficient algorithm for the steering and targeting of chaotic systems.
Urey Prize Lecture - Chaotic dynamics in the solar system
NASA Technical Reports Server (NTRS)
Wisdom, Jack
1987-01-01
Attention is given to solar system cases in which chaotic solutions of Newton's equations are important, as in chaotic rotation and orbital evolution. Hyperion is noted to be tumbling chaotically; chaotic orbital evolution is suggested to be of fundamental importance to an accounting for the Kirkwood gaps in asteroid distribution and for the phase space boundary of the chaotic zone at the 3/1 mean-motion commensurability with Jupiter. In addition, chaotic trajectories in the 2/1 chaotic zone reach very high eccentricities by a route that carries them to high inclinations temporarily.
Quantum Computing and the Onset of Quantum Chaotic Motion
2007-11-02
for Nuclear Theory Program on "Chaos and Interactions: from Nuclei to Quantum Dots’", University of Washington, Seattle, USA, 17 July, 2002. I...to Quantum Dots’", University of Washington, Seattle, USA, 17 July, 2002. G. Casati “Quantum computers and quantum chaos” Institute for Nuclear...Theory Program on "Chaos and Interactions: from Nuclei to Quantum Dots’", University of Washington, Seattle, USA, 17 July, 2002. 2. Scientific
Different Synchronization Schemes for Chaotic Rikitake Systems
NASA Astrophysics Data System (ADS)
Khan, M. Ali
2013-06-01
This paper presents the chaos synchronization by designing a different type of controllers. Firstly, we propose the synchronization of bi-directional coupled chaotic Rikitake systems via hybrid feedback control. Secondly, we study the synchronization of unidirectionally coupled Rikitake systems using hybrid feedback control. Lastly, we investigate the synchronization of unidirectionally coupled Rikitake chaotic systems using tracking control. Comparing all the results, finally, we conclude that tracking control is more effective than feedback control. Simulation results are presented to show the efficiency of synchronization schemes.
Desktop chaotic systems: Intuition and visualization
NASA Technical Reports Server (NTRS)
Bright, Michelle M.; Melcher, Kevin J.; Qammar, Helen K.; Hartley, Tom T.
1993-01-01
This paper presents a dynamic study of the Wildwood Pendulum, a commercially available desktop system which exhibits a strange attractor. The purpose of studying this chaotic pendulum is twofold: to gain insight in the paradigmatic approach of modeling, simulating, and determining chaos in nonlinear systems; and to provide a desktop model of chaos as a visual tool. For this study, the nonlinear behavior of this chaotic pendulum is modeled, a computer simulation is performed, and an experimental performance is measured. An assessment of the pendulum in the phase plane shows the strange attractor. Through the use of a box-assisted correlation dimension methodology, the attractor dimension is determined for both the model and the experimental pendulum systems. Correlation dimension results indicate that the pendulum and the model are chaotic and their fractal dimensions are similar.
Phase synchronization of a new chaotic system
NASA Astrophysics Data System (ADS)
Vahedi, Shahed; Md Noorani, Mohd Salmi
2013-09-01
In this paper, we are going to apply phase and anti-phase synchronization on a recently studied chaotic system by the authors. The technique we employ to extract the phase at each time is EMD and we show that the corresponding intrinsic modes of the two systems are well phase locked after activating the control functions.
Effective production of orbital quantum entanglement in chaotic quantum dots with nonideal contacts
NASA Astrophysics Data System (ADS)
Santos, E. H.; Almeida, F. A. G.
2016-09-01
We study orbital entanglement production in a chaotic quantum dot with two-channel leads by varying the opacity of the contacts in the unitary and orthogonal Wigner-Dyson ensembles. We computed the occurrence probability of entangled states (squared norm) and its concurrence (entanglement level). We also define an entanglement production factor to properly evaluate the entanglement behavior in the system considering effective aspects. The results are numerically obtained through (i) integrations over random matrix ensembles (exact results) for the scenario of one contact ideally fixed and (ii) random matrix simulations for arbitrary contact opacities (sampling). Those outcomes are in mutual agreement and indicate that the optimum effective production of orbital entanglement is achieved when both contacts are ideal and the time-reversal symmetry is broken.
Complexity and synchronization in stochastic chaotic systems
NASA Astrophysics Data System (ADS)
Dang, Thai Son; Palit, Sanjay Kumar; Mukherjee, Sayan; Hoang, Thang Manh; Banerjee, Santo
2016-02-01
We investigate the complexity of a hyperchaotic dynamical system perturbed by noise and various nonlinear speech and music signals. The complexity is measured by the weighted recurrence entropy of the hyperchaotic and stochastic systems. The synchronization phenomenon between two stochastic systems with complex coupling is also investigated. These criteria are tested on chaotic and perturbed systems by mean conditional recurrence and normalized synchronization error. Numerical results including surface plots, normalized synchronization errors, complexity variations etc show the effectiveness of the proposed analysis.
The study of effects of small perturbations on chaotic systems
Grebogi, C.; Yorke, J.A.
1991-12-01
This report discusses the following topics: controlling chaotic dynamical systems; embedding of experimental data; effect of noise on critical exponents of crises; transition to chaotic scattering; and distribution of floaters on a fluid surface. (LSP)
Design and Realisation of Chaotic Encryption Systems
NASA Astrophysics Data System (ADS)
Schwarz, Wolfgang; Falk, Thomas
2002-07-01
Chaotic signal transmission systems are often claimed to be secure by itself. Using a simple example it is shown, that this is not true and that exact design criteria have to be set up before starting the design of a chaotic encryption system. Then, beginning with statistical design objectives an information encryption system is systematically designed. The structure design leads to a controlled filter structure with overflow nonlinearity, the parameter design has to assure chaotic behaviour and mixing properties of the encoded signal. This defines the limits for the choice of the parameter set representing the key for the encryption. After developing the system structure the system is realized by electronic circuitry. Discrete and IC versions of the solution are presented. In order to prove that the system meets the design requirements experimental results are provided. It can be shown that in a n-th order system the statistical characteristics up to the n-th order of the output signal will not be affected by the input signal. The paper closes with some security estimates for the designed system.
Chaotic Orbits for Systems of Nonlocal Equations
NASA Astrophysics Data System (ADS)
Dipierro, Serena; Patrizi, Stefania; Valdinoci, Enrico
2017-01-01
We consider a system of nonlocal equations driven by a perturbed periodic potential. We construct multibump solutions that connect one integer point to another one in a prescribed way. In particular, heteroclinic, homoclinic and chaotic trajectories are constructed. This is the first attempt to consider a nonlocal version of this type of dynamical systems in a variational setting and the first result regarding symbolic dynamics in a fractional framework.
Observation of 'scarred' wavefunctions in a quantum well with chaotic electron dynamics
NASA Astrophysics Data System (ADS)
Wilkinson, P. B.; Fromhold, T. M.; Eaves, L.; Sheard, F. W.; Miura, N.; Takamasu, T.
1996-04-01
QUALITATIVE insight into the properties of a quantum-mechanical system can be gained from the study of the relationship between the system's classical newtonian dynamics, and its quantum dynamics as described by the Schrödinger equation. The Bohr-Sommerfeld quantization scheme-which underlies the historically important Bohr model for hydrogen-like atoms-describes the relationship between the classical and quantum-mechanical regimes, but only for systems with stable, periodic or quasi-periodic orbits1. Only recently has progress been made in understanding the quantization of systems that exhibit non-periodic, chaotic motion. The spectra of quantized energy levels for such systems are irregular, and show fluctuations associated with unstable periodic orbits of the corresponding classical system1-3. These orbits appear as 'scars'-concentrations of probability amplitude-in the wavefunction of the system4. Although wavefunction scarring has been the subject of extensive theoretical investigation5-10, it has not hitherto been observed experimentally in a quantum system. Here we use tunnel-current spectroscopy to map the quantum-mechanical energy levels of an electron confined in a semiconductor quantum well in a high magnetic field10-13. We find clear experimental evidence for wavefunction scarring, in full agreement with theoretical predictions10.
Synchronization of chaotic systems with different orders
NASA Astrophysics Data System (ADS)
Lü, Ling; Luan, Ling; Guo, Zhi-An
2007-02-01
A controller is designed to realize the synchronization between chaotic systems with different orders. The structure of the controller, the error equations and the Lyapunov functions are determined based on stability theory. Hyperchaotic Chen system and Rossler system are taken for example to demonstrate the method to be effective and feasible. Simulation results show that all the state variables of Rossler system can be synchronized with those of hyperchaotic Chen system by using only one controller, and the error signals approach zero smoothly and quickly.
Control uncertain continuous-time chaotic dynamical system.
Qi, Dong-Lian; Zhao, Guang-Zhou
2003-01-01
The new chaos control method presented in this paper is useful for taking advantage of chaos. Based on sliding mode control theory, this paper provides a switching manifold controlling strategy of chaotic system, and also gives a kind of adaptive parameters estimated method to estimate the unknown systems' parameters by which chaotic dynamical system can be synchronized. Taking the Lorenz system as example, and with the help of this controlling strategy, we can synchronize chaotic systems with unknown parameters and different initial conditions.
Localization in chaotic systems with a single-channel opening.
Lippolis, Domenico; Ryu, Jung-Wan; Kim, Sang Wook
2015-07-01
We introduce a single-channel opening in a random Hamiltonian and a quantized chaotic map: localization on the opening occurs as a sensible deviation of the wave-function statistics from the predictions of random matrix theory, even in the semiclassical limit. Increasing the coupling to the open channel in the quantum model, we observe a similar picture to resonance trapping, made of a few fast-decaying states, whose left (right) eigenfunctions are entirely localized on the (preimage of the) opening, and plentiful long-lived states, whose probability density is instead suppressed at the opening. For the latter, we derive and test a linear relation between the wave-function intensities and the decay rates, similar to the Breit-Wigner law. We then analyze the statistics of the eigenfunctions of the corresponding (discretized) classical propagator, finding a similar behavior to the quantum system only in the weak-coupling regime.
Stream cipher system based on chaotic maps
NASA Astrophysics Data System (ADS)
Argenti, Fabrizio; Benzi, Simone; Del Re, Enrico; Genesio, Roberto
2000-11-01
Secure transmission of information is an important aspect of modern telecommunication systems. Data encryption is applied in several contexts, whenever privacy is a fundamental aspect, e.g., in modern mobile networks. In this work, a stream cipher based on discrete time nonlinear dynamic systems is proposed. The Henon's map is used to generate a chaotic signal. Its samples are quantized and processed to produce a sequence of data as much uncorrelated as possible. The proposed scheme demonstrates high sensitivity to the parameters of the map as well as to initial conditions. The resulting binary sequence is used to mask the stream of information bits.
An Improved Chaotic Masking Scheme via System-Alternating
NASA Astrophysics Data System (ADS)
Wang, Xing-Yuan; Xu, Bing; Ma, Yutian
2013-10-01
Aiming at the drawbacks of the chaotic masking scheme, this paper optimizes this conventional scheme by using improved state observer method and system-alternating method, proposes a new secure communication scheme which can improve these drawbacks of chaotic method: (1) Restriction that the power of useful signal must be smaller than that of chaotic signal. (2) Low security. In addition, the model of this whole communication system is constructed under the system simulation environment of Simulink.
Berkolaiko, Gregory; Kuipers, Jack
2012-04-01
Electronic transport through chaotic quantum dots exhibits universal, system-independent properties, consistent with random-matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the classical scattering trajectories. Correlations between such trajectories can be organized diagrammatically and have been shown to yield universal answers for some observables. Here, we develop the general combinatorial treatment of the semiclassical diagrams, through a connection to factorizations of permutations. We show agreement between the semiclassical and random matrix approaches to the moments of the transmission eigenvalues. The result is valid for all moments to all orders of the expansion in inverse channel number for all three main symmetry classes (with and without time-reversal symmetry and spin-orbit interaction) and extends to nonlinear statistics. This finally explains the applicability of random-matrix theory to chaotic quantum transport in terms of the underlying dynamics as well as providing semiclassical access to the probability density of the transmission eigenvalues.
Adaptive tracking control for a class of uncertain chaotic systems
NASA Astrophysics Data System (ADS)
Chen, Feng-Xiang; Wang, Wei; Zhang, Wei-Dong
2007-09-01
The paper is concerned with adaptive tracking problem for a class of chaotic system with time-varying uncertainty, but bounded by norm polynomial. Based on adaptive technique, it proposes a novel controller to asymptotically track the arbitrary desired bounded trajectory. Simulation on the Rossler chaotic system is performed and the result verifies the effectiveness of the proposed method.
Cryptography based on spatial chaotic system
NASA Astrophysics Data System (ADS)
Sun, Fuyan; Lü, Zongwang
2010-08-01
Encryption of images is different from that of texts due to some intrinsic features of images such as bulk data capacity and high redundancy, which is generally difficult to handle by traditional methods. This paper proposes a new spatial chaos system(SCS), which is investigated by conducting FIPS 140-1 statistic test, and is especially useful for encryption of digital images. It is shown how to adapt a two dimensional(2D) ergodic matrix obtained from SCS to permute the positions of image pixels and confuse the relationship between the cipher image and plain image simultaneously. Experimental results show that the performance and security of the proposed cryptographic system are better than those of existing lower dimensional chaotic cryptographic systems.
Dual synchronization based on two different chaotic systems
NASA Astrophysics Data System (ADS)
Ning, Di; Lu, Jun-An; Han, Xiuping
2007-09-01
In this paper, we improve and extend the works of Liu and Davids [Dual synchronization of chaos, Phys. Rev. E 61 (2000) 2176-2179] which only introduce the dual synchronization of 1-D discrete chaotic systems. The dual synchronization of two different 3-D continuous chaotic systems, Lorenz systems and Rossler systems, is discussed. And a sufficient condition of dual synchronization about the two different chaotic systems is obtained. Theories and numerical simulations show the possibility of dual synchronization and the effectiveness of the method.
Chaotic carrier pulse position modulation communication system and method
Abarbanel, Henry D. I.; Larson, Lawrence E.; Rulkov, Nikolai F.; Sushchik, Mikhail M.; Tsimring, Lev S.; Volkovskii, Alexander R.
2001-01-01
A chaotic carrier pulse position modulation communication system and method is disclosed. The system includes a transmitter and receiver having matched chaotic pulse regenerators. The chaotic pulse regenerator in the receiver produces a synchronized replica of a chaotic pulse train generated by the regenerator in the transmitter. The pulse train from the transmitter can therefore act as a carrier signal. Data is encoded by the transmitter through selectively altering the interpulse timing between pulses in the chaotic pulse train. The altered pulse train is transmitted as a pulse signal. The receiver can detect whether a particular interpulse interval in the pulse signal has been altered by reference to the synchronized replica it generates, and can therefore detect the data transmitted by the receiver. Preferably, the receiver predicts the earliest moment in time it can expect a next pulse after observation of at least two consecutive pulses. It then decodes the pulse signal beginning at a short time before expected arrival of a pulse.
The chaotic "sculpting" of the Solar System
NASA Astrophysics Data System (ADS)
Tsiganis, K.
2006-01-01
The orbits of the large celestial bodies in our Solar System are stable for very long times, as can be shown by numerical simulation. This gives the erroneous impression of perpetual stability of the system. It is only when we study the orbital distribution of the numerous minor bodies in the Solar System that we discover the rich variety of complex dynamical processes that have in fact shaped our system. During the last decade, enormous progress has been made, in understanding the evolution of the system over the last ~3.9 Gy. However, it also became clear that, in order to unveil its behaviour during the first ~700 million years of its lifetime, we have to find convincing explanations for observations that appear as details of its dynamical architecture. In the following we are going to show how the two best known - and up to now unexplained - observations in the Solar System, namely (i) the heavily cratered surface of the Moon and (ii) the elliptic (and not circular) motion of the planets, lead us to the discovery of the chaotic sculpting of the Solar System [1]-[3].
Complexity analyses of multi-wing chaotic systems
NASA Astrophysics Data System (ADS)
He, Shao-Bo; Sun, Ke-Hui; Zhu, Cong-Xu
2013-05-01
The complexities of multi-wing chaotic systems based on the modified Chen system and a multi-segment quadratic function are investigated by employing the statistical complexity measure (SCM) and the spectral entropy (SE) algorithm. How to choose the parameters of the SCM and SE algorithms is discussed. The results show that the complexity of the multi-wing chaotic system does not increase as the number of wings increases, and it is consistent with the results of the Grassberger—Procaccia (GP) algorithm and the largest Lyapunov exponent (LLE) of the multi-wing chaotic system.
Sliding mode control for chaotic systems based on LMI
NASA Astrophysics Data System (ADS)
Wang, Hua; Han, Zheng-zhi; Xie, Qi-yue; Zhang, Wei
2009-04-01
This paper investigates the chaos control problem for a general class of chaotic systems. A feedback controller is established to guarantee asymptotical stability of the chaotic systems based on the sliding mode control theory. A new reaching law is introduced to solve the chattering problem that is produced by traditional sliding mode control. A dynamic compensator is designed to improve the performance of the closed-loop system in sliding mode, and its parameter is obtained from a linear matrix inequality (LMI). Simulation results for the well known Chua's circuit and Lorenz chaotic system are provided to illustrate the effectiveness of the proposed scheme.
An optical CDMA system based on chaotic sequences
NASA Astrophysics Data System (ADS)
Liu, Xiao-lei; En, De; Wang, Li-guo
2014-03-01
In this paper, a coherent asynchronous optical code division multiple access (OCDMA) system is proposed, whose encoder/decoder is an all-optical generator. This all-optical generator can generate analog and bipolar chaotic sequences satisfying the logistic maps. The formula of bit error rate (BER) is derived, and the relationship of BER and the number of simultaneous transmissions is analyzed. Due to the good property of correlation, this coherent OCDMA system based on these bipolar chaotic sequences can support a large number of simultaneous users, which shows that these chaotic sequences are suitable for asynchronous OCDMA system.
CHAOTIC DISINTEGRATION OF THE INNER SOLAR SYSTEM
Batygin, Konstantin; Morbidelli, Alessandro; Holman, Mathew J.
2015-02-01
On timescales that greatly exceed an orbital period, typical planetary orbits evolve in a stochastic yet stable fashion. On even longer timescales, however, planetary orbits can spontaneously transition from bounded to unbound chaotic states. Large-scale instabilities associated with such behavior appear to play a dominant role in shaping the architectures of planetary systems, including our own. Here we show how such transitions are possible, focusing on the specific case of the long-term evolution of Mercury. We develop a simple analytical model for Mercury's dynamics and elucidate the origins of its short-term stochastic behavior as well as of its sudden progression to unbounded chaos. Our model allows us to estimate the timescale on which this transition is likely to be triggered, i.e., the dynamical lifetime of the solar system as we know it. The formulated theory is consistent with the results of numerical simulations and is broadly applicable to extrasolar planetary systems dominated by secular interactions. These results constitute a significant advancement in our understanding of the processes responsible for sculpting of the dynamical structures of generic planetary systems.
NASA Astrophysics Data System (ADS)
Hur, Gwang-Ok
The -kicked rotor is a paradigm of quantum chaos. Its realisation with clouds of cold atoms in pulsed optical lattices demonstrated the well-known quantum chaos phenomenon of 'dynamical localisation'. In those experi ments by several groups world-wide, the £-kicks were applied at equal time intervals. However, recent theoretical and experimental work by the cold atom group at UCL Monteiro et al 2002, Jonckheere et al 2003, Jones et al 2004 showed that novel quantum and classical dynamics arises if the atomic cloud is pulsed with repeating sequences of unequally spaced kicks. In Mon teiro et al 2002 it was found that the energy absorption rates depend on the momentum of the atoms relative to the optical lattice hence a type of chaotic ratchet was proposed. In Jonckheere et al and Jones et al, a possible mechanism for selecting atoms according to their momenta (velocity filter) was investigated. The aim of this thesis was to study the properties of the underlying eigen values and eigenstates. Despite the unequally-spaced kicks, these systems are still time-periodic, so we in fact investigated the Floquet states, which are eigenstates of U(T), the one-period time evolution operator. The Floquet states and corresponding eigenvalues were obtained by diagonalising a ma trix representation of the operator U(T). It was found that the form of the eigenstates enables us to analyse qual itatively the atomic momentum probability distributions, N(p) measured experimentally. In particular, the momentum width of the individual eigen states varies strongly with < p > as expected from the theoretical and ex- perimental results obtained previously. In addition, at specific < p > close to values which in the experiment yield directed motion (ratchet transport), the probability distribution of the individual Floquet states is asymmetric, mirroring the asymmetric N(p) measured in clouds of cesium atoms. In the penultimate chapter, the spectral fluctuations (eigenvalue statis tics) are
Unfolding of the spectrum for chaotic and mixed systems
NASA Astrophysics Data System (ADS)
Abul-Magd, Ashraf A.; Abul-Magd, Adel Y.
2014-02-01
Random Matrix Theory (RMT) is capable of making predictions for the spectral fluctuations of a physical system only after removing the influence of the level density by unfolding the spectra. When the level density is known, unfolding is done by using the integrated level density to transform the eigenvalues into dimensionless variables with unit mean spacing. When it is not known, as in most practical cases, one usually approximates the level staircase function by a polynomial. We here study the effect of unfolding procedure on the spectral fluctuation of two systems for which the level density is known asymptotically. The first is a time-reversal-invariant chaotic system, which is modeled in RMT by a Gaussian Orthogonal Ensemble (GOE). The second is the case of chaotic systems in which m quantum numbers remain almost undistorted in the early stage of the stochastic transition. The Hamiltonian of a system may be represented by a block diagonal matrix with m blocks of the same size, in which each block is a GOE. Unfolding is done once by using the asymptotic level densities for the eigenvalues of the m blocks and once by representing the integrated level density in terms of polynomials of different orders. We find that the spacing distribution of the eigenvalues shows a little sensitivity to the unfolding method. On the other hand, the variance of level number Σ2(L) is sensitive to the choice of the unfolding function. Unfolding that utilizes low order polynomials enhances Σ2(L) relative to the theoretical value, while the use of high order polynomial reduces it. The optimal value of the order of the unfolding polynomial depends on the dimension of the corresponding ensemble.
Chaotic motions of a tethered satellite system in circular orbit
NASA Astrophysics Data System (ADS)
Jin, D. P.; PANG, Z. J.; Wen, H.; Yu, B. S.
2016-09-01
This paper studies the chaotic motions of a tethered satellite system by utilizing a ground-based experimental system. Based on dynamics similarity principle, a dynamical equivalent model between the on-orbit tethered satellite and its ground physical model is obtained. As a result, the space dynamics environment of the tethered satellite can be simulated via the thrust forces and the torque of a momentum wheel on the satellite simulator. The numerical results of the on-orbit tethered satellite show the chaotic motions of the attitude motion of mother satellite. The experiment shows that the torque of momentum wheel as a negative damping is able to suppress the chaotic motion.
Anti-synchronization of two different chaotic systems
NASA Astrophysics Data System (ADS)
Li, Wenlin; Chen, Xiuqin; Zhiping, Shen
2008-06-01
In this paper, the anti-synchronization of two different chaotic systems is investigated. On the basis of a nonlinear control scheme and Lyapunov theory, sufficient conditions for the stability of the error dynamics are derived, where the controllers are designed by using the sum of the relevant variables in chaotic systems. Numerical simulations are performed for the Genesio-Rossler system to demonstrate the effectiveness of the proposed control strategy.
Interaction effects in a chaotic graphene quantum billiard
NASA Astrophysics Data System (ADS)
Hagymási, Imre; Vancsó, Péter; Pálinkás, András; Osváth, Zoltán
2017-02-01
We investigate the local electronic structure of a Sinai-like, quadrilateral graphene quantum billiard with zigzag and armchair edges using scanning tunneling microscopy (STM) at room temperature. It is revealed that besides the (√{3 }×√{3 }) R 30∘ superstructure, which is caused by the intervalley scattering, its overtones also appear in the STM measurements, which are attributed to the Umklapp processes. We point out that these results can be well understood by taking into account the Coulomb interaction in the quantum billiard, accounting for both the measured density of state values and the experimentally observed topography patterns. The analysis of the level-spacing distribution substantiates the experimental findings as well. We also reveal the magnetic properties of our system which should be relevant in future graphene based electronic and spintronic applications.
Is the Outer Solar System Really Chaotic?
NASA Astrophysics Data System (ADS)
Hayes, Wayne B.
2006-09-01
The existence of chaos among the system of Jovian planets (Jupiter, Saturn, Uranus, and Neptune) is not yet firmly established. Although Laskar originally found no chaos in the outer Solar System, his "averaged" integrations did not account for the possibility of mean-motion resonances. Once full n-body integrations were performed, a dichotomy arose. On one hand, many investigators (Sussman, Wisdom, Murray, Holman, among many others) consistently measured a Lyapunov time of between 5 and 12 million years in the outer Solar System; the chaos can even be explained as the overlap of three-body resonances (Murray + Holman, Science 283, 1999). Furthermore, Murray + Holman's theory has been recently corroborated across a wide range of system parameters (Guzzo 2005), and the chaos does not disappear with decreasing timestep. On the other hand, some other investigators (Newman, Grazier, and Varadi, among several others) have compelling evidence against chaos. Namely, they have convincingly demonstrated that a sympletic integration using the famous Wisdom + Holman (1992) symplectic mapping with a 400-day timestep reproduces the chaos seen by others, but that the chaos disappears and the orbit converges to being regular as the timestep decreases. Their integration remains regular, showing beautiful convergence with decreasing timestep, down to a 2 day timestep. The resolution of this apparent paradox is simple. The orbital positions of the Jovian planets is known only to a few parts in 107, and it turns out that within that observational error ball, there exist both chaotic and regular solutions. I will demonstrate this fact using several initial conditions and several accurate integration algorithms. Thus, whether a particular investigator will see chaos or not depends (essentially randomly) upon the details of how that investigator draws their initial conditions. Thus, some investigators legitimately find chaos, while others legitimately find no chaos.
NASA Astrophysics Data System (ADS)
Kemih, K.; Halimi, M.; Ghanes, M.; Zhang, G.
2011-12-01
In this paper, we study the design and implementation of analog secure communication systems via synchronized chaotic Chua's circuit with sliding mode observer. For this, we adopt an approach based on an inclusion of the message in the transmitter and in the receiver; we use a sliding mode observer with un-known input in order to recover the information. Finally, an analog electronic circuit with Multisim software is designed to physically realize the complete system (transmitter-receiver).
Insights into the softening of chaotic statistical models by quantum considerations
NASA Astrophysics Data System (ADS)
Cafaro, C.; Giffin, A.; Lupo, C.; Mancini, S.
2012-05-01
We analyze the information geometry and the entropic dynamics of a 3D Gaussian statistical model and compare our analysis to that of a 2D Gaussian statistical model obtained from the higher-dimensional model via introduction of an additional information constraint that resembles the quantum mechanical canonical minimum uncertainty relation. We uncover that the chaoticity of the 2D Gaussian statistical model, quantified by means of the Information Geometric Entropy (IGE), is softened with respect to the chaoticity of the 3D Gaussian statistical model.
Initial rectified attractors for perfect synchronization of chaotic systems
NASA Astrophysics Data System (ADS)
Sun, Mingxuan; He, Xiongxiong; Yu, Li
2005-12-01
The controlled attractor with initial rectifying action, referred to as initial rectified attractor (IRA) in this Letter, is introduced for the purpose of chaos synchronization. An IRA-based design is presented to make the states of the drive system and the response system synchronized within finite time. The reaching time is shown independent of initial conditions and dynamics of the chaotic systems, and can be pre-specified. With numerical experiments we demonstrate that such perfect synchronization can be achieved for modified Chua's circuit systems and Genesio chaotic systems.
Statistics of quantum transport in weakly nonideal chaotic cavities.
Rodríguez-Pérez, Sergio; Marino, Ricardo; Novaes, Marcel; Vivo, Pierpaolo
2013-11-01
We consider statistics of electronic transport in chaotic cavities where time-reversal symmetry is broken and one of the leads is weakly nonideal; that is, it contains tunnel barriers characterized by tunneling probabilities Γ(i). Using symmetric function expansions and a generalized Selberg integral, we develop a systematic perturbation theory in 1-Γ(i) valid for an arbitrary number of channels and obtain explicit formulas up to second order for the average and variance of the conductance and for the average shot noise. Higher moments of the conductance are considered to leading order.
Stabilizing Near-Nonhyperbolic Chaotic Systems with Applications
NASA Astrophysics Data System (ADS)
Huang, Debin
2004-11-01
Based on the invariance principle of differential equations a simple, systematic, and rigorous feedback scheme with the variable feedback strength is proposed to stabilize nonlinearly finite-dimensional chaotic systems without any prior analytical knowledge of the systems. Especially the method may be used to control near-nonhyperbolic chaotic systems, which, although arising naturally from models in astrophysics to those for neurobiology, all Ott-Grebogi-York type methods will fail to stabilize. The technique is successfully used for the famous Hindmarsh-Rose neuron model, the FitzHugh-Rinzel neuron model, and the Rössler hyperchaos system, respectively.
Constructing a Chaotic System with an Infinite Number of Equilibrium Points
NASA Astrophysics Data System (ADS)
Pham, Viet-Thanh; Jafari, Sajad; Kapitaniak, Tomasz
2016-12-01
The chaotic systems with hidden attractors, such as chaotic systems with a stable equilibrium, chaotic systems with infinite equilibria or chaotic systems with no equilibrium have been investigated recently. However, the relationships between them still need to be discovered. This work explains how to transform a system with one stable equilibrium into a new system with an infinite number of equilibrium points by using a memristive device. Furthermore, some other new systems with infinite equilibria are also constructed to illustrate the introduced methodology.
Active synchronization between two different chaotic dynamical system
NASA Astrophysics Data System (ADS)
Maheri, M.; Arifin, N. Md; Ismail, F.
2015-05-01
In this paper we investigate on the synchronization problem between two different chaotic dynamical system based on the Lyapunov stability theorem by using nonlinear control functions. Active control schemes are used for synchronization Liu system as drive and Rossler system as response. Numerical simulation by using Maple software are used to show effectiveness of the proposed schemes.
Active synchronization between two different chaotic dynamical system
Maheri, M.; Arifin, N. Md; Ismail, F.
2015-05-15
In this paper we investigate on the synchronization problem between two different chaotic dynamical system based on the Lyapunov stability theorem by using nonlinear control functions. Active control schemes are used for synchronization Liu system as drive and Rossler system as response. Numerical simulation by using Maple software are used to show effectiveness of the proposed schemes.
Image encryption based on synchronization of fractional chaotic systems
NASA Astrophysics Data System (ADS)
Xu, Yong; Wang, Hua; Li, Yongge; Pei, Bin
2014-10-01
This paper deals with a synchronization scheme for two fractional chaotic systems which is applied in image encryption. Based on Pecora and Carroll (PC) synchronization, fractional-order Lorenz-like system forms a master-slave configuration, and the sufficient conditions are derived to realize synchronization between these two systems via the Laplace transformation theory. An image encryption algorithm is introduced where the original image is encoded by a nonlinear function of a fractional chaotic state. Simulation results show that the original image is well masked in the cipher texts and recovered successfully through chaotic signals. Further, the cryptanalysis is conducted in detail through histogram, information entropy, key space and sensitivity to verify the high security.
Novel Public Key Encryption Technique Based on Multiple Chaotic Systems
NASA Astrophysics Data System (ADS)
Bose, Ranjan
2005-08-01
Public key encryption was first introduced by Diffie and Hellman in 1976. Since then, the Diffie-Hellman key exchange protocol has been used in developing public key systems such as Rivest-Shamir-Adleman and elliptic curve cryptography. Chaotic functions, so far, have been used for symmetric cryptography only. In this Letter we propose, for the first time, a methodology to use multiple chaotic systems and a set of linear functions for key exchange over an insecure channel. To the best of our knowledge, this is the first Letter that reports the use of chaotic systems for public key cryptography. We have shown that the security of the proposed algorithm grows as (NP)m, where N, P, and m are large numbers that can be chosen as the parameters of the cryptosystem.
Novel public key encryption technique based on multiple chaotic systems.
Bose, Ranjan
2005-08-26
Public key encryption was first introduced by Diffie and Hellman in 1976. Since then, the Diffie-Hellman key exchange protocol has been used in developing public key systems such as Rivest-Shamir-Adleman and elliptic curve cryptography. Chaotic functions, so far, have been used for symmetric cryptography only. In this Letter we propose, for the first time, a methodology to use multiple chaotic systems and a set of linear functions for key exchange over an insecure channel. To the best of our knowledge, this is the first Letter that reports the use of chaotic systems for public key cryptography. We have shown that the security of the proposed algorithm grows as (NP)(m), where N, P, and m are large numbers that can be chosen as the parameters of the cryptosystem.
Fundamentals of synchronization in chaotic systems, concepts, and applications.
Pecora, Louis M.; Carroll, Thomas L.; Johnson, Gregg A.; Mar, Douglas J.; Heagy, James F.
1997-12-01
The field of chaotic synchronization has grown considerably since its advent in 1990. Several subdisciplines and "cottage industries" have emerged that have taken on bona fide lives of their own. Our purpose in this paper is to collect results from these various areas in a review article format with a tutorial emphasis. Fundamentals of chaotic synchronization are reviewed first with emphases on the geometry of synchronization and stability criteria. Several widely used coupling configurations are examined and, when available, experimental demonstrations of their success (generally with chaotic circuit systems) are described. Particular focus is given to the recent notion of synchronous substitution-a method to synchronize chaotic systems using a larger class of scalar chaotic coupling signals than previously thought possible. Connections between this technique and well-known control theory results are also outlined. Extensions of the technique are presented that allow so-called hyperchaotic systems (systems with more than one positive Lyapunov exponent) to be synchronized. Several proposals for "secure" communication schemes have been advanced; major ones are reviewed and their strengths and weaknesses are touched upon. Arrays of coupled chaotic systems have received a great deal of attention lately and have spawned a host of interesting and, in some cases, counterintuitive phenomena including bursting above synchronization thresholds, destabilizing transitions as coupling increases (short-wavelength bifurcations), and riddled basins. In addition, a general mathematical framework for analyzing the stability of arrays with arbitrary coupling configurations is outlined. Finally, the topic of generalized synchronization is discussed, along with data analysis techniques that can be used to decide whether two systems satisfy the mathematical requirements of generalized synchronization. (c) 1997 American Institute of Physics.
Quantum smearing in hybrid inflation with chaotic potentials
NASA Astrophysics Data System (ADS)
Ahmed, Waqas; Ishaque, Ommair; Rehman, Mansoor Ur
2016-01-01
We study the impact of 1-loop radiative corrections in a nonsupersymmetric model of hybrid inflation (HI) with chaotic (polynomial-like) potential, V0 + λpϕp. These corrections can arise from the possible couplings of inflaton with other fields which can play an active role in the reheating process. The tree-level predictions of these models are shown to lie outside of the Planck’s latest bounds on the scalar spectral index ns and the tensor to scalar ratio r. However, the radiatively corrected version of these models, V0 + λpϕp + Aϕ4ln ϕ, is fully consistent with the Planck’s data. More specifically, fermionic radiative correction (A < 0) reduces the tensor to scalar ratio significantly and a red-tilted spectral index ns < 1, consistent with Planck’s data, is obtained even for sub-Planckian field-values.
Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry
Novaes, Marcel
2015-10-15
We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory.
Synchronization of an uncertain chaotic system via recurrent neural networks
NASA Astrophysics Data System (ADS)
Tan, Wen; Wang, Yao-Nan
2005-01-01
Incorporating distributed recurrent networks with high-order connections between neurons, the identification and synchronization problem of an unknown chaotic system in the presence of unmodelled dynamics is investigated. Based on the Lyapunov stability theory, the weights learning algorithm for the recurrent high-order neural network model is presented. Also, analytical results concerning the stability properties of the scheme are obtained. Then adaptive control law for eliminating synchronization error of uncertain chaotic plant is developed via Lyapunov methodology. The proposed scheme is applied to model and synchronize an unknown Rossler system.
Jamming and chaotic dynamics in different granular systems
NASA Astrophysics Data System (ADS)
Maghsoodi, Homayoon; Luijten, Erik
Although common in nature and industry, the jamming transition has long eluded a concrete, mechanistic explanation. Recently, Banigan et al. (Nat. Phys. 9, 288-292, 2013) proposed a method for characterizing this transition in a granular system in terms of the system's chaotic properties, as quantified by the largest Lyapunov exponent. They demonstrated that in a two-dimensional shear cell the jamming transition coincides with the bulk density at which the system's largest Lyapunov exponent changes sign, indicating a transition between chaotic and non-chaotic regimes. To examine the applicability of this observation to realistic granular systems, we study a model that includes frictional forces within an expanded phase space. Furthermore, we test the generality of the relation between chaos and jamming by investigating the relationship between jamming and the chaotic properties of several other granular systems, notably sheared systems (Howell, D., Behringer R. P., Veje C., Phys. Rev. Lett. 82, 5241-5244, 1999) and systems with a free boundary. Finally, we quantify correlations between the largest Lyapunov vector and collective rearrangements of the system to demonstrate the predictive capabilities enabled by adopting this perspective of jamming.
Stabilization and synchronization of chaotic systems via intermittent control
NASA Astrophysics Data System (ADS)
Zhu, Huibin; Cui, Baotong
2010-11-01
In this paper, we consider the stabilization and synchronization of chaotic systems via intermittent control with time varying control period and control width. Compared to existing results, some less conservative conditions are derived to guarantee the stabilization of nonlinear system. An effective adaptive-intermittent control law is also presented. Two examples are given to verify our proposed results.
Experimental chaotic quantification in bistable vortex induced vibration systems
NASA Astrophysics Data System (ADS)
Huynh, B. H.; Tjahjowidodo, T.
2017-02-01
The study of energy harvesting by means of vortex induced vibration systems has been initiated a few years ago and it is considered to be potential as a low water current energy source. The energy harvester is realized by exposing an elastically supported blunt structure under water flow. However, it is realized that the system will only perform at a limited operating range (water flow) that is attributed to the resonance phenomenon that occurs only at a frequency that corresponds to the fluid flow. An introduction of nonlinear elements seems to be a prominent solution to overcome the problem. Among many nonlinear elements, a bistable spring is known to be able to improve the harvested power by a vortex induced vibrations (VIV) based energy converter at the low velocity water flows. However, it is also observed that chaotic vibrations will occur at different operating ranges that will erratically diminish the harvested power and cause a difficulty in controlling the system that is due to the unpredictability in motions of the VIV structure. In order to design a bistable VIV energy converter with improved harvested power and minimum negative effect of chaotic vibrations, the bifurcation map of the system for varying governing parameters is highly on demand. In this study, chaotic vibrations of a VIV energy converter enhanced by a bistable stiffness element are quantified in a wide range of the governing parameters, i.e. damping and bistable gap. Chaotic vibrations of the bistable VIV energy converter are simulated by utilization of a wake oscillator model and quantified based on the calculation of the Lyapunov exponent. Ultimately, a series of experiments of the system in a water tunnel, facilitated by a computer-based force-feedback testing platform, is carried out to validate the existence of chaotic responses. The main challenge in dealing with experimental data is in distinguishing chaotic response from noise-contaminated periodic responses as noise will smear
Persistent Currents and Addition Spectrum in Strongly Interacting Chaotic Quantum Dots
NASA Astrophysics Data System (ADS)
Herman, Damir; Mathur, H.; Murthy, Ganpathy
2003-03-01
Murthy and Shankar(Ganpathy Murthy, R. Shankar, Quantum Dots with Disorder and Interactions: A Solvable Large-g Limit), family cond-mat/0209136 have introduced a non-perturbative approach to analyzing the effects of interaction and randomness in chaotic quantum dots in the limit of large Thouless number. Using this framework we study two experimentally observable quantities in the strongly interacting regime. First we compare the Coulomb blockade peak spacing distribution in the strong coupling regime to the distribution in the weak coupling regime (described by the ``universal Hamiltonian''). Second we study persistent currents in mesoscopic rings in the regime of strong interaction.
Regular and chaotic quantum dynamics in atom-diatom reactive collisions
Gevorkyan, A. S.; Nyman, G.
2008-05-15
A new microirreversible 3D theory of quantum multichannel scattering in the three-body system is developed. The quantum approach is constructed on the generating trajectory tubes which allow taking into account influence of classical nonintegrability of the dynamical quantum system. When the volume of classical chaos in phase space is larger than the quantum cell in the corresponding quantum system, quantum chaos is generated. The probability of quantum transitions is constructed for this case. The collinear collision of the Li + (FH) {sup {yields}}(LiF) + H system is used for numerical illustration of a system generating quantum (wave) chaos.
Inverse Optimal Pinning Control for Complex Networks of Chaotic Systems
NASA Astrophysics Data System (ADS)
Sanchez, Edgar N.; Rodriguez, David I.
In this paper, a control strategy based on the inverse optimal control approach is applied for pinning weighted complex networks with chaotic systems at their nodes; additionally, a cost functional is minimized. This control strategy does not require to have the same coupling strength for all node connections.
Modification for synchronization of Rossler and Chen chaotic systems
NASA Astrophysics Data System (ADS)
Li, Zhi; Han, Chongzhao; Shi, Songjiao
2002-08-01
Active control is an effective method for making two identical Rossler and Chen systems be synchronized. However, this method works only for a certain class of chaotic systems with known parameters both in drive systems and response systems. Modification based on Lyapunov stability theory is proposed in order to overcome this limitation. An adaptive synchronization controller, which can make the states of two identical Rossler and Chen systems globally asymptotically synchronized in the presence of system's unknown constant parameters, is derived. Especially, when some unknown parameters are positive, we can make the controller more simple, besides, the controller is independent of those positive uncertain parameters. At last, when the condition that arbitrary unknown parameters in two systems are identical constants is cancelled, we demonstrate that it is possible to synchronize two chaotic systems. All results are proved using a well-known Lyapunov stability theorem. Numerical simulations are given to validate the proposed synchronization approach.
Generation of chaotic attractors without equilibria via piecewise linear systems
NASA Astrophysics Data System (ADS)
Escalante-González, R. J.; Campos-Cantón, E.
In this paper, we present a mechanism of generation of a class of switched dynamical system without equilibrium points that generates a chaotic attractor. The switched dynamical systems are based on piecewise linear (PWL) systems. The theoretical results are formally given through a theorem and corollary which give necessary and sufficient conditions to guarantee that a linear affine dynamical system has no equilibria. Numerical results are in accordance with the theory.
Grebogi, C.; Yorke, J.A.
1991-12-01
This report discusses the following topics: controlling chaotic dynamical systems; embedding of experimental data; effect of noise on critical exponents of crises; transition to chaotic scattering; and distribution of floaters on a fluid surface. (LSP)
Trail, Collin M; Madhok, Vaibhav; Deutsch, Ivan H
2008-10-01
We study the dynamical generation of entanglement as a signature of chaos in a system of periodically kicked coupled tops, where chaos and entanglement arise from the same physical mechanism. The long-time-averaged entanglement as a function of the position of an initially localized wave packet very closely correlates with the classical phase space surface of section--it is nearly uniform in the chaotic sea, and reproduces the detailed structure of the regular islands. The uniform value in the chaotic sea is explained by the random state conjecture. As classically chaotic dynamics take localized distributions in phase space to random distributions, quantized versions take localized coherent states to pseudorandom states in Hilbert space. Such random states are highly entangled, with an average value near that of the maximally entangled state. For a map with global chaos, we derive that value based on analytic results for the entropy of random states. For a mixed phase space, we use the Percival conjecture to identify a "chaotic subspace" of the Hilbert space. The typical entanglement, averaged over the unitarily invariant Haar measure in this subspace, agrees with the long-time-averaged entanglement for initial states in the chaotic sea. In all cases the dynamically generated entanglement is that of a random complex vector, even though the system is time-reversal invariant, and the Floquet operator is a member of the circular orthogonal ensemble.
Quantum Response of Weakly Chaotic Systems
2010-10-01
Pecora2 and D. Cohen1(a) 1Department of Physics, Ben-Gurion University - Beer -Sheva 84105, Israel 2 Code 6362, Naval Research Lab - Washington, DC...AND ADDRESS(ES) Department of Physics,Ben-Gurion University - Beer -Sheva 8401, Israel, , , 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING...Stotland, L. M. Pecora and D. Cohen. Affiliations Department of Physics, Ben-Gurion University - Beer -Sheva 84105, Israel. 2 Code 6362, Naval Research Lab
Classical and quantum chaotic angular-momentum pumps.
Dittrich, T; Dubeibe, F L
2015-03-06
We study directed transport of charge and intrinsic angular momentum by periodically driven scattering in the regime of fast and strong driving. A spin-orbit coupling through a kicked magnetic field confined to a compact region in space leads to irregular scattering and triggers spin flips in a spatially asymmetric manner which allows us to generate polarized currents. The dynamical mechanisms responsible for the spin separation carry over to the quantum level and give rise to spin pumping. Our theory based on the Floquet formalism is confirmed by numerical solutions of the time-dependent inhomogeneous Schrödinger equation with a continuous source term.
Chaotic Motion in the Solar System and Beyond
NASA Technical Reports Server (NTRS)
Lissauer, Jack; DeVincenzi, Donald (Technical Monitor)
2001-01-01
The motion of planetary bodies is the archetypal clockwork system. Indeed, clocks and calendars were developed to keep track of the relative motions of the Earth, the Sun and the Moon. However, studies over the past few decades imply that this predictable regularity does not extend to small bodies, nor does it apply to the precise trajectories of the planets themselves over long timescale.s. Various examples of chaotic motion within our Solar System and, extrasolar planetary systems will be discussed.
NASA Astrophysics Data System (ADS)
Liu, Ping
2013-07-01
This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems, respectively. The two controllers are simple, and one of the uncertain unified chaotic complex systems is robust. For the design of a finite-time controller on uncertain unified chaotic complex systems, only some of the unknown parameters need to be bounded. Simulation results for the chaotic complex Lorenz, Lü and Chen systems are presented to validate the design and analysis.
Understanding quantum work in a quantum many-body system
NASA Astrophysics Data System (ADS)
Wang, Qian; Quan, H. T.
2017-03-01
Based on previous studies in a single-particle system in both the integrable [Jarzynski, Quan, and Rahav, Phys. Rev. X 5, 031038 (2015), 10.1103/PhysRevX.5.031038] and the chaotic systems [Zhu, Gong, Wu, and Quan, Phys. Rev. E 93, 062108 (2016), 10.1103/PhysRevE.93.062108], we study the the correspondence principle between quantum and classical work distributions in a quantum many-body system. Even though the interaction and the indistinguishability of identical particles increase the complexity of the system, we find that for a quantum many-body system the quantum work distribution still converges to its classical counterpart in the semiclassical limit. Our results imply that there exists a correspondence principle between quantum and classical work distributions in an interacting quantum many-body system, especially in the large particle number limit, and further justify the definition of quantum work via two-point energy measurements in quantum many-body systems.
Generation and dynamics analysis of N-scrolls existence in new translation-type chaotic systems
NASA Astrophysics Data System (ADS)
Liu, Yue; Guo, Shuxu
2016-11-01
In this paper, we propose two kinds of translation type chaotic systems for creating 2 N + 1-and 2(N + 1)-scrolls chaotic attractors from a simple three-dimensional system, which are named the translation-2 chaotic system (a12a21 < 0) and the translation-3 chaotic system (a12a21 > 0). We also propose the successful design criterion for constructing 2 N + 1-and 2(N + 1)-scrolls, respectively. Then, the dynamics property of the translation-2 chaotic system is studied in detail. MATLAB simulation results show that very sophisticated dynamical behaviors and unique chaotic behaviors of the system. Finally, the definition and criterion of multi-scroll attractors for the translation-3 chaotic system is obtained. Three representative examples are shown in some classical chaotic systems that can be equally obtained via the set parameters of the translation type chaotic system. Furthermore, we show that the translation type chaotic systems have similar but topologically non-equivalent chaotic attractors, and they are the three-dimensional ordinary differential equations.
An exponential polynomial observer for synchronization of chaotic systems
NASA Astrophysics Data System (ADS)
Mata-Machuca, J. L.; Martínez-Guerra, R.; Aguilar-López, R.
2010-12-01
In this paper, we consider the synchronization problem via nonlinear observer design. A new exponential polynomial observer for a class of nonlinear oscillators is proposed, which is robust against output noises. A sufficient condition for synchronization is derived analytically with the help of Lyapunov stability theory. The proposed technique has been applied to synchronize chaotic systems (Rikitake and Rössler systems) by means of numerical simulation.
Urbina, Juan Diego; Richter, Klaus
2006-11-24
We present a semiclassical approach to eigenfunction statistics in chaotic and weakly disordered quantum systems which goes beyond random matrix theory, supersymmetry techniques, and existing semiclassical methods. The approach is based on a generalization of Berry's random wave model, combined with a consistent semiclassical representation of spatial two-point correlations. We derive closed expressions for arbitrary wave-function averages in terms of universal coefficients and sums over classical paths, which contain, besides the supersymmetry results, novel oscillatory contributions. Their physical relevance is demonstrated in the context of Coulomb blockade physics.
Predicting mixing microstructure in three-dimensional chaotic systems
NASA Astrophysics Data System (ADS)
Szalai, E. S.; Muzzio, F. J.
2003-11-01
This paper explores the application of asymptotic directionality to three-dimensional (3D) chaotic periodic flows by examining flow in a tank agitated by four impellers. Numerical simulations and experimental methods are employed to reveal the spatial structure of the evolving mixing patterns and its statistical properties. It is demonstrated that there exists an invariant field of orientations in the system that creates self-similar mixing structures. As a result, the frequency distributions of stretching can be collapsed onto an invariant curve by a simple homogeneous scaling. This statistical scaling behavior is a direct consequence of the asymptotic directionality property. It is also shown that striation thickness distributions (STDs) can be predicted directly from the stretching distributions in fully 3D chaotic systems, thus providing a method for calculation of STDs in complex flows.
Dynamic controller design for exponential synchronization of Chen chaotic system
NASA Astrophysics Data System (ADS)
Park, Ju H.; Lee, S. M.; Kwon, O. M.
2007-07-01
The Letter considers synchronization of Chen chaotic system. The problems of determining the exponential stability and estimating the exponential convergence rate for the synchronization are investigated by employing the Lyapunov functional method and linear matrix inequality (LMI) technique. For this end, a dynamic controller is proposed for the first time and a criterion for existence of the controller is given in terms of LMIs. Finally, numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.
Linear optimal control of continuous time chaotic systems.
Merat, Kaveh; Abbaszadeh Chekan, Jafar; Salarieh, Hassan; Alasty, Aria
2014-07-01
In this research study, chaos control of continuous time systems has been performed by using dynamic programming technique. In the first step by crossing the response orbits with a selected Poincare section and subsequently applying linear regression method, the continuous time system is converted to a discrete type. Then, by solving the Riccati equation a sub-optimal algorithm has been devised for the obtained discrete chaotic systems. In the next step, by implementing the acquired algorithm on the quantized continuous time system, the chaos has been suppressed in the Rossler and AFM systems as some case studies.
Gross-Pitaevski map as a chaotic dynamical system
NASA Astrophysics Data System (ADS)
Guarneri, Italo
2017-03-01
The Gross-Pitaevski map is a discrete time, split-operator version of the Gross-Pitaevski dynamics in the circle, for which exponential instability has been recently reported. Here it is studied as a classical dynamical system in its own right. A systematic analysis of Lyapunov exponents exposes strongly chaotic behavior. Exponential growth of energy is then shown to be a direct consequence of rotational invariance and for stationary solutions the full spectrum of Lyapunov exponents is analytically computed. The present analysis includes the "resonant" case, when the free rotation period is commensurate to 2 π , and the map has countably many constants of the motion. Except for lowest-order resonances, this case exhibits an integrable-chaotic transition.
Optimized synchronization of chaotic and hyperchaotic systems
NASA Astrophysics Data System (ADS)
Bryant, Paul H.
2010-07-01
A method of synchronization is presented which, unlike existing methods, can, for generic dynamical systems, force all conditional Lyapunov exponents to go to -∞ . It also has improved noise immunity compared to existing methods, and unlike most of them it can synchronize hyperchaotic systems with almost any single coupling variable from the drive system. Results are presented for the Rossler hyperchaos system and the Lorenz system.
Gravitational ionization: a chaotic net in the Kepler system
NASA Astrophysics Data System (ADS)
Chicone, C.; Mashhoon, B.; Retzloff, D. G.
1997-03-01
The long-term nonlinear dynamics of a Keplerian binary system under the combined influences of gravitational radiation damping and external tidal perturbations is analysed. Gravitational radiation reaction leads the binary system towards eventual collapse, while the external periodic perturbations could lead to the ionization of the system via Arnold diffusion. When these two opposing tendencies nearly balance each other, interesting chaotic behaviour occurs which is briefly studied in this paper. It is possible to show that periodic orbits can exist in this system for sufficiently small damping. Moreover, we employ the method of averaging to investigate the phenomenon of capture into resonance.
Pluhacek, Michal; Davendra, Donald; Oplatková Kominkova, Zuzana
2014-01-01
Evolutionary technique differential evolution (DE) is used for the evolutionary tuning of controller parameters for the stabilization of set of different chaotic systems. The novelty of the approach is that the selected controlled discrete dissipative chaotic system is used also as the chaotic pseudorandom number generator to drive the mutation and crossover process in the DE. The idea was to utilize the hidden chaotic dynamics in pseudorandom sequences given by chaotic map to help differential evolution algorithm search for the best controller settings for the very same chaotic system. The optimizations were performed for three different chaotic systems, two types of case studies and developed cost functions. PMID:25243230
Thermalization in closed quantum systems: Semiclassical approach
NASA Astrophysics Data System (ADS)
Cosme, J. G.; Fialko, O.
2014-11-01
Thermalization in closed quantum systems can be understood either by means of the eigenstate thermalization hypothesis or the concept of canonical typicality. Both concepts are based on quantum-mechanical formalism, such as spectral properties of the eigenstates or entanglement between subsystems, respectively. Here we study instead the onset of thermalization of Bose particles in a two-band double-well potential using the truncated Wigner approximation. This allows us to use the familiar classical formalism to understand quantum thermalization in this system. In particular, we demonstrate that sampling of an initial quantum state mimics a statistical mechanical ensemble, while subsequent chaotic classical evolution turns the initial quantum state into the thermal state.
Communications with chaotic optoelectronic systems cryptography and multiplexing
NASA Astrophysics Data System (ADS)
Rontani, Damien
With the rapid development of optical communications and the increasing amount of data exchanged, it has become utterly important to provide effective architectures to protect sensitive data. The use of chaotic optoelectronic devices has already demonstrated great potential in terms of additional computational security at the physical layer of the optical network. However, the determination of the security level and the lack of a multi-user framework are two hurdles which have prevented their deployment on a large scale. In this thesis, we propose to address these two issues. First, we investigate the security of a widely used chaotic generator, the external cavity semiconductor laser (ECSL). This is a time-delay system known for providing complex and high-dimensional chaos, but with a low level of security regarding the identification of its most critical parameter, the time delay. We perform a detailed analysis of the in uence of the ECSL parameters to devise how higher levels of security can be achieved and provide a physical interpretation of their origin. Second, we devise new architectures to multiplex optical chaotic signals and realize multi-user communications at high bit rates. We propose two different approaches exploiting known chaotic optoelectronic devices. The first one uses mutually coupled ECSL and extends typical chaos-based encryption strategies, such as chaos-shift keying (CSK) and chaos modulation (CMo). The second one uses an electro-optical oscillator (EOO) with multiple delayed feedback loops and aims first at transposing coded-division multiple access (CDMA) and then at developing novel strategies of encryption and decryption, when the time-delays of each feedback loop are time-dependent.
Transcritical loss of synchronization in coupled chaotic systems
NASA Astrophysics Data System (ADS)
Popovych, O.; Maistrenko, Yu; Mosekilde, E.; Pikovsky, A.; Kurths, J.
2000-10-01
The synchronization transition is described for a system of two asymmetrically coupled chaotic oscillators. Such a system can represent the two-cluster state in a large ensemble of globally coupled oscillators. It is shown that the transition can be typically mediated by a transcritical transversal bifurcation. The latter has a hard brunch that dominates the global dynamics, so that the synchronization transition is normally hard. For a particular example of coupled logistic maps a diversity of transition scenaria includes both local and global riddling. In the case of small non-identity of the interacting systems the riddling is shown to turn into an exterior or interior crisis.
The chaotic history of the Solar System
NASA Astrophysics Data System (ADS)
Morbidelli, Alessandro
2015-08-01
I will provide a review of the models proposed to explain the structure of the Solar System, with emphasis on their predicitions regarding the origin of asteroids and comets and the build-up of the two major cometary reservoirs: the scattered disk and the Oort cloud
Sequential synchronization of chaotic systems with an application to communication.
Kim, Chil-Min; Rim, Sunghwan; Kye, Won-Ho
2002-01-07
We propose a hierarchically structured communication system by using sequentially synchronized chaotic systems. Sequential synchronization is attained by first feeding a noiselike signal to a variable of the first transmitter and its receiver simultaneously and then feeding a variable of the first transmitter and its receiver to a variable of the second transmitter and its receiver, respectively, for subsequent feedings of variables in sequence. When this is applied to communication, the hierarchical structure enables selective protection of information due to the sequential property. We illustrate this in sequentially synchronized Navier-Stokes and Lorenz equations.
The equal combination synchronization of a class of chaotic systems with discontinuous output
Luo, Runzi; Zeng, Yanhui
2015-11-15
This paper investigates the equal combination synchronization of a class of chaotic systems. The chaotic systems are assumed that only the output state variable is available and the output may be discontinuous state variable. By constructing proper observers, some novel criteria for the equal combination synchronization are proposed. The Lorenz chaotic system is taken as an example to demonstrate the efficiency of the proposed approach.
On Chaotic and Hyperchaotic Complex Nonlinear Dynamical Systems
NASA Astrophysics Data System (ADS)
Mahmoud, Gamal M.
Dynamical systems described by real and complex variables are currently one of the most popular areas of scientific research. These systems play an important role in several fields of physics, engineering, and computer sciences, for example, laser systems, control (or chaos suppression), secure communications, and information science. Dynamical basic properties, chaos (hyperchaos) synchronization, chaos control, and generating hyperchaotic behavior of these systems are briefly summarized. The main advantage of introducing complex variables is the reduction of phase space dimensions by a half. They are also used to describe and simulate the physics of detuned laser and thermal convection of liquid flows, where the electric field and the atomic polarization amplitudes are both complex. Clearly, if the variables of the system are complex the equations involve twice as many variables and control parameters, thus making it that much harder for a hostile agent to intercept and decipher the coded message. Chaotic and hyperchaotic complex systems are stated as examples. Finally there are many open problems in the study of chaotic and hyperchaotic complex nonlinear dynamical systems, which need further investigations. Some of these open problems are given.
Synchronization and an application of a novel fractional order King Cobra chaotic system.
Muthukumar, P; Balasubramaniam, P; Ratnavelu, K
2014-09-01
In this paper, we design a new three dimensional King Cobra face shaped fractional order chaotic system. The multi-scale synchronization scheme of two fractional order chaotic systems is described. The necessary conditions for the multi-scale synchronization of two identical fractional order King Cobra chaotic systems are derived through feedback control. A new cryptosystem is proposed for an image encryption and decryption by using synchronized fractional order King Cobra chaotic systems with the supports of multiple cryptographic assumptions. The security of the proposed cryptosystem is analyzed by the well known algebraic attacks. Numerical simulations are given to show the effectiveness of the proposed theoretical results.
Synchronization and an application of a novel fractional order King Cobra chaotic system
Muthukumar, P. Balasubramaniam, P.; Ratnavelu, K.
2014-09-01
In this paper, we design a new three dimensional King Cobra face shaped fractional order chaotic system. The multi-scale synchronization scheme of two fractional order chaotic systems is described. The necessary conditions for the multi-scale synchronization of two identical fractional order King Cobra chaotic systems are derived through feedback control. A new cryptosystem is proposed for an image encryption and decryption by using synchronized fractional order King Cobra chaotic systems with the supports of multiple cryptographic assumptions. The security of the proposed cryptosystem is analyzed by the well known algebraic attacks. Numerical simulations are given to show the effectiveness of the proposed theoretical results.
Stability of uncertain impulsive complex-variable chaotic systems with time-varying delays.
Zheng, Song
2015-09-01
In this paper, the robust exponential stabilization of uncertain impulsive complex-variable chaotic delayed systems is considered with parameters perturbation and delayed impulses. It is assumed that the considered complex-variable chaotic systems have bounded parametric uncertainties together with the state variables on the impulses related to the time-varying delays. Based on the theories of adaptive control and impulsive control, some less conservative and easily verified stability criteria are established for a class of complex-variable chaotic delayed systems with delayed impulses. Some numerical simulations are given to validate the effectiveness of the proposed criteria of impulsive stabilization for uncertain complex-variable chaotic delayed systems.
Diffusion in very chaotic hamiltonian systems
Abarbanel, Henry D. I.; Crawford, John David
1981-04-20
In this paper, we study nonintegrable hamiltonian dynamics: H(I,θ) = H_{0}(I) + kH_{1}(I,θ), for large k, that is, far from integrability. An integral representation is given for the conditional probability P(I,θ, t¦I_{0}, θ_{0}, t_{0}) that the system is at I, θ at t, given it was at I_{0}, θ_{0} at t_{0}. By discretizing time into steps of size ϵ, we show how to evaluate physical observables for large k, fixed ϵ. An explicit calculation of a diffusion coefficient in a two degrees of freedom problem is reported. Finally, passage to ϵ = 0, the original hamiltonian flow, is discussed.
Properties of numerical experiments in chaotic dynamical systems
NASA Astrophysics Data System (ADS)
Yuan, Guo-Cheng
1999-10-01
This dissertation contains four projects that I have worked on during my graduate study at University of Maryland at College Park. These projects are all related to numerical simulations of chaotic dynamical systems. In particular, the two conjectures in Chapter 1 are inspired by the numerical discoveries in Hunt and Ott [1, 2]. In Chapter 2, statistical properties of scalar transport in chaotic flows are investigated by using numerical simulations. In Chapters 3 and 4, I take a different angle and discuss the limitations of numerical simulations; i.e. for certain ``bad'' systems numerical simulations will yield incorrect or at least unreliable results no matter how many digits of precision are used. Chapter 1 discusses the properties of optimal orbits. Given a dynamical system and a function f from the state space to the real numbers, an optimal orbit for f is an orbit over which the average of f is maximal. In this chapter we discuss some basic mathematical aspects of optimal orbits: existence, sensitivity to perturbations of f, and approximability by periodic orbits with low period. For hyperbolic systems, we conjecture that (1)for (topologically) generic smooth functions, there exists an optimal periodic orbit, and (2)the optimal average can be approximated exponentially well by averages over certain periodic orbits with increasing period. In Chapter 2 we theoretically study the power spectrum of passive scalars transported in two dimensional chaotic fluid flows. Using a wave-packet method introduced by Antonsen et al. [3] [4], we numerically investigate several model flows, and confirm that the power spectrum has the k -l- scaling predicted by Batchelor [5]. In Chapter 3 we consider a class of nonhyperbolic systems, for which there are two fixed points in an attractor having a dense trajectory; the unstable manifold of one fixed point has dimension one and the other's is two dimensional. Under the condition that there exists a direction which is more expanding
A mixed analog/digital chaotic neuro-computer system for quadratic assignment problems.
Horio, Yoshihiko; Ikeguchi, Tohru; Aihara, Kazuyuki
2005-01-01
We construct a mixed analog/digital chaotic neuro-computer prototype system for quadratic assignment problems (QAPs). The QAP is one of the difficult NP-hard problems, and includes several real-world applications. Chaotic neural networks have been used to solve combinatorial optimization problems through chaotic search dynamics, which efficiently searches optimal or near optimal solutions. However, preliminary experiments have shown that, although it obtained good feasible solutions, the Hopfield-type chaotic neuro-computer hardware system could not obtain the optimal solution of the QAP. Therefore, in the present study, we improve the system performance by adopting a solution construction method, which constructs a feasible solution using the analog internal state values of the chaotic neurons at each iteration. In order to include the construction method into our hardware, we install a multi-channel analog-to-digital conversion system to observe the internal states of the chaotic neurons. We show experimentally that a great improvement in the system performance over the original Hopfield-type chaotic neuro-computer is obtained. That is, we obtain the optimal solution for the size-10 QAP in less than 1000 iterations. In addition, we propose a guideline for parameter tuning of the chaotic neuro-computer system according to the observation of the internal states of several chaotic neurons in the network.
Advanced quantum communication systems
NASA Astrophysics Data System (ADS)
Jeffrey, Evan Robert
Quantum communication provides several examples of communication protocols which cannot be implemented securely using only classical communication. Currently, the most widely known of these is quantum cryptography, which allows secure key exchange between parties sharing a quantum channel subject to an eavesdropper. This thesis explores and extends the realm of quantum communication. Two new quantum communication protocols are described. The first is a new form of quantum cryptography---relativistic quantum cryptography---which increases communication efficiency by exploiting a relativistic bound on the power of an eavesdropper, in addition to the usual quantum mechanical restrictions intrinsic to quantum cryptography. By doing so, we have observed over 170% improvement in communication efficiency over a similar protocol not utilizing relativity. A second protocol, Quantum Orienteering, allows two cooperating parties to communicate a specific direction in space. This application shows the possibility of using joint measurements, or projections onto an entangled state, in order to extract the maximum useful information from quantum bits. For two-qubit communication, the maximal fidelity of communication using only separable operations is 73.6%, while joint measurements can improve the efficiency to 78.9%. In addition to implementing these protocols, we have improved several resources for quantum communication and quantum computing. Specifically, we have developed improved sources of polarization-entangled photons, a low-loss quantum memory for polarization qubits, and a quantum random number generator. These tools may be applied to a wide variety of future quantum and classical information systems.
An Anti-Cheating Visual Cryptography Scheme Based on Chaotic Encryption System
NASA Astrophysics Data System (ADS)
Han, Yanyan; Xu, Zhuolin; Ge, Xiaonan; He, Wencai
By chaotic encryption system and introducing the trusted third party (TTP), in this paper, an anti-cheating visual cryptography scheme (VCS) is proposed. The scheme solved the problem of dishonest participants and improved the security of chaotic encryption system. Simulation results and analysis show that the recovery image is acceptable, the system can detect the cheating in participants effectively and with high security.
Multiswitching combination-combination synchronization of chaotic systems
NASA Astrophysics Data System (ADS)
Khan, Ayub; Khattar, Dinesh; Prajapati, Nitish
2017-03-01
In this paper, a novel synchronization scheme is investigated for a class of chaotic systems. The multiswitching synchronization scheme is extended to the combination-combination synchronization scheme such that the combination of state variables of two drive systems synchronize with different combination of state variables of two response systems, simultaneously. The new scheme, multiswitching combination-combination synchronization (MSCCS), is a notable extension of the earlier multiswitching schemes concerning only the single drive-response system model. Various multiswitching modified projective synchronization schemes are obtained as special cases of MSCCS, for a suitable choice of scaling factors. Suitable controllers have been designed and using Lyapunov stability theory sufficient condition is obtained to achieve MSCCS between four hyperchaotic systems and the corresponding theoretical proof is given. Numerical simulations are performed to validate the theoretical results.
Quantum chaos and thermalization in gapped systems
Rigol, Marcos; Santos, Lea F.
2010-07-15
We investigate the onset of thermalization and quantum chaos in finite one-dimensional gapped systems of hard-core bosons. Integrability in these systems is broken by next-nearest-neighbor repulsive interactions, which also generate a superfluid to insulator transition. By employing full exact diagonalization, we study chaos indicators and few-body observables. We show that with increasing system size, chaotic behavior is seen over a broader range of parameters and, in particular, deeper into the insulating phase. Concomitantly, we observe that, as the system size increases, the eigenstate thermalization hypothesis extends its range of validity inside the insulating phase and is accompanied by the thermalization of the system.
Chaos pass filter: linear response of synchronized chaotic systems.
Zeeb, Steffen; Kestler, Johannes; Kanter, Ido; Kinzel, Wolfgang
2013-04-01
The linear response of synchronized time-delayed chaotic systems to small external perturbations, i.e., the phenomenon of chaos pass filter, is investigated for iterated maps. The distribution of distances, i.e., the deviations between two synchronized chaotic units due to external perturbations on the transferred signal, is used as a measure of the linear response. It is calculated numerically and, for some special cases, analytically. Depending on the model parameters this distribution has power law tails in the region of synchronization leading to diverging moments of distances. This is a consequence of multiplicative and additive noise in the corresponding linear equations due to chaos and external perturbations. The linear response can also be quantified by the bit error rate of a transmitted binary message which perturbs the synchronized system. The bit error rate is given by an integral over the distribution of distances and is calculated analytically and numerically. It displays a complex nonmonotonic behavior in the region of synchronization. For special cases the distribution of distances has a fractal structure leading to a devil's staircase for the bit error rate as a function of coupling strength. The response to small harmonic perturbations shows resonances related to coupling and feedback delay times. A bidirectionally coupled chain of three units can completely filter out the perturbation. Thus the second moment and the bit error rate become zero.
NASA Astrophysics Data System (ADS)
Aguirre, Luis Antonio; Billings, S. A.
This paper investigates the identification of global models from chaotic data corrupted by additive noise. It is verified that noise has a strong influence on the identification of chaotic systems. In particular, there seems to be a critical noise level beyond which the accurate estimation of polynomial models from chaotic data becomes very difficult. Similarities with the estimation of the largest Lyapunov exponent from noisy data suggest that part of the problem might be related to the limited ability of predicting the data records when these are chaotic. A nonlinear filtering scheme is suggested in order to reduce the noise in the data and thereby enable the estimation of good models. This prediction-based filtering incorporates a resetting mechanism which enables the filtering of chaotic data and which is also applicable to non-chaotic data.
A new cryptosystem based on spatial chaotic system
NASA Astrophysics Data System (ADS)
Sun, Fuyan; Lü, Zongwang; Liu, Shutang
2010-05-01
Encryption of images is different from that of texts due to some intrinsic features of images such as bulk data capacity and high redundancy, which is generally difficult to handle by traditional methods. This paper proposes a new spatial chaos system (SCS), which is investigated by conducting FIPS 140-1 statistic test, and is especially useful for encryption of digital images. It is shown how to adapt a two dimensional (2D) ergodic matrix obtained from SCS to permute the positions of image pixels and confuse the relationship between the cipher image and plain image simultaneously. Experimental results show that the performance and security of the proposed cryptographic system are better than those of existing lower dimensional chaotic cryptographic systems.
Adaptive synchronization of two chaotic systems with stochastic unknown parameters
NASA Astrophysics Data System (ADS)
Salarieh, Hassan; Alasty, Aria
2009-02-01
Using the Lyapunov stability theory an adaptive control is proposed for chaos synchronization between two different systems which have stochastically time varying unknown coefficients. The stochastic variations of the coefficients about their unknown mean values are modeled through white Gaussian noise produced by the Weiner process. It is shown that using the proposed adaptive control the mean square of synchronization error converges to an arbitrarily small bound around zero. To demonstrate the effectiveness of the proposed technique, it is applied to the Lorenz-Chen and the Chen-Rossler dynamical systems, as some case studies. Simulation results indicate that the proposed adaptive controller has a high performance in synchronization of chaotic systems in noisy environment.
NASA Astrophysics Data System (ADS)
Cahill, Reginald T.
2002-10-01
So far proposed quantum computers use fragile and environmentally sensitive natural quantum systems. Here we explore the new notion that synthetic quantum systems suitable for quantum computation may be fabricated from smart nanostructures using topological excitations of a stochastic neural-type network that can mimic natural quantum systems. These developments are a technological application of process physics which is an information theory of reality in which space and quantum phenomena are emergent, and so indicates the deep origins of quantum phenomena. Analogous complex stochastic dynamical systems have recently been proposed within neurobiology to deal with the emergent complexity of biosystems, particularly the biodynamics of higher brain function. The reasons for analogous discoveries in fundamental physics and neurobiology are discussed.
Mixed quantum-classical versus full quantum dynamics: Coupled quasiparticle-oscillator system
NASA Astrophysics Data System (ADS)
Schanz, Holger; Esser, Bernd
1997-05-01
The relation between the dynamical properties of a coupled quasiparticle-oscillator system in the mixed quantum-classical and fully quantized descriptions is investigated. The system is considered as a model for applying a stepwise quantization. Features of the nonlinear dynamics in the mixed description such as the presence of a separatrix structure or regular and chaotic motion are shown to be reflected in the evolu- tion of the quantum state vector of the fully quantized system. In particular, it is demonstrated how wave packets propagate along the separatrix structure of the mixed description, and that chaotic dynamics leads to a strongly entangled quantum state vector. Special emphasis is given to viewing the system from a dyn- amical Born-Oppenheimer approximation defining integrable reference oscillators, and elucidating the role of the nonadiabatic couplings which complement this approximation into a rigorous quantization scheme.
Chaotic behavior of magnetic field lines near simplest current systems
NASA Astrophysics Data System (ADS)
Veselovsky, I. S.; Lukashenko, A. T.
2016-12-01
In the context of studying the problem of simulation of magnetic fields on the Sun, the structure of the field in the vicinity of two circular current loops with different mutual arrangement in space is considered. When the symmetry in the arrangement is sufficient, a system of magnetic surfaces created by the closed field lines arises. With a reduction in symmetry, isolated closed lines may exist. For the case of two identical current loops coupled perpendicularly, it is shown that the subsystems of these lines may be ordered in space in a complex manner. At large distances, a system of loops is equivalent to a dipole with a high degree of accuracy, while an approximate winding of the lines on the deformed toroids, encircling each of the loops, occurs at small distances. At intermediate distances, there are regions of both ordered and chaotic behavior of field lines. Results were obtained with the use of the numerical simulation method.
Emergent thermodynamics in a system of macroscopic, chaotic surface waves
NASA Astrophysics Data System (ADS)
Welch, Kyle J.
The properties of conventional materials are inextricably linked with their molecular composition; to make water flow like wine would require changing its molecular identity. To circumvent this restriction, I have constructed and characterized a two-dimensional metafluid, so-called because its constitutive dynamics are derived not from atoms and molecules but from macroscopic, chaotic surface waves excited on a vertically agitated fluid. Unlike in conventional fluids, the viscosity and temperature of this metafluid are independently tunable. Despite this unconventional property, our system is surprisingly consistent with equilibrium thermodynamics, despite being constructed from macroscopic, non-equilibrium elements. As a programmable material, our metafluid represents a new platform on which to study complex phenomena such as self-assembly and pattern formation. We demonstrate one such application in our study of short-chain polymer analogs embedded in our system.
Accurate determination of heteroclinic orbits in chaotic dynamical systems
NASA Astrophysics Data System (ADS)
Li, Jizhou; Tomsovic, Steven
2017-03-01
Accurate calculation of heteroclinic and homoclinic orbits can be of significant importance in some classes of dynamical system problems. Yet for very strongly chaotic systems initial deviations from a true orbit will be magnified by a large exponential rate making direct computational methods fail quickly. In this paper, a method is developed that avoids direct calculation of the orbit by making use of the well-known stability property of the invariant unstable and stable manifolds. Under an area-preserving map, this property assures that any initial deviation from the stable (unstable) manifold collapses onto them under inverse (forward) iterations of the map. Using a set of judiciously chosen auxiliary points on the manifolds, long orbit segments can be calculated using the stable and unstable manifold intersections of the heteroclinic (homoclinic) tangle. Detailed calculations using the example of the kicked rotor are provided along with verification of the relation between action differences and certain areas bounded by the manifolds.
Relativistic quantum Darwinism in Dirac fermion and graphene systems
NASA Astrophysics Data System (ADS)
Ni, Xuan; Huang, Liang; Lai, Ying-Cheng; Pecora, Louis
2012-02-01
We solve the Dirac equation in two spatial dimensions in the setting of resonant tunneling, where the system consists of two symmetric cavities connected by a finite potential barrier. The shape of the cavities can be chosen to yield both regular and chaotic dynamics in the classical limit. We find that certain pointer states about classical periodic orbits can exist, which are signatures of relativistic quantum Darwinism (RQD). These localized states suppress quantum tunneling, and the effect becomes less severe as the underlying classical dynamics in the cavity is chaotic, leading to regularization of quantum tunneling. Qualitatively similar phenomena have been observed in graphene. A physical theory is developed to explain relativistic quantum Darwinism and its effects based on the spectrum of complex eigenenergies of the non-Hermitian Hamiltonian describing the open cavity system.
Sorting quantum systems efficiently
Ionicioiu, Radu
2016-01-01
Measuring the state of a quantum system is a fundamental process in quantum mechanics and plays an essential role in quantum information and quantum technologies. One method to measure a quantum observable is to sort the system in different spatial modes according to the measured value, followed by single-particle detectors on each mode. Examples of quantum sorters are polarizing beam-splitters (PBS) – which direct photons according to their polarization – and Stern-Gerlach devices. Here we propose a general scheme to sort a quantum system according to the value of any d-dimensional degree of freedom, such as spin, orbital angular momentum (OAM), wavelength etc. Our scheme is universal, works at the single-particle level and has a theoretical efficiency of 100%. As an application we design an efficient OAM sorter consisting of a single multi-path interferometer which is suitable for a photonic chip implementation. PMID:27142705
A Signal Processing Framework for the Analysis and Application of Chaotic Systems
1995-05-01
for the Analysis and Application of Chaotic Systems by Steven Hamilton Isabelle Submitted to the Department of Electrical Engineering and Computer...deconvolve a chaotic signal from a filtered observation. Thesis Supervisor: Alan V. Oppenheim Title: Distinguished Professor of Electrical Engineering Thesis...Supervisor: Gregory W. Wornell Title: Assistant Professor of Electrical Engineering 3 Acknowledgments Sometimes things work out better that you could
NASA Astrophysics Data System (ADS)
Eyre, T. M. W.
Given a polynomial function f of classical stochastic integrator processes whose differentials satisfy a closed Ito multiplication table, we can express the stochastic derivative of f as
Quantum system identification.
Burgarth, Daniel; Yuasa, Kazuya
2012-02-24
The aim of quantum system identification is to estimate the ingredients inside a black box, in which some quantum-mechanical unitary process takes place, by just looking at its input-output behavior. Here we establish a basic and general framework for quantum system identification, that allows us to classify how much knowledge about the quantum system is attainable, in principle, from a given experimental setup. We show that controllable closed quantum systems can be estimated up to unitary conjugation. Prior knowledge on some elements of the black box helps the system identification. We present an example in which a Bell measurement is more efficient to identify the system. When the topology of the system is known, the framework enables us to establish a general criterion for the estimability of the coupling constants in its Hamiltonian.
Hybrid internal model control and proportional control of chaotic dynamical systems.
Qi, Dong-lian; Yao, Liang-bin
2004-01-01
A new chaos control method is proposed to take advantage of chaos or avoid it. The hybrid Internal Model Control and Proportional Control learning scheme are introduced. In order to gain the desired robust performance and ensure the system's stability, Adaptive Momentum Algorithms are also developed. Through properly designing the neural network plant model and neural network controller, the chaotic dynamical systems are controlled while the parameters of the BP neural network are modified. Taking the Lorenz chaotic system as example, the results show that chaotic dynamical systems can be stabilized at the desired orbits by this control strategy.
Method to modify random matrix theory using short-time behavior in chaotic systems.
Smith, A Matthew; Kaplan, Lev
2009-09-01
We discuss a modification to random matrix theory (RMT) eigenstate statistics that systematically takes into account the nonuniversal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian, instead requiring only knowledge of short-time dynamics for a chaotic system or ensemble of similar systems. Standard RMT and semiclassical predictions are recovered in the limits of zero Ehrenfest time and infinite Heisenberg time, respectively. As examples, we discuss wave-function autocorrelations and cross correlations and show how the approach leads to a significant improvement in the accuracy for simple chaotic systems where comparison can be made with brute-force diagonalization.
Fuzzy adaptive synchronization of uncertain chaotic systems via delayed feedback control
NASA Astrophysics Data System (ADS)
Zhang, Lingling; Huang, Lihong; Zhang, Zhizhou; Wang, Zengyun
2008-09-01
Based on the T-S fuzzy model and the delayed feedback control (DFC) scheme, this Letter presents a robust synchronization strategy for a class of chaotic system with unknown parameters and disturbances. Being the response system, the designed robust observer can adaptively track the drive system globally. The T-S fuzzy model of the 4D chaotic system (Lorenz-Stenflo) is developed as an example for illustration. Numerical simulations are shown to verify the results.
Development of adaptive control applied to chaotic systems
NASA Astrophysics Data System (ADS)
Rhode, Martin Andreas
1997-12-01
Continuous-time derivative control and adaptive map-based recursive feedback control techniques are used to control chaos in a variety of systems and in situations that are of practical interest. The theoretical part of the research includes the review of fundamental concept of control theory in the context of its applications to deterministic chaotic systems, the development of a new adaptive algorithm to identify the linear system properties necessary for control, and the extension of the recursive proportional feedback control technique, RPF, to high dimensional systems. Chaos control was applied to models of a thermal pulsed combustor, electro-chemical dissolution and the hyperchaotic Rossler system. Important implications for combustion engineering were suggested by successful control of the model of the thermal pulsed combustor. The system was automatically tracked while maintaining control into regions of parameter and state space where no stable attractors exist. In a simulation of the electrochemical dissolution system, application of derivative control to stabilize a steady state, and adaptive RPF to stabilize a period one orbit, was demonstrated. The high dimensional adaptive control algorithm was applied in a simulation using the Rossler hyperchaotic system, where a period-two orbit with two unstable directions was stabilized and tracked over a wide range of a system parameter. In the experimental part, the electrochemical system was studied in parameter space, by scanning the applied potential and the frequency of the rotating copper disk. The automated control algorithm is demonstrated to be effective when applied to stabilize a period-one orbit in the experiment. We show the necessity of small random perturbations applied to the system in order to both learn the dynamics and control the system at the same time. The simultaneous learning and control capability is shown to be an important part of the active feedback control.
Synchronization of coupled chaotic FitzHugh-Nagumo systems
NASA Astrophysics Data System (ADS)
Aqil, Muhammad; Hong, Keum-Shik; Jeong, Myung-Yung
2012-04-01
This paper addresses dynamic synchronization of two FitzHugh-Nagumo (FHN) systems coupled with gap junctions. All the states of the coupled chaotic system, treating either as single-input or two-input control system, are synchronized by stabilizing their error dynamics, using simplest and locally robust control laws. The local asymptotic stability, chosen by utilizing the local Lipschitz nonlinear property of the model to address additionally the non-failure of the achieved synchronization, is ensured by formulating the matrix inequalities on the basis of Lyapunov stability theory. In the presence of disturbances, it ensures the local uniform ultimate boundedness. Furthermore, the robustness of the proposed methods is ensured against bounded disturbances besides providing the upper bound on disturbances. To the best of our knowledge, this is the computationally simplest solution for synchronization of coupled FHN modeled systems along with unique advantages of less conservative local asymptotic stability of synchronization errors with robustness. Numerical simulations are carried out to successfully validate the proposed control strategies.
2008-03-15
0603048 (2006) [3] Q. Zhang et al, Experimental Quantum Teleportation of a Two-Qubit Composite System, quant-ph/0609129 (2006) [4] G. Y. Xiang et...AFOSR project “ Quantum Communication Systems” University of Oxford and UMK Torun Final Report 15 March 2008 Summary This document...temporal characterization by interference with a local oscillator and the theoretical study of their propagation in lossy quantum channels. Also, their
Quantum electromechanical systems
NASA Astrophysics Data System (ADS)
Milburn, Gerard J.; Polkinghorne, Rodney
2001-11-01
We discuss the conditions under which electromechanical systems, fabricated on a sub micron scale, require a quantum description. We illustrate the discussion with the example of a mechanical electroscope for which the resonant frequency of a cantilever changes in response to a local charge. We show how such devices may be used as a quantum noise limited apparatus for detection of a single charge or spin with applications to quantum computing.
NASA Astrophysics Data System (ADS)
Sepantaie, Marc M.; Namazi, Nader M.; Sepantaie, Amir M.
2016-05-01
This paper is devoted to addressing the synchronization, and detection of random binary data exposed to inherent channel variations existing in Free Space Optical (FSO) communication systems. This task is achieved by utilizing the identical synchronization methodology of Lorenz chaotic communication system, and its synergetic interaction in adversities imposed by the FSO channel. Moreover, the Lorenz system has been analyzed, and revealed to induce Stochastic Resonance (SR) once exposed to Additive White Gaussian Noise (AWGN). In particular, the resiliency of the Lorenz chaotic system, in light of channel adversities, has been attributed to the success of the proposed communication system. Furthermore, this paper advocates the use of Haar wavelet transform for enhanced detection capability of the proposed chaotic communication system, which utilizes Chaotic Parameter Modulation (CPM) technique for means of transmission.
Dynamics of Attractively and Repulsively Coupled Elementary Chaotic Systems
NASA Astrophysics Data System (ADS)
Trinschek, Sarah; Linz, Stefan J.
We investigate an elementary model for doubly coupled dynamical systems that consists of two identical, mutually interacting minimal chaotic flows in the form of jerky dynamics. The coupling mechanisms allow for the simultaneous presence of attractive and repulsive interactions between the systems. Despite its functional simplicity, the model is capable of exhibiting diverse types of dynamical phenomena induced by the presence of the couplings. We provide an in-depth numerical investigation of the dynamics depending on the coupling strengths and the autonomous dynamical behavior of the subsystems. Partly, the dynamics of the system can be analytically understood using the Poincaré-Lindstedt method. An approximation of periodic orbits is carried out in the vicinity of a phase-flip transition that leads to deeper insights into the organization of the appearing dynamics in the parameter space. In addition, we propose a circuit that enables an electronic implementation of the model. A variation of the coupling mechanism to a coupling in conjugate variables leads to a regime of amplitude death.
On the predictability of chaotic systems with respect to maximally effective computation time
NASA Astrophysics Data System (ADS)
Xinquan, Gao; Guolin, Feng; Wenjie, Dong; Jifan, Chou
2003-04-01
The round-off error introduces uncertainty in the numerical solution. A computational uncertainty principle is explained and validated by using chaotic systems, such as the climatic model, the Rossler and super chaos system. Maximally effective computation time (MECT) and optimal stepsize (OS) are discussed and obtained via an optimal searching method. Under OS in solving nonlinear ordinary differential equations, the self-memorization equations of chaotic systems are set up, thus a new approach to numerical weather forecast is described.
The Painlevé test for nonlinear system of differential equations with complex chaotic behavior
NASA Astrophysics Data System (ADS)
Tsegel’nik, V.
2017-01-01
The Painlevé-analysis was performed for solutions of nonlinear third-order autonomous system of differential equations with quadratic nonlinearities on their right-hand sides. At certain values of two constant parameters incorporated into the system, the latter exhibits complex chaotic behavior. When the parameters attain the values corresponding to complex chaotic behavior, the system was found not to possess the Painlevé property.
Parameter estimation for chaotic systems based on improved boundary chicken swarm optimization
NASA Astrophysics Data System (ADS)
Chen, Shaolong; Yan, Renhuan
2016-10-01
Estimating unknown parameters for chaotic system is a key problem in the field of chaos control and synchronization. Through constructing an appropriate fitness function, parameter estimation of chaotic system could be converted to a multidimensional parameter optimization problem. In this paper, a new method base on improved boundary chicken swarm optimization (IBCSO) algorithm is proposed for solving the problem of parameter estimation in chaotic system. However, to the best of our knowledge, there is no published research work on chicken swarm optimization for parameters estimation of chaotic system. Computer simulation based on Lorenz system and comparisons with chicken swarm optimization, particle swarm optimization, and genetic algorithm shows the effectiveness and feasibility of the proposed method.
NASA Astrophysics Data System (ADS)
Wei, Qing-Lai; Liu, De-Rong; Xu, Yan-Cai
2015-03-01
A policy iteration algorithm of adaptive dynamic programming (ADP) is developed to solve the optimal tracking control for a class of discrete-time chaotic systems. By system transformations, the optimal tracking problem is transformed into an optimal regulation one. The policy iteration algorithm for discrete-time chaotic systems is first described. Then, the convergence and admissibility properties of the developed policy iteration algorithm are presented, which show that the transformed chaotic system can be stabilized under an arbitrary iterative control law and the iterative performance index function simultaneously converges to the optimum. By implementing the policy iteration algorithm via neural networks, the developed optimal tracking control scheme for chaotic systems is verified by a simulation. Project supported by the National Natural Science Foundation of China (Grant Nos. 61034002, 61233001, 61273140, 61304086, and 61374105) and the Beijing Natural Science Foundation, China (Grant No. 4132078).
Delocalization and quantum chaos in atom-field systems.
Bastarrachea-Magnani, M A; López-del-Carpio, B; Chávez-Carlos, J; Lerma-Hernández, S; Hirsch, J G
2016-02-01
Employing efficient diagonalization techniques, we perform a detailed quantitative study of the regular and chaotic regions in phase space in the simplest nonintegrable atom-field system, the Dicke model. A close correlation between the classical Lyapunov exponents and the quantum Participation Ratio of coherent states on the eigenenergy basis is exhibited for different points in the phase space. It is also shown that the Participation Ratio scales linearly with the number of atoms in chaotic regions and with its square root in the regular ones.
Blended particle filters for large-dimensional chaotic dynamical systems.
Majda, Andrew J; Qi, Di; Sapsis, Themistoklis P
2014-05-27
A major challenge in contemporary data science is the development of statistically accurate particle filters to capture non-Gaussian features in large-dimensional chaotic dynamical systems. Blended particle filters that capture non-Gaussian features in an adaptively evolving low-dimensional subspace through particles interacting with evolving Gaussian statistics on the remaining portion of phase space are introduced here. These blended particle filters are constructed in this paper through a mathematical formalism involving conditional Gaussian mixtures combined with statistically nonlinear forecast models compatible with this structure developed recently with high skill for uncertainty quantification. Stringent test cases for filtering involving the 40-dimensional Lorenz 96 model with a 5-dimensional adaptive subspace for nonlinear blended filtering in various turbulent regimes with at least nine positive Lyapunov exponents are used here. These cases demonstrate the high skill of the blended particle filter algorithms in capturing both highly non-Gaussian dynamical features as well as crucial nonlinear statistics for accurate filtering in extreme filtering regimes with sparse infrequent high-quality observations. The formalism developed here is also useful for multiscale filtering of turbulent systems and a simple application is sketched below.
NASA Astrophysics Data System (ADS)
Qiu, Junchao; Zhang, Lin; Li, Diyang; Liu, Xingcheng
2016-06-01
Chaotic sequences can be applied to realize multiple user access and improve the system security for a visible light communication (VLC) system. However, since the map patterns of chaotic sequences are usually well known, eavesdroppers can possibly derive the key parameters of chaotic sequences and subsequently retrieve the information. We design an advanced encryption standard (AES) interleaving aided multiple user access scheme to enhance the security of a chaotic code division multiple access-based visible light communication (C-CDMA-VLC) system. We propose to spread the information with chaotic sequences, and then the spread information is interleaved by an AES algorithm and transmitted over VLC channels. Since the computation complexity of performing inverse operations to deinterleave the information is high, the eavesdroppers in a high speed VLC system cannot retrieve the information in real time; thus, the system security will be enhanced. Moreover, we build a mathematical model for the AES-aided VLC system and derive the theoretical information leakage to analyze the system security. The simulations are performed over VLC channels, and the results demonstrate the effectiveness and high security of our presented AES interleaving aided chaotic CDMA-VLC system.
a Novel Algorithm for Image Encryption Based on Couple Chaotic Systems
NASA Astrophysics Data System (ADS)
Wang, Xing-Yuan; Wang, Tian
2012-12-01
In this paper, an image encryption algorithm based on couple multiple chaotic systems is presented. It made the one-dimensional Coupled Map Lattice (CML) formed by Skew Tent map as spatiotemporal chaotic system and made its output sequence as the initial value of logistic and meanwhile did iterative of specific times to get the final key sequence, and then did XOR operations with corresponding pixels to finish the encryption. Numerical analysis expresses that this algorithm has large enough space and high security.
Efficient sensitivity analysis method for chaotic dynamical systems
Liao, Haitao
2016-05-15
The direct differentiation and improved least squares shadowing methods are both developed for accurately and efficiently calculating the sensitivity coefficients of time averaged quantities for chaotic dynamical systems. The key idea is to recast the time averaged integration term in the form of differential equation before applying the sensitivity analysis method. An additional constraint-based equation which forms the augmented equations of motion is proposed to calculate the time averaged integration variable and the sensitivity coefficients are obtained as a result of solving the augmented differential equations. The application of the least squares shadowing formulation to the augmented equations results in an explicit expression for the sensitivity coefficient which is dependent on the final state of the Lagrange multipliers. The LU factorization technique to calculate the Lagrange multipliers leads to a better performance for the convergence problem and the computational expense. Numerical experiments on a set of problems selected from the literature are presented to illustrate the developed methods. The numerical results demonstrate the correctness and effectiveness of the present approaches and some short impulsive sensitivity coefficients are observed by using the direct differentiation sensitivity analysis method.
Saiki, Yoshitaka; Yamada, Michio
2009-01-01
It has recently been found in some dynamical systems in fluid dynamics that only a few unstable periodic orbits (UPOs) with low periods can give good approximations to the mean properties of turbulent (chaotic) solutions. By employing three chaotic systems described by ordinary differential equations, we compare time-averaged properties of a set of UPOs and those of a set of segments of chaotic orbits. For every chaotic system we study, the distributions of a time average of a dynamical variable along UPOs with lower and higher periods are similar to each other and the variance of the distribution is small, in contrast with that along chaotic segments. The distribution seems to converge to some limiting distribution with nonzero variance as the period of the UPO increases, although that along chaotic orbits inclines to converge to a delta -like distribution. These properties seem to lie in the background of why only a few UPOs with low periods can give good mean statistical properties in dynamical systems in fluid dynamics.
Danilov, Viatcheslav; Nagaitsev, Sergei; /Fermilab
2011-11-01
Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and nonlinear integrable plasma traps. Now, all classical results are carried over to a nonrelativistic quantum case. In this paper we have described an extension of the Ermakov-like transformation to the Schroedinger and Pauli equations. It is shown that these newly found transformations create a vast variety of time dependent quantum equations that can be solved in analytic functions, or, at least, can be reduced to time-independent ones.
NASA Astrophysics Data System (ADS)
Xu, Fei
In this article, we present a systematic approach to design chaos generators using integer order and fractional order differential equation systems. A series of multiwing chaotic attractors and grid multiwing chaotic attractors are obtained using linear integer order differential equation systems with switching controls. The existence of chaotic attractors in the corresponding fractional order differential equation systems is also investigated. We show that, using the nonlinear fractional order differential equation system, or linear fractional order differential equation systems with switching controls, a series of multiwing chaotic attractors can be obtained.
Eigenstate tracking in open quantum systems
NASA Astrophysics Data System (ADS)
Jing, Jun; Sarandy, Marcelo S.; Lidar, Daniel A.; Luo, Da-Wei; Wu, Lian-Ao
2016-10-01
Keeping a quantum system in a given instantaneous eigenstate is a control problem with numerous applications, e.g., in quantum information processing. The problem is even more challenging in the setting of open quantum systems, where environment-mediated transitions introduce additional decoherence channels. Adiabatic passage is a well-established solution but requires a sufficiently slow evolution time that is dictated by the adiabatic theorem. Here we develop a systematic projection theory formulation for the transitionless evolution of general open quantum systems described by time-local master equations. We derive a time-convolutionless dynamical equation for the target instantaneous eigenstate of a given time-dependent Hamiltonian. A transitionless dynamics then arises in terms of a competition between the average Hamiltonian gap and the decoherence rate, which implies optimal adiabaticity timescales. We show how eigenstate tracking can be accomplished via control pulses, without explicitly incorporating counter-diabatic driving, thus offering an alternative route to accelerate adiabaticity. We examine rectangular pulses, chaotic signals, and white noise, and find that, remarkably, the effectiveness of eigenstate tracking hardly depends on the details of the control functions. In all cases the control protocol keeps the system in the desired instantaneous eigenstate throughout the entire evolution, along an accelerated adiabatic path.
Engineering quantum communication systems
NASA Astrophysics Data System (ADS)
Pinto, Armando N.; Almeida, Álvaro J.; Silva, Nuno A.; Muga, Nelson J.; Martins, Luis M.
2012-06-01
Quantum communications can provide almost perfect security through the use of quantum laws to detect any possible leak of information. We discuss critical issues in the implementation of quantum communication systems over installed optical fibers. We use stimulated four-wave mixing to generate single photons inside optical fibers, and by tuning the separation between the pump and the signal we adjust the average number of photons per pulse. We report measurements of the source statistics and show that it goes from a thermal to Poisson distribution with the increase of the pump power. We generate entangled photons pairs through spontaneous four-wave mixing. We report results for different type of fibers to approach the maximum value of the Bell inequality. We model the impact of polarization rotation, attenuation and Raman scattering and present optimum configurations to increase the degree of entanglement. We encode information in the photons polarization and assess the use of wavelength and time division multiplexing based control systems to compensate for the random rotation of the polarization during transmission. We show that time division multiplexing systems provide a more robust solution considering the values of PMD of nowadays installed fibers. We evaluate the impact on the quantum channel of co-propagating classical channels, and present guidelines for adding quantum channels to installed WDM optical communication systems without strongly penalizing the performance of the quantum channel. We discuss the process of retrieving information from the photons polarization. We identify the major impairments that limit the speed and distance of the quantum channel. Finally, we model theoretically the QBER and present results of an experimental performance assessment of the system quality through QBER measurements.
Quantum Image Encryption Algorithm Based on Quantum Image XOR Operations
NASA Astrophysics Data System (ADS)
Gong, Li-Hua; He, Xiang-Tao; Cheng, Shan; Hua, Tian-Xiang; Zhou, Nan-Run
2016-07-01
A novel encryption algorithm for quantum images based on quantum image XOR operations is designed. The quantum image XOR operations are designed by using the hyper-chaotic sequences generated with the Chen's hyper-chaotic system to control the control-NOT operation, which is used to encode gray-level information. The initial conditions of the Chen's hyper-chaotic system are the keys, which guarantee the security of the proposed quantum image encryption algorithm. Numerical simulations and theoretical analyses demonstrate that the proposed quantum image encryption algorithm has larger key space, higher key sensitivity, stronger resistance of statistical analysis and lower computational complexity than its classical counterparts.
Eigenstate Gibbs ensemble in integrable quantum systems
NASA Astrophysics Data System (ADS)
Nandy, Sourav; Sen, Arnab; Das, Arnab; Dhar, Abhishek
2016-12-01
The eigenstate thermalization hypothesis conjectures that for a thermodynamically large system in one of its energy eigenstates, the reduced density matrix describing any finite subsystem is determined solely by a set of relevant conserved quantities. In a chaotic quantum system, only the energy is expected to play that role and hence eigenstates appear locally thermal. Integrable systems, on the other hand, possess an extensive number of such conserved quantities and therefore the reduced density matrix requires specification of all the corresponding parameters (generalized Gibbs ensemble). However, here we show by unbiased statistical sampling of the individual eigenstates with a given finite energy density that the local description of an overwhelming majority of these states of even such an integrable system is actually Gibbs-like, i.e., requires only the energy density of the eigenstate. Rare eigenstates that cannot be represented by the Gibbs ensemble can also be sampled efficiently by our method and their local properties are then shown to be described by appropriately truncated generalized Gibbs ensembles. We further show that the presence of these rare eigenstates differentiates the model from the chaotic case and leads to the system being described by a generalized Gibbs ensemble at long time under a unitary dynamics following a sudden quench, even when the initial state is a typical (Gibbs-like) eigenstate of the prequench Hamiltonian.
Integrating random matrix theory predictions with short-time dynamical effects in chaotic systems.
Smith, A Matthew; Kaplan, Lev
2010-07-01
We discuss a modification to random matrix theory eigenstate statistics that systematically takes into account the nonuniversal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian; instead it requires only knowledge of short-time dynamics for a chaotic system or ensemble of similar systems. Standard random matrix theory and semiclassical predictions are recovered in the limits of zero Ehrenfest time and infinite Heisenberg time, respectively. As examples, we discuss wave-function autocorrelations and cross correlations, and show that significant improvement in accuracy is obtained for simple chaotic systems where comparison can be made with brute-force diagonalization. The accuracy of the method persists even when the short-time dynamics of the system or ensemble is known only in a classical approximation. Further improvement in the rate of convergence is obtained when the method is combined with the correlation function bootstrapping approach introduced previously.
Robust synchronization of chaotic Lur'e systems via delayed feedback control
NASA Astrophysics Data System (ADS)
Chen, Cailian; Feng, Gang; Guan, Xinping
2004-02-01
This Letter presents a robust synchronization method for a class of chaotic Lur'e systems based on its T-S fuzzy model and the delayed feedback control (DFC) scheme. The controlled slave system can adaptively track the master system under the circumstances of system uncertainties and external disturbances.
Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
NASA Astrophysics Data System (ADS)
Rozenbaum, Efim B.; Ganeshan, Sriram; Galitski, Victor
2017-02-01
It was proposed recently that the out-of-time-ordered four-point correlator (OTOC) may serve as a useful characteristic of quantum-chaotic behavior, because, in the semiclassical limit ℏ→0 , its rate of exponential growth resembles the classical Lyapunov exponent. Here, we calculate the four-point correlator C (t ) for the classical and quantum kicked rotor—a textbook driven chaotic system—and compare its growth rate at initial times with the standard definition of the classical Lyapunov exponent. Using both quantum and classical arguments, we show that the OTOC's growth rate and the Lyapunov exponent are, in general, distinct quantities, corresponding to the logarithm of the phase-space averaged divergence rate of classical trajectories and to the phase-space average of the logarithm, respectively. The difference appears to be more pronounced in the regime of low kicking strength K , where no classical chaos exists globally. In this case, the Lyapunov exponent quickly decreases as K →0 , while the OTOC's growth rate may decrease much slower, showing a higher sensitivity to small chaotic islands in the phase space. We also show that the quantum correlator as a function of time exhibits a clear singularity at the Ehrenfest time tE: transitioning from a time-independent value of t-1ln C (t ) at t
Scheme of thinking quantum systems
NASA Astrophysics Data System (ADS)
Yukalov, V. I.; Sornette, D.
2009-11-01
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of probability operators, associated with the possible options available to the decision maker, plays the role of the algebra of observables in quantum theory of measurements. A scheme is advanced for a practical realization of decision procedures by thinking quantum systems. Such thinking quantum systems can be realized by using spin lattices, systems of magnetic molecules, cold atoms trapped in optical lattices, ensembles of quantum dots, or multilevel atomic systems interacting with electromagnetic field.
Physical layer security in CO-OFDM transmission system using chaotic scrambling
NASA Astrophysics Data System (ADS)
Liu, Bo; Zhang, Lijia; Xin, Xiangjun; Yu, Jianjun
2013-03-01
This paper proposes a novel method for the optical OFDM system to improve the physical layer security based on chaotic scrambling. The 1-D Logistic map is adopted for chaos mapping. The chaotic scrambling algorithm can dynamically change the scrambling matrices according to the secure key, which further enhances the confidentiality of the physical layer. The experiment with Logistic mapped chaos scrambling is also given to demonstrate the efficiency of security algorithm. Meanwhile, the benchmark performance of the optical OFDM system is experimentally investigated in terms of the bit error rate (BER). The analysis indicates that the system can be robust against eavesdropping.
Chaotic transition in a three-coupled phase-locked loop system.
Tsuruda, Hidekatsu; Shirahama, Hiroyuki; Fukushima, Kazuhiro; Nagadome, Masakazu; Inoue, Masayoshi
2001-06-01
The chaotic transition is observed in a three-coupled phase-locked loop (PLL) system in both experiments and numerical simulations. In this system, three PLL oscillators are connected with the periodic boundary condition. Intermittency is found in partially synchronized phase, in which two of three oscillators synchronize with each other and form a pair, and the chaotic transition occurs due to the recombination of synchronized pairs so that different pair is re-formed. In this phase, on-off intermittency is also observed and statistical analyses are carried out for on-off intermittent time series. This intermittency is considered as a hybrid type of intermittency with both on-off intermittency and intermittency due to the recombination of synchronized pairs present in the same time series. We also show the chaotic transition phenomena in a three-coupled logistic map system. (c) 2001 American Institute of Physics.
Control of long-period orbits and arbitrary trajectories in chaotic systems using dynamic limiting.
Corron, Ned J.; Pethel, Shawn D.
2002-03-01
We demonstrate experimental control of long-period orbits and arbitrary chaotic trajectories using a new chaos control technique called dynamic limiting. Based on limiter control, dynamic limiting uses a predetermined sequence of limiter levels applied to the chaotic system to stabilize natural states of the system. The limiter sequence is clocked by the natural return time of the chaotic system such that the oscillator sees a new limiter level for each peak return. We demonstrate control of period-8 and period-34 unstable periodic orbits in a low-frequency circuit and provide evidence that the control perturbations are minimal. We also demonstrate control of an arbitrary waveform by replaying a sequence captured from the uncontrolled oscillator, achieving a form of delayed self-synchronization. Finally, we discuss the use of dynamic limiting for high-frequency chaos communications. (c) 2002 American Institute of Physics.
Experimental verification of chaotic control of an underactuated tethered satellite system
NASA Astrophysics Data System (ADS)
Pang, Zhaojun; Jin, Dongping
2016-03-01
This paper studies chaotic control of a tethered satellite system (TSS) driven only by a momentum-exchange device during its attitude adjustment. In dealing with such the underactuated system, an extended time-delay autosynchronization (ETDAS) is employed to stabilize the chaotic motion to a periodic motion. To obtain the control domains of the ETDAS method, a stability analysis of the controlled tethered satellite system in elliptical orbit is implemented. According to the principle of dynamic similarity, then, ground-based experiment setups are proposed and designed to emulate the in-plane motions of the TSS. Representative experiments are presented to demonstrate the effectiveness of the ETDAS scheme in controlling the chaotic motion of the underactuated TSS.
Wang, Jun; Zhou, Bihua; Zhou, Shudao
2016-01-01
This paper proposes an improved cuckoo search (ICS) algorithm to establish the parameters of chaotic systems. In order to improve the optimization capability of the basic cuckoo search (CS) algorithm, the orthogonal design and simulated annealing operation are incorporated in the CS algorithm to enhance the exploitation search ability. Then the proposed algorithm is used to establish parameters of the Lorenz chaotic system and Chen chaotic system under the noiseless and noise condition, respectively. The numerical results demonstrate that the algorithm can estimate parameters with high accuracy and reliability. Finally, the results are compared with the CS algorithm, genetic algorithm, and particle swarm optimization algorithm, and the compared results demonstrate the method is energy-efficient and superior. PMID:26880874
Wang, Jun; Zhou, Bihua; Zhou, Shudao
2016-01-01
This paper proposes an improved cuckoo search (ICS) algorithm to establish the parameters of chaotic systems. In order to improve the optimization capability of the basic cuckoo search (CS) algorithm, the orthogonal design and simulated annealing operation are incorporated in the CS algorithm to enhance the exploitation search ability. Then the proposed algorithm is used to establish parameters of the Lorenz chaotic system and Chen chaotic system under the noiseless and noise condition, respectively. The numerical results demonstrate that the algorithm can estimate parameters with high accuracy and reliability. Finally, the results are compared with the CS algorithm, genetic algorithm, and particle swarm optimization algorithm, and the compared results demonstrate the method is energy-efficient and superior.
Characterization of normality of chaotic systems including prediction and detection of anomalies
NASA Astrophysics Data System (ADS)
Engler, Joseph John
Accurate prediction and control pervades domains such as engineering, physics, chemistry, and biology. Often, it is discovered that the systems under consideration cannot be well represented by linear, periodic nor random data. It has been shown that these systems exhibit deterministic chaos behavior. Deterministic chaos describes systems which are governed by deterministic rules but whose data appear to be random or quasi-periodic distributions. Deterministically chaotic systems characteristically exhibit sensitive dependence upon initial conditions manifested through rapid divergence of states initially close to one another. Due to this characterization, it has been deemed impossible to accurately predict future states of these systems for longer time scales. Fortunately, the deterministic nature of these systems allows for accurate short term predictions, given the dynamics of the system are well understood. This fact has been exploited in the research community and has resulted in various algorithms for short term predictions. Detection of normality in deterministically chaotic systems is critical in understanding the system sufficiently to able to predict future states. Due to the sensitivity to initial conditions, the detection of normal operational states for a deterministically chaotic system can be challenging. The addition of small perturbations to the system, which may result in bifurcation of the normal states, further complicates the problem. The detection of anomalies and prediction of future states of the chaotic system allows for greater understanding of these systems. The goal of this research is to produce methodologies for determining states of normality for deterministically chaotic systems, detection of anomalous behavior, and the more accurate prediction of future states of the system. Additionally, the ability to detect subtle system state changes is discussed. The dissertation addresses these goals by proposing new representational
Wave chaotic experiments and models for complicated wave scattering systems
NASA Astrophysics Data System (ADS)
Yeh, Jen-Hao
Wave scattering in a complicated environment is a common challenge in many engineering fields because the complexity makes exact solutions impractical to find, and the sensitivity to detail in the short-wavelength limit makes a numerical solution relevant only to a specific realization. On the other hand, wave chaos offers a statistical approach to understand the properties of complicated wave systems through the use of random matrix theory (RMT). A bridge between the theory and practical applications is the random coupling model (RCM) which connects the universal features predicted by RMT and the specific details of a real wave scattering system. The RCM gives a complete model for many wave properties and is beneficial for many physical and engineering fields that involve complicated wave scattering systems. One major contribution of this dissertation is that I have utilized three microwave systems to thoroughly test the RCM in complicated wave systems with varied loss, including a cryogenic system with a superconducting microwave cavity for testing the extremely-low-loss case. I have also experimentally tested an extension of the RCM that includes short-orbit corrections. Another novel result is development of a complete model based on the RCM for the fading phenomenon extensively studied in the wireless communication fields. This fading model encompasses the traditional fading models as its high-loss limit case and further predicts the fading statistics in the low-loss limit. This model provides the first physical explanation for the fitting parameters used in fading models. I have also applied the RCM to additional experimental wave properties of a complicated wave system, such as the impedance matrix, the scattering matrix, the variance ratio, and the thermopower. These predictions are significant for nuclear scattering, atomic physics, quantum transport in condensed matter systems, electromagnetics, acoustics, geophysics, etc.
NASA Astrophysics Data System (ADS)
Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Perez-Pinacho, Claudia A.
2014-06-01
The main issue of this work is related with the design of a class of nonlinear observer in order to synchronize chaotic dynamical systems in a master-slave scheme, considering different initial conditions. The oscillator of Chen is proposed as a benchmark model and a bounded-type observer is proposed to reach synchronicity between both two chaotic systems. The proposed observer contains a proportional and sigmoid form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Some numerical simulations were carrying out in order to show the operation of the proposed methodology, with possible applications to secure data communications issues.
NASA Astrophysics Data System (ADS)
Bogomolov, Sergey A.; Slepnev, Andrei V.; Strelkova, Galina I.; Schöll, Eckehard; Anishchenko, Vadim S.
2017-02-01
We explore the bifurcation transition from coherence to incoherence in ensembles of nonlocally coupled chaotic systems. It is firstly shown that two types of chimera states, namely, amplitude and phase, can be found in a network of coupled logistic maps, while only amplitude chimera states can be observed in a ring of continuous-time chaotic systems. We reveal a bifurcation mechanism by analyzing the evolution of space-time profiles and the coupling function with varying coupling coefficient and formulate the necessary and sufficient conditions for realizing the chimera states in the ensembles.
Synchronization in node of complex networks consist of complex chaotic system
Wei, Qiang; Xie, Cheng-jun; Liu, Hong-jun; Li, Yan-hui
2014-07-15
A new synchronization method is investigated for node of complex networks consists of complex chaotic system. When complex networks realize synchronization, different component of complex state variable synchronize up to different scaling complex function by a designed complex feedback controller. This paper change synchronization scaling function from real field to complex field for synchronization in node of complex networks with complex chaotic system. Synchronization in constant delay and time-varying coupling delay complex networks are investigated, respectively. Numerical simulations are provided to show the effectiveness of the proposed method.
Analysis of the time structure of synchronization in multidimensional chaotic systems
Makarenko, A. V.
2015-05-15
A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during synchronization of chaotic oscillations in the T-synchronization mode. A system of two identical logistic mappings with unidirectional coupling that operate in the developed chaos regime is analyzed. It is shown that the widely used approach, in which only synchronization patterns are subjected to analysis while desynchronization areas are considered as a background signal and removed from analysis, should be regarded as methodologically incomplete.
Predictive Poincaré control: A control theory for chaotic systems
NASA Astrophysics Data System (ADS)
Schweizer, Jörg; Kennedy, Michael Peter
1995-11-01
One of the most interesting features of chaotic systems is the large number of unstable orbits embedded in a chaotic attractor. In this work, we propose a global chaos-control technique called predictive Poincaré control (PPC) that permits stabilization of a predefined solution, using only small control pulses. We prove this result for a large class of n-dimensional chaotic systems. The predefined solution can be a periodic or nonperiodic oscillation, expressed by a periodic or nonperiodic symbolic sequence [S. Hayes, C. Grebogi, and E. Ott, Phys. Rev. Lett. 70, 3031 (1993)]. We apply the general PPC scheme to the well known Lorenz model and study its robustness with respect to parasitic effects.
Kolovsky, A.R.
1997-08-01
We study the spectral properties of the evolution operator of a quantum particle subject to a space-periodic time-dependent potential. Two qualitatively different regimes of the system dynamics are compared: case (i), when the spreading of the wave packet is asymptotically ballistic; and case (ii), when the wave packet spreads diffusively. As time increases, the spectrum is shown to approach Poisson statistics in case (i) and circular unitary ensemble statistics in case (ii). A scaling relation for the velocity and curvature distributions of the spectral bands are found. {copyright} {ital 1997} {ital The American Physical Society}
NASA Astrophysics Data System (ADS)
Drótos, G.; Jung, C.
2016-06-01
The topic of this paper is hyperbolic chaotic scattering in a three degrees of freedom system. We generalize how shadows in the domain of the doubly differential cross-section are found: they are traced out by the appropriately filtered unstable manifolds of the periodic trajectories in the chaotic saddle. These shadows are related to the rainbow singularities in the doubly differential cross-section. As a result of this relation, we discover a method of how to recognize in the cross section a smoothly deformed image of the chaotic saddle, allowing the reconstruction of the symbolic dynamics of the chaotic saddle, its topology and its scaling factors.
Chaotic component obscured by strong periodicity in voice production system
Tao, Chao; Jiang, Jack J.
2010-01-01
The effect of glottal aerodynamics in producing the nonlinear characteristics of voice is investigated by comparing the outputs of the asymmetric composite model and the two-mass model. The two-mass model assumes the glottal airflow to be laminar, nonviscous, and incompressible. In this model, when the asymmetric factor is decreased from 0.65 to 0.35, only 1:1 and 1:2 modes are detectable. However, with the same parameters, four vibratory modes (1:1, 1:2, 2:4, 2:6) are found in the asymmetric composite model using the Navier-Stokes equations to describe the complex aerodynamics in the glottis. Moreover, the amplitude of the waveform is modulated by a small-amplitude noiselike series. The nonlinear detection method reveals that this noiselike modulation is not random, but rather it is deterministic chaos. This result agrees with the phenomenon often seen in voice, in which the voice signal is strongly periodic but modulated by a small-amplitude chaotic component. The only difference between the two-mass model and the composite model is in their descriptions of glottal airflow. Therefore, the complex aerodynamic characteristics of glottal airflow could be important in generating the nonlinear dynamic behavior of voice production, including bifurcation and a small-amplitude chaotic component obscured by strong periodicity. PMID:18643315
Ergodic dynamics and thermalization in an isolated quantum system
NASA Astrophysics Data System (ADS)
Neill, C.; Roushan, P.; Fang, M.; Chen, Y.; Kolodrubetz, M.; Chen, Z.; Megrant, A.; Barends, R.; Campbell, B.; Chiaro, B.; Dunsworth, A.; Jeffrey, E.; Kelly, J.; Mutus, J.; O'Malley, P. J. J.; Quintana, C.; Sank, D.; Vainsencher, A.; Wenner, J.; White, T. C.; Polkovnikov, A.; Martinis, J. M.
2016-11-01
Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however, the occurrence of ergodic behaviour has remained an outstanding question. Here, we demonstrate ergodic dynamics in a small quantum system consisting of only three superconducting qubits. The qubits undergo a sequence of rotations and interactions and we measure the evolution of the density matrix. Maps of the entanglement entropy show that the full system can act like a reservoir for individual qubits, increasing their entropy through entanglement. Surprisingly, these maps bear a strong resemblance to the phase space dynamics in the classical limit; classically, chaotic motion coincides with higher entanglement entropy. We further show that in regions of high entropy the full multi-qubit system undergoes ergodic dynamics. Our work illustrates how controllable quantum systems can investigate fundamental questions in non-equilibrium thermodynamics.
A Double-Wing Chaotic System Based on Ion Migration Memristor and Its Sliding Mode Control
NASA Astrophysics Data System (ADS)
Min, Guoqi; Duan, Shukai; Wang, Lidan
The ion migration memristor is a nonlinear element with memory function and nanoscale size, it is considered as a potential candidate to reduce system power consumption and circuit size. When it works as the nonlinear part of the chaotic system, rich nonlinear curves will be produced, and at the same time, the complexity of chaotic systems and the randomness of signals will be enhanced. So in this paper, by Matlab numerical simulation, a new double-wing chaotic system based on an ion migration memristor is designed. In reality, there are many systems interfered inevitably by random noise, so in this paper the random bounded noises are also considered. The power spectrum, Lyapunov exponent spectrum, Poincaré map and bifurcation diagram are used to investigate its complex dynamic characteristics. Then, a SPICE-based analog circuit is presented to verify the feasibility of the system, for which the simulation results are consistent with the numerical simulation. Finally, the sliding mode variable structure control is applied to overcome the shortcomings of traditional control method, so that the chaotic orbits can be controlled to any fixed points or periodic orbits, and this provides an insight into chaos control in power electronics systems.
NASA Astrophysics Data System (ADS)
Manos, Thanos; Robnik, Marko
2013-06-01
We study the kicked rotator in the classically fully chaotic regime using Izrailev's N-dimensional model for various N≤4000, which in the limit N→∞ tends to the quantized kicked rotator. We do treat not only the case K=5, as studied previously, but also many different values of the classical kick parameter 5≤K≤35 and many different values of the quantum parameter k∈[5,60]. We describe the features of dynamical localization of chaotic eigenstates as a paradigm for other both time-periodic and time-independent (autonomous) fully chaotic or/and mixed-type Hamilton systems. We generalize the scaling variable Λ=l∞/N to the case of anomalous diffusion in the classical phase space by deriving the localization length l∞ for the case of generalized classical diffusion. We greatly improve the accuracy and statistical significance of the numerical calculations, giving rise to the following conclusions: (1) The level-spacing distribution of the eigenphases (or quasienergies) is very well described by the Brody distribution, systematically better than by other proposed models, for various Brody exponents βBR. (2) We study the eigenfunctions of the Floquet operator and characterize their localization properties using the information entropy measure, which after normalization is given by βloc in the interval [0,1]. The level repulsion parameters βBR and βloc are almost linearly related, close to the identity line. (3) We show the existence of a scaling law between βloc and the relative localization length Λ, now including the regimes of anomalous diffusion. The above findings are important also for chaotic eigenstates in time-independent systems [Batistić and Robnik, J. Phys. A: Math. Gen.1751-811310.1088/1751-8113/43/21/215101 43, 215101 (2010); arXiv:1302.7174 (2013)], where the Brody distribution is confirmed to a very high degree of precision for dynamically localized chaotic eigenstates, even in the mixed-type systems (after separation of regular and
2013-02-15
Universiti Teknikal Malaysia Melaka in Malaysia. The project was then used to partially support a new PhD student, Mr Shanon Vuglar (who is a former...method based on cascade realization of quantum systems is used and a conference and journal paper have been produced. In another approach, a method...based on singular perturbation is used and a conference and journal paper have resulted. This work was extended by the graduate student Shanon Vuglar to
Application of Ica-Eemd to Secure Communications in Chaotic Systems
NASA Astrophysics Data System (ADS)
Lin, Shih-Lin; Tung, Pi-Cheng; Huang, Norden E.
2012-04-01
We propose the application of ICA-EEMD to secure communication systems. ICA-EEMD is employed to retrieve the message data encrypted by a mixture of Gaussian white noise and chaotic noise. The results showed that ICA-EEMD can effectively extract the two original message data.
NASA Astrophysics Data System (ADS)
Fallahi, Kia; Raoufi, Reza; Khoshbin, Hossein
2008-07-01
In recent years chaotic secure communication and chaos synchronization have received ever increasing attention. In this paper a chaotic communication method using extended Kalman filter is presented. The chaotic synchronization is implemented by EKF design in the presence of channel additive noise and processing noise. Encoding chaotic communication is used to achieve a satisfactory, typical secure communication scheme. In the proposed system, a multi-shift cipher algorithm is also used to enhance the security and the key cipher is chosen as one of the chaos states. The key estimate is employed to recover the primary data. To illustrate the effectiveness of the proposed scheme, a numerical example based on Chen dynamical system is presented and the results are compared to two other chaotic systems.
Wang, Rong; Gao, Jin-Yue
2005-09-01
In this paper we propose a new scheme to achieve chaos control and synchronization in Bragg acousto-optic bistable systems. In the scheme, we use the output of one system to drive two identical chaotic systems. Using the maximal conditional Lyapunov exponent (MCLE) as the criterion, we analyze the conditions for realizing chaos synchronization. Numerical calculation shows that the two identical systems in chaos with negative MCLEs and driven by a chaotic system can go into chaotic synchronization whether or not they were in chaos initially. The two systems can go into different periodic states from chaos following an inverse period-doubling bifurcation route as well when driven by a periodic system.
A solid-state microwave-range self-oscillating chaotic system with a simplified structure
NASA Astrophysics Data System (ADS)
Maksimov, N. A.; Panas, A. I.
2017-02-01
A solid-state self-oscillating system that provides generation of ultra-wideband chaotic signals in the microwave range has been proposed, implemented, and studied. The system has a simple structure comprising an active element (bipolar transistor) and a single reactive element (inductance). An experimental study of bifurcation phenomena and typical oscillation modes in the system has been carried out. The energy efficiency of the system and the possibility of its implementation in the form of a chip structure are analyzed.
Projective synchronization in coupled fractional order chaotic Rossler system and its control
NASA Astrophysics Data System (ADS)
Shao, Shi-Quan; Gao, Xin; Liu, Xing-Wen
2007-09-01
This paper proposes a method to achieve projective synchronization of the fractional order chaotic Rossler system. First, construct the fractional order Rossler system's corresponding approximate integer order system, then a control method based on a partially linear decomposition and negative feedback of state errors is utilized on the new integer order system. Mathematic analyses prove the feasibility and the numerical simulations show the effectiveness of the proposed method.
Chaotic attractors based on unstable dissipative systems via third-order differential equation
NASA Astrophysics Data System (ADS)
Campos-Cantón, E.
2016-07-01
In this paper, we present an approach how to yield 1D, 2D and 3D-grid multi-scroll chaotic systems in R3 based on unstable dissipative systems via third-order differential equation. This class of systems is constructed by a switching control law(SCL) changing the equilibrium point of an unstable dissipative system. The switching control law that governs the position of the equilibrium point varies according to the number of scrolls displayed in the attractor.
Shooshtari, Behnaz Koocheck; Forouzanfar, AbdolMohammad; Molaei, MohammadReza
2016-01-01
In this article a non-autonomous unified chaotic system with continuous periodic switch between the Chen and Lorenz systems is introduced. Dynamical behaviors of this system are investigated. We consider the identical (complete) synchronization of the bi-directionally coupled between two identical systems of this type and then analyze its stability by estimating the entire Lyapunov characteristic exponent spectrum. Numerical and graphical works are done with Mathematica.
Multivariate permutation entropy and its application for complexity analysis of chaotic systems
NASA Astrophysics Data System (ADS)
He, Shaobo; Sun, Kehui; Wang, Huihai
2016-11-01
To measure the complexity of multivariate systems, the multivariate permutation entropy (MvPE) algorithm is proposed. It is employed to measure complexity of multivariate system in the phase space. As an application, MvPE is applied to analyze the complexity of chaotic systems, including hyperchaotic Hénon map, fractional-order simplified Lorenz system and financial chaotic system. Results show that MvPE algorithm is effective for analyzing the complexity of the multivariate systems. It also shows that fractional-order system does not become more complex with derivative order varying. Compared with PE, MvPE has better robustness for noise and sampling interval, and the results are not affected by different normalization methods.
Roadmap on quantum optical systems
NASA Astrophysics Data System (ADS)
Dumke, Rainer; Lu, Zehuang; Close, John; Robins, Nick; Weis, Antoine; Mukherjee, Manas; Birkl, Gerhard; Hufnagel, Christoph; Amico, Luigi; Boshier, Malcolm G.; Dieckmann, Kai; Li, Wenhui; Killian, Thomas C.
2016-09-01
This roadmap bundles fast developing topics in experimental optical quantum sciences, addressing current challenges as well as potential advances in future research. We have focused on three main areas: quantum assisted high precision measurements, quantum information/simulation, and quantum gases. Quantum assisted high precision measurements are discussed in the first three sections, which review optical clocks, atom interferometry, and optical magnetometry. These fields are already successfully utilized in various applied areas. We will discuss approaches to extend this impact even further. In the quantum information/simulation section, we start with the traditionally successful employed systems based on neutral atoms and ions. In addition the marvelous demonstrations of systems suitable for quantum information is not progressing, unsolved challenges remain and will be discussed. We will also review, as an alternative approach, the utilization of hybrid quantum systems based on superconducting quantum devices and ultracold atoms. Novel developments in atomtronics promise unique access in exploring solid-state systems with ultracold gases and are investigated in depth. The sections discussing the continuously fast-developing quantum gases include a review on dipolar heteronuclear diatomic gases, Rydberg gases, and ultracold plasma. Overall, we have accomplished a roadmap of selected areas undergoing rapid progress in quantum optics, highlighting current advances and future challenges. These exciting developments and vast advances will shape the field of quantum optics in the future.
NASA Astrophysics Data System (ADS)
Vaidyanathan, S.
2014-06-01
This paper proposes a eight-term 3-D polynomial chaotic system with three quadratic nonlinearities and describes its properties. The maximal Lyapunov exponent (MLE) of the proposed 3-D chaotic system is obtained as L 1 = 6.5294. Next, new results are derived for the global chaos synchronization of the identical eight-term 3-D chaotic systems with unknown system parameters using adaptive control. Lyapunov stability theory has been applied for establishing the adaptive synchronization results. Numerical simulations are shown using MATLAB to describe the main results derived in this paper.
From generalized synchrony to topological decoherence: emergent sets in coupled chaotic systems.
Barreto, E; So, P; Gluckman, B J; Schiff, S J
2000-02-21
We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical transition point in its development (the decoherence transition). For asymmetric systems we also describe a migration of unstable periodic orbits that is of central importance in understanding these systems. Our framework provides an experimentally measurable transition, even in situations where previously described bifurcation structures are inapplicable.
Time fluctuations in isolated quantum systems of interacting particles.
Zangara, Pablo R; Dente, Axel D; Torres-Herrera, E J; Pastawski, Horacio M; Iucci, Aníbal; Santos, Lea F
2013-09-01
Numerically, we study the time fluctuations of few-body observables after relaxation in isolated dynamical quantum systems of interacting particles. Our results suggest that they decay exponentially with system size in both regimes, integrable and chaotic. The integrable systems considered are solvable with the Bethe ansatz and have a highly nondegenerate spectrum. This is in contrast with integrable Hamiltonians mappable to noninteracting ones. We show that the coefficient of the exponential decay depends on the level of delocalization of the initial state with respect to the energy shell.
NASA Astrophysics Data System (ADS)
Li, Xiang-Tao; Yin, Ming-Hao
2012-05-01
We study the parameter estimation of a nonlinear chaotic system, which can be essentially formulated as a multidimensional optimization problem. In this paper, an orthogonal learning cuckoo search algorithm is used to estimate the parameters of chaotic systems. This algorithm can combine the stochastic exploration of the cuckoo search and the exploitation capability of the orthogonal learning strategy. Experiments are conducted on the Lorenz system and the Chen system. The proposed algorithm is used to estimate the parameters for these two systems. Simulation results and comparisons demonstrate that the proposed algorithm is better or at least comparable to the particle swarm optimization and the genetic algorithm when considering the quality of the solutions obtained.
Robust adaptive synchronization of Rossler and Chen chaotic systems via slide technique
NASA Astrophysics Data System (ADS)
Li, Zhi; Shi, Songjiao
2003-05-01
This Letter considers the robust adaptive synchronization problem of Rossler and Chen chaotic systems with different time-varying unknown parameters. When system's unknown parameters vary in bound intervals and the bounds of intervals are unknown, a robust adaptive controller is designed. In order to increase the robustness of the closed loop systems, the key idea is that a sliding mode type of controller is employed. Besides, instead of the estimate values of systems' unknown parameters being taken as updating object, a new updating object is introduced in constructing controller. The proposed controller can make the states of Rossler and Chen chaotic systems globally asymptotically robustly synchronized. Simulation results are given to show the effectiveness of the proposed method.
NASA Astrophysics Data System (ADS)
Sudheer, K. Sebastian; Sabir, M.
2011-02-01
In this Letter we consider modified function projective synchronization of unidirectionally coupled multiple time-delayed Rossler chaotic systems using adaptive controls. Recently, delay differential equations have attracted much attention in the field of nonlinear dynamics. The high complexity of the multiple time-delayed systems can provide a new architecture for enhancing message security in chaos based encryption systems. Adaptive control can be used for synchronization when the parameters of the system are unknown. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two chaotic systems are function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.
Manjunath, G; Fournier-Prunaret, D
2011-06-01
It is widely believed that when two discrete time chaotic systems are coupled together then there is a contraction in the phase space (where the essential dynamics takes place) when compared with the phase space in the uncoupled case. Contrary to such a popular belief, we produce a counter example--we consider two discrete time chaotic systems both with an identical attractor A, and show that the two systems could be nonlinearly coupled in a way such that the coupled system's attractor persists strongly, i.e., it is A × A despite the coupling strength is varied from zero to a nonzero value. To show this, we prove robust topological mixing on A × A. Also, it is of interest that the studied coupled system can exhibit a type of synchronization called generalized partial synchronization which is also robust.
Image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing
NASA Astrophysics Data System (ADS)
Zhou, Nanrun; Pan, Shumin; Cheng, Shan; Zhou, Zhihong
2016-08-01
Most image encryption algorithms based on low-dimensional chaos systems bear security risks and suffer encryption data expansion when adopting nonlinear transformation directly. To overcome these weaknesses and reduce the possible transmission burden, an efficient image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing is proposed. The original image is measured by the measurement matrices in two directions to achieve compression and encryption simultaneously, and then the resulting image is re-encrypted by the cycle shift operation controlled by a hyper-chaotic system. Cycle shift operation can change the values of the pixels efficiently. The proposed cryptosystem decreases the volume of data to be transmitted and simplifies the keys distribution simultaneously as a nonlinear encryption system. Simulation results verify the validity and the reliability of the proposed algorithm with acceptable compression and security performance.
Relation between delayed feedback and delay-coupled systems and its application to chaotic lasers
Soriano, Miguel C. Flunkert, Valentin; Fischer, Ingo
2013-12-15
We present a systematic approach to identify the similarities and differences between a chaotic system with delayed feedback and two mutually delay-coupled systems. We consider the general case in which the coupled systems are either unsynchronized or in a generally synchronized state, in contrast to the mostly studied case of identical synchronization. We construct a new time-series for each of the two coupling schemes, respectively, and present analytic evidence and numerical confirmation that these two constructed time-series are statistically equivalent. From the construction, it then follows that the distribution of time-series segments that are small compared to the overall delay in the system is independent of the value of the delay and of the coupling scheme. By focusing on numerical simulations of delay-coupled chaotic lasers, we present a practical example of our findings.
Wang, Zhiheng; Huo, Zhanqiang; Shi, Wenbo
2015-01-01
With rapid development of computer technology and wide use of mobile devices, the telecare medicine information system has become universal in the field of medical care. To protect patients' privacy and medial data's security, many authentication schemes for the telecare medicine information system have been proposed. Due to its better performance, chaotic maps have been used in the design of authentication schemes for the telecare medicine information system. However, most of them cannot provide user's anonymity. Recently, Lin proposed a dynamic identity based authentication scheme using chaotic maps for the telecare medicine information system and claimed that their scheme was secure against existential active attacks. In this paper, we will demonstrate that their scheme cannot provide user anonymity and is vulnerable to the impersonation attack. Further, we propose an improved scheme to fix security flaws in Lin's scheme and demonstrate the proposed scheme could withstand various attacks.
NASA Astrophysics Data System (ADS)
Akpojotor, Godfrey; Ehwerhemuepha, Louis; Amromanoh, Ogheneriobororue
2013-03-01
The presence of physical systems whose characteristics change in a seemingly erratic manner gives rise to the study of chaotic systems. The characteristics of these systems are due to their hypersensitivity to changes in initial conditions. In order to understand chaotic systems, some sort of simulation and visualization is pertinent. Consequently, in this work, we have simulated and graphically visualized chaos in a driven nonlinear pendulum as a means of introducing chaotic systems. The results obtained which highlight the hypersensitivity of the pendulum are used to discuss the effectiveness of teaching and learning the physics of chaotic system using Python. This study is one of the many studies under the African Computational Science and Engineering Tour Project (PASET) which is using Python to model, simulate and visualize concepts, laws and phenomena in Science and Engineering to compliment the teaching/learning of theory and experiment.
Numerical test for hyperbolicity of chaotic dynamics in time-delay systems.
Kuptsov, Pavel V; Kuznetsov, Sergey P
2016-07-01
We develop a numerical test of hyperbolicity of chaotic dynamics in time-delay systems. The test is based on the angle criterion and includes computation of angle distributions between expanding, contracting, and neutral manifolds of trajectories on the attractor. Three examples are tested. For two of them, previously predicted hyperbolicity is confirmed. The third one provides an example of a time-delay system with nonhyperbolic chaos.
Synchronization-based approach for estimating all model parameters of chaotic systems.
Konnur, Rahul
2003-02-01
The problem of dynamic estimation of all parameters of a model representing chaotic and hyperchaotic systems using information from a scalar measured output is solved. The variational calculus based method is robust in the presence of noise, enables online estimation of the parameters and is also able to rapidly track changes in operating parameters of the experimental system. The method is demonstrated using the Lorenz, Rossler chaos, and hyperchaos models. Its possible application in decoding communications using chaos is discussed.
Synchronization-based approach for estimating all model parameters of chaotic systems
NASA Astrophysics Data System (ADS)
Konnur, Rahul
2003-02-01
The problem of dynamic estimation of all parameters of a model representing chaotic and hyperchaotic systems using information from a scalar measured output is solved. The variational calculus based method is robust in the presence of noise, enables online estimation of the parameters and is also able to rapidly track changes in operating parameters of the experimental system. The method is demonstrated using the Lorenz, Rossler chaos, and hyperchaos models. Its possible application in decoding communications using chaos is discussed.
Regular and Chaotic Quantum Dynamics of Two-Level Atoms in a Selfconsistent Radiation Field
NASA Technical Reports Server (NTRS)
Konkov, L. E.; Prants, S. V.
1996-01-01
Dynamics of two-level atoms interacting with their own radiation field in a single-mode high-quality resonator is considered. The dynamical system consists of two second-order differential equations, one for the atomic SU(2) dynamical-group parameter and another for the field strength. With the help of the maximal Lyapunov exponent for this set, we numerically investigate transitions from regularity to deterministic quantum chaos in such a simple model. Increasing the collective coupling constant b is identical with 8(pi)N(sub 0)(d(exp 2))/hw, we observed for initially unexcited atoms a usual sharp transition to chaos at b(sub c) approx. equal to 1. If we take the dimensionless individual Rabi frequency a = Omega/2w as a control parameter, then a sequence of order-to-chaos transitions has been observed starting with the critical value a(sub c) approx. equal to 0.25 at the same initial conditions.
Stabilizing the unstable periodic orbits of a hybrid chaotic system using optimal control
NASA Astrophysics Data System (ADS)
Miladi, Yosra; Feki, Moez; Derbel, Nabil
2015-03-01
In this paper, we are interested in the control of a chaotic hybrid system with an application to Chua's system. It is known that chaotic attractors contain an infinite number of unstable periodic orbits (UPO) with different lengths, our idea consists in stabilizing a predetermined orbit of a given length by using an optimal control method. Our approach is to determine the switching instants from one subsystem to the other while minimizing the difference between two successive orbits. Should the switchings be state dependent, as is the case for the well known Chua's circuit, then our approach consists in perturbing the switching boundaries such that the system trajectory hits those boundaries at the specified instants. Numerical simulations illustrating the efficiency of the proposed method are presented.
Modified Levenberg-Marquardt Method for RÖSSLER Chaotic System Fuzzy Modeling Training
NASA Astrophysics Data System (ADS)
Wang, Yu-Hui; Wu, Qing-Xian; Jiang, Chang-Sheng; Xue, Ya-Li; Fang, Wei
Generally, fuzzy approximation models require some human knowledge and experience. Operator's experience is involved in the mathematics of fuzzy theory as a collection of heuristic rules. The main goal of this paper is to present a new method for identifying unknown nonlinear dynamics such as Rössler system without any human knowledge. Instead of heuristic rules, the presented method uses the input-output data pairs to identify the Rössler chaotic system. The training algorithm is a modified Levenberg-Marquardt (L-M) method, which can adjust the parameters of each linear polynomial and fuzzy membership functions on line, and do not rely on experts' experience excessively. Finally, it is applied to training Rössler chaotic system fuzzy identification. Comparing this method with the standard L-M method, the convergence speed is accelerated. The simulation results demonstrate the effectiveness of the proposed method.
Fuzzy modeling for chaotic systems via interval type-2 T-S fuzzy model with parametric uncertainty
NASA Astrophysics Data System (ADS)
Hasanifard, Goran; Gharaveisi, Ali Akbar; Vali, Mohammad Ali
2014-02-01
A motivation for using fuzzy systems stems in part from the fact that they are particularly suitable for processes when the physical systems or qualitative criteria are too complex to model and they have provided an efficient and effective way in the control of complex uncertain nonlinear systems. To realize a fuzzy model-based design for chaotic systems, it is mostly preferred to represent them by T-S fuzzy models. In this paper, a new fuzzy modeling method has been introduced for chaotic systems via the interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy model. An IT2 fuzzy model is proposed to represent a chaotic system subjected to parametric uncertainty, covered by the lower and upper membership functions of the interval type-2 fuzzy sets. Investigating many well-known chaotic systems, it is obvious that nonlinear terms have a single common variable or they depend only on one variable. If it is taken as the premise variable of fuzzy rules and another premise variable is defined subject to parametric uncertainties, a simple IT2 T-S fuzzy dynamical model can be obtained and will represent many well-known chaotic systems. This IT2 T-S fuzzy model can be used for physical application, chaotic synchronization, etc. The proposed approach is numerically applied to the well-known Lorenz system and Rossler system in MATLAB environment.
NASA Astrophysics Data System (ADS)
Iqbal, A.; Toor, A. H.
2002-03-01
We investigate the role of quantum mechanical effects in the central stability concept of evolutionary game theory, i.e., an evolutionarily stable strategy (ESS). Using two and three-player symmetric quantum games we show how the presence of quantum phenomenon of entanglement can be crucial to decide the course of evolutionary dynamics in a population of interacting individuals.
Spatial Structure of Regular and Chaotic Orbits in A Self-Consistent Triaxial Stellar System
NASA Astrophysics Data System (ADS)
Muzzio, J. C.; Carpintero, D. D.; Wachlin, F. C.
2005-01-01
We created a triaxial stellar system through the cold dissipationless collapse of 100,000 particles whose evolution was followed with a multipolar code. Once an equilibrium system had been obtained, the multipolar expansion was freezed and smoothed in order to get a stationary smooth potential. The resulting model was self-consistent and the orbits and Lyapunov exponents could then be computed for a randomly selected sample of 3472 of the bodies that make up the system. More than half of the orbits (52.7 % ) turned out to be chaotic. Regular orbits were then classified using the frequency analysis automatic code of Carpintero and Aguilar (1998, MNRAS 298(1), 1 21). We present plots of the distributions of the different kinds of orbits projected on the symmetry planes of the system. We distinguish chaotic orbits with only one non-zero Lyapunov exponent from those with two non-zero exponents and show that their spatial distributions differ, that of the former being more similar to the one of the regular orbits. Most of the regular orbits are boxes and boxlets, but the minor axis tubes play an important role filling in the wasp waists of the boxes and helping to give a lentil shape to the system. We see no problem in building stable triaxial models with substantial amounts of chaotic orbits; the difficulties found by other authors may be due not to a physical cause but to a limitation of Schwarzschild’s method.
Shinbrot, T.; Ditto, W.; Grebogi, C.; Ott, E.; Spano, M.; Yorke, J.A. Department of Physics, The College of Wooster, Wooster, Ohio 44691 Naval Surface Warfare Center, Silver Spring, Maryland 20902 )
1992-05-11
In this paper we present the first experimental verification that the sensitivity of a chaotic system to small perturbations (the butterfly effect'') can be used to rapidly direct orbits from an arbitrary initial state to an arbitrary accessible desired state.
NASA Astrophysics Data System (ADS)
Cheng, Chao-Jung; Cheng, Chi-Bin
2013-10-01
Chaotic dynamics provide a fast and simple means to create an excellent image cryptosystem, because it is extremely sensitive to initial conditions and system parameters, pseudorandomness, and non-periodicity. However, most chaos-based image encryption schemes are symmetric cryptographic techniques, which have been proven to be more vulnerable, compared to an asymmetric cryptosystem. This paper develops an asymmetric image cryptosystem, based on the adaptive synchronization of two different chaotic systems, namely a unified chaotic system and a cellular neural network. An adaptive controller with parameter update laws is formulated, using the Lyapunov stability theory, to asymptotically synchronize the two chaotic systems. The synchronization controller is embedded in the image cryptosystem and generates a pair of asymmetric keys, for image encryption and decryption. Using numerical simulations, three sets of experiments are conducted to evaluate the feasibility and reliability of the proposed chaos-based image cryptosystem.
NASA Astrophysics Data System (ADS)
Chao, Luo
2015-11-01
In this paper, a novel digital secure communication scheme is firstly proposed. Different from the usual secure communication schemes based on chaotic synchronization, the proposed scheme employs asynchronous communication which avoids the weakness of synchronous systems and is susceptible to environmental interference. Moreover, as to the transmission errors and data loss in the process of communication, the proposed scheme has the ability to be error-checking and error-correcting in real time. In order to guarantee security, the fractional-order complex chaotic system with the shifting of order is utilized to modulate the transmitted signal, which has high nonlinearity and complexity in both frequency and time domains. The corresponding numerical simulations demonstrate the effectiveness and feasibility of the scheme.
A Double-function Digital Watermarking Algorithm Based on Chaotic System and LWT
NASA Astrophysics Data System (ADS)
Yuxia, Zhao; Jingbo, Fan
A double- function digital watermarking technology is studied and a double-function digital watermarking algorithm of colored image is presented based on chaotic system and the lifting wavelet transformation (LWT).The algorithm has realized the double aims of the copyright protection and the integrity authentication of image content. Making use of feature of human visual system (HVS), the watermark image is embedded into the color image's low frequency component and middle frequency components by different means. The algorithm has great security by using two kinds chaotic mappings and Arnold to scramble the watermark image at the same time. The algorithm has good efficiency by using LWT. The emulation experiment indicates the algorithm has great efficiency and security, and the effect of concealing is really good.
Operator entanglement entropy of the time evolution operator in chaotic systems
NASA Astrophysics Data System (ADS)
Zhou, Tianci; Luitz, David J.
2017-03-01
We study the growth of the operator entanglement entropy (EE) of the time evolution operator in chaotic, many-body localized (MBL) and Floquet systems. In the random-field Heisenberg model we find a universal power-law growth of the operator EE at weak disorder, a logarithmic growth at strong disorder, and extensive saturation values in both cases. In a Floquet spin model, the saturation value after an initial linear growth is identical to the value of a random unitary operator (the Page value). We understand these properties by mapping the operator EE to a global quench problem evolved with a similar parent Hamiltonian in an enlarged Hilbert space with the same chaotic, MBL, and Floquet properties as the original Hamiltonian. The scaling and saturation properties reflect the spreading of the state EE of the corresponding time evolution. We conclude that the EE of the evolution operator should characterize the propagation of information in these systems.
Encrypting three-dimensional information system based on integral imaging and multiple chaotic maps
NASA Astrophysics Data System (ADS)
Xing, Yan; Wang, Qiong-Hua; Xiong, Zhao-Long; Deng, Huan
2016-02-01
An encrypting three-dimensional (3-D) information system based on integral imaging (II) and multiple chaotic maps is proposed. In the encrypting process, the elemental image array (EIA) which represents spatial and angular information of the real 3-D scene is picked up by a microlens array. Subsequently, R, G, and B color components decomposed by the EIA are encrypted using multiple chaotic maps. Finally, these three encrypted components are interwoven to obtain the cipher information. The decryption process implements the reverse operation of the encryption process for retrieving the high-quality 3-D images. Since the encrypted EIA has the data redundancy property due to II, and all parameters of the pickup part are the secret keys of the encrypting system, the system sensitivity on the changes of the plaintext and secret keys can be significantly improved. Moreover, the algorithm based on multiple chaotic maps can effectively enhance the security. A preliminary experiment is carried out, and the experimental results verify the effectiveness, robustness, and security of the proposed system.
Backstepping synchronization of uncertain chaotic systems by a single driving variable
NASA Astrophysics Data System (ADS)
Lu, Ling; Zhang, Qing-Ling; Guo, Zhi-An
2008-02-01
In this paper a parameter observer and a synchronization controller are designed to synchronize unknown chaotic systems with diverse structures. Based on stability theory the structures of the observer and the controller are presented. The unknown Coullet system and Rossler system are taken for examples to demonstrate that the method is effective and feasible. The artificial simulation results show that global synchronization between the unknown Coullet system and the Rossler system can be achieved by a single driving variable with co-operation of the observer and the controller, and all parameters of the Coullet system can be identified at the same time.
Impulsive stabilization and synchronization of a class of chaotic delay systems.
Li, Chuandong; Liao, Xiaofeng; Yang, Xiaofan; Huang, Tingwen
2005-12-01
The problems of control and synchronization of a class of chaotic systems with time delay via the impulsive control approach are investigated. Based on the Lyapunov-like stability theory for impulsive functional differential equations, several sufficient conditions are derived to guarantee chaos control and synchronization. Furthermore, we address the chaos quasisynchronization in the presence of single-parameter mismatch. Several illustrated examples are also given to show the effectiveness of the proposed methods.
Another limitation of DFC when stabilizing unstable fixed points of continuous chaotic systems
NASA Astrophysics Data System (ADS)
Chen, Mao-Yin; Han, Zheng-Zhi; Shang, Yun
2003-05-01
Using stability theory of delayed differential equation (DDE), we show that there exists another limitation of delayed feedback control (DFC) with arbitrary delayed time when stabilizing unstable fixed points (UFPs) of continuous chaotic systems. This limitation is called by zero real part limitation, that is, if Jacobian matrix at a UFP has a characteristic exponent with zero real part, the UFP cannot be stabilized by linear DFC with arbitrary delayed time.
Quantum Effects in Biological Systems
NASA Astrophysics Data System (ADS)
Roy, Sisir
2014-07-01
The debates about the trivial and non-trivial effects in biological systems have drawn much attention during the last decade or so. What might these non-trivial sorts of quantum effects be? There is no consensus so far among the physicists and biologists regarding the meaning of "non-trivial quantum effects". However, there is no doubt about the implications of the challenging research into quantum effects relevant to biology such as coherent excitations of biomolecules and photosynthesis, quantum tunneling of protons, van der Waals forces, ultrafast dynamics through conical intersections, and phonon-assisted electron tunneling as the basis for our sense of smell, environment assisted transport of ions and entanglement in ion channels, role of quantum vacuum in consciousness. Several authors have discussed the non-trivial quantum effects and classified them into four broad categories: (a) Quantum life principle; (b) Quantum computing in the brain; (c) Quantum computing in genetics; and (d) Quantum consciousness. First, I will review the above developments. I will then discuss in detail the ion transport in the ion channel and the relevance of quantum theory in brain function. The ion transport in the ion channel plays a key role in information processing by the brain.
Enhancing chaoticity of spatiotemporal chaos.
Li, Xiaowen; Zhang, Heqiao; Xue, Yu; Hu, Gang
2005-01-01
In some practical situations strong chaos is needed. This introduces the task of chaos control with enhancing chaoticity rather than suppressing chaoticity. In this paper a simple method of linear amplifications incorporating modulo operations is suggested to make spatiotemporal systems, which may be originally chaotic or nonchaotic, strongly chaotic. Specifically, this control can eliminate periodic windows, increase the values and the number of positive Lyapunov exponents, make the probability distributions of the output chaotic sequences more homogeneous, and reduce the correlations of chaotic outputs for different times and different space units. The applicability of the method to practical tasks, in particular to random number generators and secure communications, is briefly discussed.
A Novel Medical Image Protection Scheme Using a 3-Dimensional Chaotic System
Fu, Chong; Zhang, Gao-yuan; Bian, Ou; Lei, Wei-min; Ma, Hong-feng
2014-01-01
Recently, great concerns have been raised regarding the issue of medical image protection due to the increasing demand for telemedicine services, especially the teleradiology service. To meet this challenge, a novel chaos-based approach is suggested in this paper. To address the security and efficiency problems encountered by many existing permutation-diffusion type image ciphers, the new scheme utilizes a single 3D chaotic system, Chen's chaotic system, for both permutation and diffusion. In the permutation stage, we introduce a novel shuffling mechanism, which shuffles each pixel in the plain image by swapping it with another pixel chosen by two of the three state variables of Chen's chaotic system. The remaining variable is used for quantification of pseudorandom keystream for diffusion. Moreover, the selection of state variables is controlled by plain pixel, which enhances the security against known/chosen-plaintext attack. Thorough experimental tests are carried out and the results indicate that the proposed scheme provides an effective and efficient way for real-time secure medical image transmission over public networks. PMID:25541941
On the chaotic orbital dynamics of the planet in the system 16 Cyg
NASA Astrophysics Data System (ADS)
Melnikov, A. V.
2016-02-01
The chaotic orbital dynamics of the planet in the wide visual binary star system 16 Cyg is considered. The only planet in this system has a significant orbital eccentricity, e = 0.69. Previously, Holman et al. suggested the possibility of chaos in the orbital dynamics of the planet due to the proximity of 16 Cyg to the separatrix of the Lidov-Kozai resonance. We have calculated the Lyapunov characteristic exponents on the set of possible orbital parameters for the planet. In all cases, the dynamics of 16 Cyg is regular with a Lyapunov time of more than 30 000 yr. The dynamics is considered in detail for several possible models of the planetary orbit; the dependences of Lyapunov exponents on the time of their calculation and the time dependences of osculating orbital elements have been constructed. Phase space sections for the system dynamics near the Lidov-Kozai resonance have been constructed for all models. A chaotic behavior in the orbital motion of the planet in 16 Cyg is shown to be unlikely, because 16 Cyg in phase space is far from the separatrix of the Lidov-Kozai resonance at admissible orbital parameters, with the chaotic layer near the separatrix being very narrow.
Quantum technologies with hybrid systems
Kurizki, Gershon; Bertet, Patrice; Kubo, Yuimaru; Mølmer, Klaus; Petrosyan, David; Rabl, Peter; Schmiedmayer, Jörg
2015-01-01
An extensively pursued current direction of research in physics aims at the development of practical technologies that exploit the effects of quantum mechanics. As part of this ongoing effort, devices for quantum information processing, secure communication, and high-precision sensing are being implemented with diverse systems, ranging from photons, atoms, and spins to mesoscopic superconducting and nanomechanical structures. Their physical properties make some of these systems better suited than others for specific tasks; thus, photons are well suited for transmitting quantum information, weakly interacting spins can serve as long-lived quantum memories, and superconducting elements can rapidly process information encoded in their quantum states. A central goal of the envisaged quantum technologies is to develop devices that can simultaneously perform several of these tasks, namely, reliably store, process, and transmit quantum information. Hybrid quantum systems composed of different physical components with complementary functionalities may provide precisely such multitasking capabilities. This article reviews some of the driving theoretical ideas and first experimental realizations of hybrid quantum systems and the opportunities and challenges they present and offers a glance at the near- and long-term perspectives of this fascinating and rapidly expanding field. PMID:25737558
Quantum technologies with hybrid systems
NASA Astrophysics Data System (ADS)
Kurizki, Gershon; Bertet, Patrice; Kubo, Yuimaru; Mølmer, Klaus; Petrosyan, David; Rabl, Peter; Schmiedmayer, Jörg
2015-03-01
An extensively pursued current direction of research in physics aims at the development of practical technologies that exploit the effects of quantum mechanics. As part of this ongoing effort, devices for quantum information processing, secure communication, and high-precision sensing are being implemented with diverse systems, ranging from photons, atoms, and spins to mesoscopic superconducting and nanomechanical structures. Their physical properties make some of these systems better suited than others for specific tasks; thus, photons are well suited for transmitting quantum information, weakly interacting spins can serve as long-lived quantum memories, and superconducting elements can rapidly process information encoded in their quantum states. A central goal of the envisaged quantum technologies is to develop devices that can simultaneously perform several of these tasks, namely, reliably store, process, and transmit quantum information. Hybrid quantum systems composed of different physical components with complementary functionalities may provide precisely such multitasking capabilities. This article reviews some of the driving theoretical ideas and first experimental realizations of hybrid quantum systems and the opportunities and challenges they present and offers a glance at the near- and long-term perspectives of this fascinating and rapidly expanding field.
Quantum technologies with hybrid systems.
Kurizki, Gershon; Bertet, Patrice; Kubo, Yuimaru; Mølmer, Klaus; Petrosyan, David; Rabl, Peter; Schmiedmayer, Jörg
2015-03-31
An extensively pursued current direction of research in physics aims at the development of practical technologies that exploit the effects of quantum mechanics. As part of this ongoing effort, devices for quantum information processing, secure communication, and high-precision sensing are being implemented with diverse systems, ranging from photons, atoms, and spins to mesoscopic superconducting and nanomechanical structures. Their physical properties make some of these systems better suited than others for specific tasks; thus, photons are well suited for transmitting quantum information, weakly interacting spins can serve as long-lived quantum memories, and superconducting elements can rapidly process information encoded in their quantum states. A central goal of the envisaged quantum technologies is to develop devices that can simultaneously perform several of these tasks, namely, reliably store, process, and transmit quantum information. Hybrid quantum systems composed of different physical components with complementary functionalities may provide precisely such multitasking capabilities. This article reviews some of the driving theoretical ideas and first experimental realizations of hybrid quantum systems and the opportunities and challenges they present and offers a glance at the near- and long-term perspectives of this fascinating and rapidly expanding field.
Towards a Social Theory of School Administrative Practice in a Complex, Chaotic, Quantum World.
ERIC Educational Resources Information Center
Beavis, Allan K.
Educational administration, like many other social sciences, has traditionally followed the rubrics of classical science with its emphasis on prediction and control and attempts to understand the whole by understanding in ever finer detail how the parts fit together. However, the "new" science (especially quantum mechanics, complexity,…
Study on a new chaotic bitwise dynamical system and its FPGA implementation
NASA Astrophysics Data System (ADS)
Wang, Qian-Xue; Yu, Si-Min; Guyeux, C.; Bahi, J.; Fang, Xiao-Le
2015-06-01
In this paper, the structure of a new chaotic bitwise dynamical system (CBDS) is described. Compared to our previous research work, it uses various random bitwise operations instead of only one. The chaotic behavior of CBDS is mathematically proven according to the Devaney's definition, and its statistical properties are verified both for uniformity and by a comprehensive, reputed and stringent battery of tests called TestU01. Furthermore, a systematic methodology developing the parallel computations is proposed for FPGA platform-based realization of this CBDS. Experiments finally validate the proposed systematic methodology. Project supported by China Postdoctoral Science Foundation (Grant No. 2014M552175), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Chinese Education Ministry, the National Natural Science Foundation of China (Grant No. 61172023), and the Specialized Research Foundation of Doctoral Subjects of Chinese Education Ministry (Grant No. 20114420110003).
Impact of quantum effects on relativistic electron motion in a chaotic regime.
Bashinov, A V; Kim, A V; Sergeev, A M
2015-10-01
The impact of quantum effects on electron dynamics in a plane linearly polarized standing wave with relativistic amplitudes is considered. Using spectral analysis of Lyapunov characteristic exponents with and without radiation losses we show that the contraction effect of phase space due to the radiation reaction force in the classical form does not occur in the quantum case when the discreteness of photon emission is taken into account. It is also demonstrated that electron bunch kinetics has a diffusion solution rather than the d'Alambert type solution as in the classical description. For this case, we applied the Markov chain formalism and showed that this method gives exact characteristics of electron bunch evolution, such as motion of the center of mass and electron bunch dimensions.
Decoherence in infinite quantum systems
Blanchard, Philippe; Hellmich, Mario
2012-09-01
We review and discuss a notion of decoherence formulated in the algebraic framework of quantum physics. Besides presenting some sufficient conditions for the appearance of decoherence in the case of Markovian time evolutions we provide an overview over possible decoherence scenarios. The framework for decoherence we establish is sufficiently general to accommodate quantum systems with infinitely many degrees of freedom.
Efficient simulation of open quantum system in duality quantum computing
NASA Astrophysics Data System (ADS)
Wei, Shi-Jie; Long, Gui-Lu
2016-11-01
Practical quantum systems are open systems due to interactions with their environment. Understanding the evolution of open systems dynamics is important for quantum noise processes , designing quantum error correcting codes, and performing simulations of open quantum systems. Here we proposed an efficient quantum algorithm for simulating the evolution of an open quantum system on a duality quantum computer. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality algorithm, the time evolution of open quantum system is realized by using Kraus operators which is naturally realized in duality quantum computing. Compared to the Lloyd's quantum algorithm [Science.273, 1073(1996)] , the dependence on the dimension of the open quantum system in our algorithm is decreased. Moreover, our algorithm uses a truncated Taylor series of the evolution operators, exponentially improving the performance on the precision compared with existing quantum simulation algorithms with unitary evolution operations.
Dynamics of the stochastic Lorenz chaotic system with long memory effects
Zeng, Caibin Yang, Qigui
2015-12-15
Little seems to be known about the ergodic dynamics of stochastic systems with fractional noise. This paper is devoted to discern such long time dynamics through the stochastic Lorenz chaotic system (SLCS) with long memory effects. By a truncation technique, the SLCS is proved to generate a continuous stochastic dynamical system Λ. Based on the Krylov-Bogoliubov criterion, the required Lyapunov function is further established to ensure the existence of the invariant measure of Λ. Meanwhile, the uniqueness of the invariant measure of Λ is proved by examining the strong Feller property, together with an irreducibility argument. Therefore, the SLCS has exactly one adapted stationary solution.
Dynamics of the stochastic Lorenz chaotic system with long memory effects
NASA Astrophysics Data System (ADS)
Zeng, Caibin; Yang, Qigui
2015-12-01
Little seems to be known about the ergodic dynamics of stochastic systems with fractional noise. This paper is devoted to discern such long time dynamics through the stochastic Lorenz chaotic system (SLCS) with long memory effects. By a truncation technique, the SLCS is proved to generate a continuous stochastic dynamical system Λ. Based on the Krylov-Bogoliubov criterion, the required Lyapunov function is further established to ensure the existence of the invariant measure of Λ. Meanwhile, the uniqueness of the invariant measure of Λ is proved by examining the strong Feller property, together with an irreducibility argument. Therefore, the SLCS has exactly one adapted stationary solution.
Chaotic LIDAR for Naval Applications
2014-08-29
signal is used with a digital receiver to form a chaotic LIDAR (CLIDAR) ranging system. The design of the chaotic fiber ring laser and the fiber ...the first fiscal year we reported the development of wideband noise-like chaotic signals using low-power fiber ring lasers operating at infrared...ytterbium-doped fiber laser (YDFL), which outputs a >1 GHz noise-like chaotic intensity modulation. This signal is amplified by a 2-stage fiber
Chaotic LIDAR for Naval Applications
2014-09-30
digital receiver to form a chaotic LIDAR (CLIDAR) ranging system. The design of the chaotic fiber ring laser and the fiber amplifiers are guided by...Progress In the first fiscal year we reported the development of wideband noise-like chaotic signals using low-power fiber ring lasers operating... fiber laser (YDFL), which outputs a >1 GHz noise-like chaotic intensity modulation. This signal is amplified by a 2-stage fiber amplifier chain to
Transient Dynamics of Electric Power Systems: Direct Stability Assessment and Chaotic Motions
NASA Astrophysics Data System (ADS)
Chu, Chia-Chi
A power system is continuously experiencing disturbances. Analyzing, predicting, and controlling transient dynamics, which describe transient behaviors of the power system following disturbances, is a major concern in the planning and operation of a power utility. Important conclusions and decisions are made based on the result of system transient behaviors. As today's power network becomes highly interconnected and much more complex, it has become essential to enhance the fundamental understanding of transient dynamics, and to develop fast and reliable computational algorithms. In this thesis, we emphasize mathematical rigor rather than physical insight. Nonlinear dynamical system theory is applied to study two fundamental topics: direct stability assessment and chaotic motions. Conventionally, power system stability is determined by calculating the time-domain transient behaviors for a given disturbance. In contrast, direct methods identify whether or not the system will remain stable once the disturbance is removed by comparing the corresponding energy value of the post-fault system to a calculated threshold value. Direct methods not only avoid the time-consuming numerical integration of the time domain approach, but also provide a quantitative measure of the degree of system stability. We present a general framework for the theoretical foundations of direct methods. Canonical representations of network-reduction models as well as network-preserving models are proposed to facilitate the analysis and the construction of energy functions of various power system models. An advanced and practical method, called the boundary of stability region based controlling unstable equilibrium point method (BCU method), of computing the controlling unstable equilibrium point is proposed along with its theoretical foundation. Numerical solution algorithms capable of supporting on-line applications of direct methods are provided. Further possible improvements and enhancements are
Statistical properties of chaotic dynamical systems which exhibit strange attractors
Jensen, R.V.; Oberman, C.R.
1981-07-01
A path integral method is developed for the calculation of the statistical properties of turbulent dynamical systems. The method is applicable to conservative systems which exhibit a transition to stochasticity as well as dissipative systems which exhibit strange attractors. A specific dissipative mapping is considered in detail which models the dynamics of a Brownian particle in a wave field with a broad frequency spectrum. Results are presented for the low order statistical moments for three turbulent regimes which exhibit strange attractors corresponding to strong, intermediate, and weak collisional damping.
Adaptive synchronization of Rossler and Chen chaotic systems
NASA Astrophysics Data System (ADS)
Li, Zhi; Han, Chong-Zhao
2002-07-01
A novel adaptive synchronization method is proposed for two identical Rossler and Chen systems with uncertain parameters. Based on Lyapunov stability theory, we derive an adaptive controller without the knowledge of the system parameters, which can make the states of two identical Rossler and Chen systems globally asymptotically synchronized. Especially, when some unknown uncertain parameters are positive, we can make the controller more simple and, besides, the controller is independent of those positive uncertain parameters. All results are proved using a well-known Lyapunov stability theorem. Numerical simulations are given to validate the proposed synchronization approach.
Trajectory-probed instability and statistics of desynchronization events in coupled chaotic systems
Oliveira, Gilson F. de Chevrollier, Martine; Oriá, Marcos; Passerat de Silans, Thierry; Souza Cavalcante, Hugo L. D. de
2015-11-15
Complex systems, such as financial markets, earthquakes, and neurological networks, exhibit extreme events whose mechanisms of formation are not still completely understood. These mechanisms may be identified and better studied in simpler systems with dynamical features similar to the ones encountered in the complex system of interest. For instance, sudden and brief departures from the synchronized state observed in coupled chaotic systems were shown to display non-normal statistical distributions similar to events observed in the complex systems cited above. The current hypothesis accepted is that these desynchronization events are influenced by the presence of unstable object(s) in the phase space of the system. Here, we present further evidence that the occurrence of large events is triggered by the visitation of the system's phase-space trajectory to the vicinity of these unstable objects. In the system studied here, this visitation is controlled by a single parameter, and we exploit this feature to observe the effect of the visitation rate in the overall instability of the synchronized state. We find that the probability of escapes from the synchronized state and the size of those desynchronization events are enhanced in attractors whose shapes permit the chaotic trajectories to approach the region of strong instability. This result shows that the occurrence of large events requires not only a large local instability to amplify noise, or to amplify the effect of parameter mismatch between the coupled subsystems, but also that the trajectories of the system wander close to this local instability.
Trajectory-probed instability and statistics of desynchronization events in coupled chaotic systems
NASA Astrophysics Data System (ADS)
de Oliveira, Gilson F.; Chevrollier, Martine; Passerat de Silans, Thierry; Oriá, Marcos; de Souza Cavalcante, Hugo L. D.
2015-11-01
Complex systems, such as financial markets, earthquakes, and neurological networks, exhibit extreme events whose mechanisms of formation are not still completely understood. These mechanisms may be identified and better studied in simpler systems with dynamical features similar to the ones encountered in the complex system of interest. For instance, sudden and brief departures from the synchronized state observed in coupled chaotic systems were shown to display non-normal statistical distributions similar to events observed in the complex systems cited above. The current hypothesis accepted is that these desynchronization events are influenced by the presence of unstable object(s) in the phase space of the system. Here, we present further evidence that the occurrence of large events is triggered by the visitation of the system's phase-space trajectory to the vicinity of these unstable objects. In the system studied here, this visitation is controlled by a single parameter, and we exploit this feature to observe the effect of the visitation rate in the overall instability of the synchronized state. We find that the probability of escapes from the synchronized state and the size of those desynchronization events are enhanced in attractors whose shapes permit the chaotic trajectories to approach the region of strong instability. This result shows that the occurrence of large events requires not only a large local instability to amplify noise, or to amplify the effect of parameter mismatch between the coupled subsystems, but also that the trajectories of the system wander close to this local instability.
Synchronization in chaotic Hamiltonian systems and a geophysical application.
Hannachi, A
1999-07-01
This paper addresses the question of the rate of synchronization of two identical systems as a function of the inserting time interval Delta t between inserted variables of the driving system in the role of the same variables of the driven system in a simplified Hamiltonian system and its application to a simplified geophysical model. We start by analyzing the synchronization in a simplified two-degree Hamiltonian system. The synchronization rate turns out to be a decreasing function of the inserting time interval Delta t up to a certain limit Delta t(o) where the process reverses and the synchronization rate becomes slower as the inserting frequency decreases. The key point of the analysis uses a second-order Taylor expansion of the system resolvent which indicates that synchronization rate is basically of order O(Delta t(2)) for small Delta t. The study is then extended to include a simplified geophysical system. A nonlinear one-dimensional shallow-water model on a periodic domain meant to represent a latitudinal circle around 45 degrees N is used. It is found that when the zonal wind is inserted, the maximum synchronization rate is obtained when the inserting time interval is approximately 4 h. When the meridional wind is inserted, it is obtained at slightly less than 4 h. It is shown, in particular, that the synchronization rate depends on the latitude (or the Coriolis parameter). A low-order simplified dynamical system derived from the one-dimensional shallow-water model is used to show that this optimum time interval Delta t(o) when the zonal wind and the geopotential, for example, are inserted varies approximately as square root of [2]/2 Omega sin phi to accuracy O(Delta t(3)). Analyses performed with a linear version of the shallow-water model reveal that this latter can be used to explain the observed convergence behavior in the nonlinear model. The only point is the choice of the stationary state for linearization purposes. It is then suggested that in
Castro-Ramírez, Joel; Martínez-Guerra, Rafael; Cruz-Victoria, Juan Crescenciano
2015-10-01
This paper deals with the master-slave synchronization scheme for partially known nonlinear chaotic systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown states. It introduced a new reduced order observer, using the concept of Algebraic Observability; we applied the results to a Sundarapandian chaotic system, and by means of some numerical simulations we show the effectiveness of the suggested approach. Finally, the proposed observer is utilized for encryption, where encryption key is the master system and decryption key is the slave system.
Castro-Ramírez, Joel; Martínez-Guerra, Rafael; Cruz-Victoria, Juan Crescenciano
2015-10-15
This paper deals with the master-slave synchronization scheme for partially known nonlinear chaotic systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown states. It introduced a new reduced order observer, using the concept of Algebraic Observability; we applied the results to a Sundarapandian chaotic system, and by means of some numerical simulations we show the effectiveness of the suggested approach. Finally, the proposed observer is utilized for encryption, where encryption key is the master system and decryption key is the slave system.
Coexisting attractors and chaotic canard explosions in a slow-fast optomechanical system.
Marino, Francesco; Marin, Francesco
2013-05-01
The multiple time scale dynamics induced by radiation pressure and photothermal effects in a high-finesse optomechanical resonator is experimentally studied. At difference with two-dimensional slow-fast systems, the transition from the quasiharmonic to the relaxational regime occurs via chaotic canard explosions, where large-amplitude relaxation spikes are separated by an irregular number of subthreshold oscillations. We also show that this regime coexists with other periodic attractors, on which the trajectories evolve on a substantially faster time scale. The experimental results are reproduced and analyzed by means of a detailed physical model of our system.
Robust control of a class of chaotic and hyperchaotic driven systems
NASA Astrophysics Data System (ADS)
Mkaouar, Hanéne; Boubaker, Olfa
2017-01-01
This paper proposes new conditions which are sufficient for robust control of a class of chaotic and hyperchaotic driven systems. The drive-driven systems are characterized by non-identical uncertain complex dynamics where complexities are mainly introduced by the switching nature of their vector fields. The controller design is achieved using linear matrix inequalities (LMIs) and the so-called S-procedure and then validated using two numerical examples. To illustrate the robustness of the proposed approach, a comparative study is also established with regard to a related approach.
A chaotic map-based authentication scheme for telecare medicine information systems.
Hao, Xinhong; Wang, Jiantao; Yang, Qinghai; Yan, Xiaopeng; Li, Ping
2013-04-01
With the development of Internet, patients could enjoy health-care delivery services through telecare medicine information systems (TMIS) in their home. To control the access to remote medical servers' resources, many authentication schemes using smart cards have been proposed. However, the performance of these schemes is not satisfactory since modular exponential operations are used in these schemes. In the paper, we propose a chaotic map-based authentication scheme for telecare medicine information systems. The security and performance analysis shows our scheme is more suitable for TMIS.
On Λ - ϕ generalized synchronization of chaotic dynamical systems in continuous-time
NASA Astrophysics Data System (ADS)
Ouannas, A.; Al-sawalha, M. M.
2016-02-01
In this paper, a new type of chaos synchronization in continuous-time is proposed by combining inverse matrix projective synchronization (IMPS) and generalized synchronization (GS). This new chaos synchronization type allows us to study synchronization between different dimensional continuous-time chaotic systems in different dimensions. Based on stability property of integer-order linear continuous-time dynamical systems and Lyapunov stability theory, effective control schemes are introduced and new synchronization criterions are derived. Numerical simulations are used to validate the theoretical results and to verify the effectiveness of the proposed schemes.
Robust synchronization of a class of chaotic systems with disturbance estimation
NASA Astrophysics Data System (ADS)
Xiang, Wei; Chen, Fangqi
2011-08-01
This paper investigates the robust synchronization problem for a class of chaotic systems with external disturbances. By using disturbance-observer-based control (DOBC) and LMI approach, the disturbance observers are developed to ensure the boundedness of the disturbance error dynamical. Then, by employing the sliding mode control technique, an adaptive control law is established to eliminate the effect of disturbance error to realize synchronization between the master and slave systems. Finally, the corresponding numerical simulations are demonstrated to verify the effectiveness of proposed method.
Wang, Chenhui
2016-01-01
In this paper, control of uncertain fractional-order financial chaotic system with input saturation and external disturbance is investigated. The unknown part of the input saturation as well as the system’s unknown nonlinear function is approximated by a fuzzy logic system. To handle the fuzzy approximation error and the estimation error of the unknown upper bound of the external disturbance, fractional-order adaptation laws are constructed. Based on fractional Lyapunov stability theorem, an adaptive fuzzy controller is designed, and the asymptotical stability can be guaranteed. Finally, simulation studies are given to indicate the effectiveness of the proposed method. PMID:27783648
Controlling Discrete Time T-S Fuzzy Chaotic Systems via Adaptive Adjustment
NASA Astrophysics Data System (ADS)
Nian, Yibei; Zheng, Yongai
In order to overcome typical drawbacks of the OGY control, i.e. the long waiting time for control to be applied and the accessible turning system parameter in advance, this paper presents a new chaos control method based on Takagi- Sugeno (T-S) fuzzy model and adaptive adjustment. This method represents a chaotic system by linear models in different state space regions based on T-S fuzzy model and then stabilize the linear models in different state space regions by the adaptive adjustment mechanism. An example for the Henon map is given to demonstrate the effectiveness of the proposed method.
Preconditioned quantum linear system algorithm.
Clader, B D; Jacobs, B C; Sprouse, C R
2013-06-21
We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize generic states, show how simple ancilla measurements can be used to calculate many quantities of interest, and integrate a quantum-compatible preconditioner that greatly expands the number of problems that can achieve exponential speedup over classical linear systems solvers. To demonstrate the algorithm's applicability, we show how it can be used to compute the electromagnetic scattering cross section of an arbitrary target exponentially faster than the best classical algorithm.
Adaptive sliding mode control for a class of chaotic systems
NASA Astrophysics Data System (ADS)
Farid, R.; Ibrahim, A.; Zalam, B.
2015-03-01
Chaos control here means to design a controller that is able to mitigating or eliminating the chaos behavior of nonlinear systems that experiencing such phenomenon. In this paper, an Adaptive Sliding Mode Controller (ASMC) is presented based on Lyapunov stability theory. The well known Chua's circuit is chosen to be our case study in this paper. The study shows the effectiveness of the proposed adaptive sliding mode controller.
Adaptive sliding mode control for a class of chaotic systems
Farid, R.; Ibrahim, A.; Zalam, B.
2015-03-30
Chaos control here means to design a controller that is able to mitigating or eliminating the chaos behavior of nonlinear systems that experiencing such phenomenon. In this paper, an Adaptive Sliding Mode Controller (ASMC) is presented based on Lyapunov stability theory. The well known Chua's circuit is chosen to be our case study in this paper. The study shows the effectiveness of the proposed adaptive sliding mode controller.
From Fault-Diagnosis and Performance Recovery of a Controlled System to Chaotic Secure Communication
NASA Astrophysics Data System (ADS)
Hsu, Wen-Teng; Tsai, Jason Sheng-Hong; Guo, Fang-Cheng; Guo, Shu-Mei; Shieh, Leang-San
Chaotic systems are often applied to encryption on secure communication, but they may not provide high-degree security. In order to improve the security of communication, chaotic systems may need to add other secure signals, but this may cause the system to diverge. In this paper, we redesign a communication scheme that could create secure communication with additional secure signals, and the proposed scheme could keep system convergence. First, we introduce the universal state-space adaptive observer-based fault diagnosis/estimator and the high-performance tracker for the sampled-data linear time-varying system with unanticipated decay factors in actuators/system states. Besides, robustness, convergence in the mean, and tracking ability are given in this paper. A residual generation scheme and a mechanism for auto-tuning switched gain is also presented, so that the introduced methodology is applicable for the fault detection and diagnosis (FDD) for actuator and state faults to yield a high tracking performance recovery. The evolutionary programming-based adaptive observer is then applied to the problem of secure communication. Whenever the tracker induces a large control input which might not conform to the input constraint of some physical systems, the proposed modified linear quadratic optimal tracker (LQT) can effectively restrict the control input within the specified constraint interval, under the acceptable tracking performance. The effectiveness of the proposed design methodology is illustrated through tracking control simulation examples.
From Butterflies to Galaxies: Testing Chaotic System Simulation
NASA Astrophysics Data System (ADS)
Hayes, W.
2005-05-01
N-body simulations have become a mainstay in modern astrophysics. They have been used to garner understanding of such varied phenomena as chaos in the solar system, to clumping of matter in the early universe. However, even the earliest practitioners realized that the results of such simulations may be suspect, because the tiniest differences between two simulations (such as what machine the simulation is run on, or old-fashioned numerical errors) can lead to vastly different simulation results. Over the decades, enormous effort has been put into studying and minimizing such errors, and the consensus today is that, although the microscopic details of large simulations are almost certainly incorrect, certain macroscopic measures are valid. However, nobody is quite sure which measures are valid and under precisely what conditions; as such, the fundamental reliability of such simulations has yet to be conclusively demonstrated. In this talk I will review some past results of simulation reliability and then introduce the concept of shadowing, which was first applied to N-body systems by Quinlan & Tremaine in 1992. A shadow of a numerical integration is an exact solution that remains close to the numerical solution for a long time. As such, an integration which has a shadow can be viewed as an observation of an exact trajectory. Unfortunately, it turns out that the full phase-space integration of a large n-body system is not shadowable. Howewver, it appears that if one is willing to allow that only some particles have reliable trajectories, then we can demonstrate that the number of reliable particles decays exponentially with time, and that the decay becomes slower with increasing simulation accuracy. Unfortunately the decay is extremely rapid for collisional systems, so that all particles have become unshadowable after just a few crossing times. However, preliminary results for collisionless systems appear to indicate that a large majority of particles can be shadowed
Mechanism for quantum speedup in open quantum systems
NASA Astrophysics Data System (ADS)
Liu, Hai-Bin; Yang, W. L.; An, Jun-Hong; Xu, Zhen-Yu
2016-02-01
The quantum speed limit (QSL) time for open system characterizes the most efficient response of the system to the environmental influences. Previous results showed that the non-Markovianity governs the quantum speedup. Via studying the dynamics of a dissipative two-level system, we reveal that the non-Markovian effect is only the dynamical way of the quantum speedup, while the formation of the system-environment bound states is the essential reason for the quantum speedup. Our attribution of the quantum speedup to the energy-spectrum character can supply another vital path for experiments when the quantum speedup shows up without any dynamical calculations. The potential experimental observation of our quantum speedup mechanism in the circuit QED system is discussed. Our results may be of both theoretical and experimental interest in exploring the ultimate QSL in realistic environments, and may open new perspectives for devising active quantum speedup devices.
Screening in quantum charged systems
NASA Astrophysics Data System (ADS)
Martin, Ph. A.; Gruber, Ch.
1984-07-01
For stationary states of quantum charged systems in ν dimensions, ν>=2, it is proven that the reduced-density matrices satisfy a set of sum rules whenever the clustering is faster than |x|-(ν+l). These sum rules, describing the screening properties, are analogous to those previously derived for classical systems. For neutral quantum fluids, it is shown that the clustering cannot be faster than the decay of the force.
Hybrid information privacy system: integration of chaotic neural network and RSA coding
NASA Astrophysics Data System (ADS)
Hsu, Ming-Kai; Willey, Jeff; Lee, Ting N.; Szu, Harold H.
2005-03-01
Electronic mails are adopted worldwide; most are easily hacked by hackers. In this paper, we purposed a free, fast and convenient hybrid privacy system to protect email communication. The privacy system is implemented by combining private security RSA algorithm with specific chaos neural network encryption process. The receiver can decrypt received email as long as it can reproduce the specified chaos neural network series, so called spatial-temporal keys. The chaotic typing and initial seed value of chaos neural network series, encrypted by the RSA algorithm, can reproduce spatial-temporal keys. The encrypted chaotic typing and initial seed value are hidden in watermark mixed nonlinearly with message media, wrapped with convolution error correction codes for wireless 3rd generation cellular phones. The message media can be an arbitrary image. The pattern noise has to be considered during transmission and it could affect/change the spatial-temporal keys. Since any change/modification on chaotic typing or initial seed value of chaos neural network series is not acceptable, the RSA codec system must be robust and fault-tolerant via wireless channel. The robust and fault-tolerant properties of chaos neural networks (CNN) were proved by a field theory of Associative Memory by Szu in 1997. The 1-D chaos generating nodes from the logistic map having arbitrarily negative slope a = p/q generating the N-shaped sigmoid was given first by Szu in 1992. In this paper, we simulated the robust and fault-tolerance properties of CNN under additive noise and pattern noise. We also implement a private version of RSA coding and chaos encryption process on messages.
A Gaussian mixture model based cost function for parameter estimation of chaotic biological systems
NASA Astrophysics Data System (ADS)
Shekofteh, Yasser; Jafari, Sajad; Sprott, Julien Clinton; Hashemi Golpayegani, S. Mohammad Reza; Almasganj, Farshad
2015-02-01
As we know, many biological systems such as neurons or the heart can exhibit chaotic behavior. Conventional methods for parameter estimation in models of these systems have some limitations caused by sensitivity to initial conditions. In this paper, a novel cost function is proposed to overcome those limitations by building a statistical model on the distribution of the real system attractor in state space. This cost function is defined by the use of a likelihood score in a Gaussian mixture model (GMM) which is fitted to the observed attractor generated by the real system. Using that learned GMM, a similarity score can be defined by the computed likelihood score of the model time series. We have applied the proposed method to the parameter estimation of two important biological systems, a neuron and a cardiac pacemaker, which show chaotic behavior. Some simulated experiments are given to verify the usefulness of the proposed approach in clean and noisy conditions. The results show the adequacy of the proposed cost function.
Quantum Communications Systems
2012-09-21
X.- M . Jin, B.J. Smith, M.B. Plenio , and I.A. Walmsley, Mapping coherence in measurement via full quantum tomog- raphy of a hybrid optical detector...K. C. Lee, B . J. Sussman, M . R. Sprague, P. Michelberger,K. F. Reim,J. Nunn, N. K. Lang- ford,P. J. Bustard, D. Jaksch, and I. A. Walmsley...Macroscopic non-classical states and tera- hertz quantum processing in room-temperature diamond, Nature Photonics 6, 41 (2011) [15] K. C. Lee, M . R. Sprague, B
A bit-level image encryption algorithm based on spatiotemporal chaotic system and self-adaptive
NASA Astrophysics Data System (ADS)
Teng, Lin; Wang, Xingyuan
2012-09-01
This paper proposes a bit-level image encryption algorithm based on spatiotemporal chaotic system which is self-adaptive. We use a bit-level encryption scheme to reduce the volume of data during encryption and decryption in order to reduce the execution time. We also use the adaptive encryption scheme to make the ciphered image dependent on the plain image to improve performance. Simulation results show that the performance and security of the proposed encryption algorithm can encrypt plaintext effectively and resist various typical attacks.
A chaotic system of two-phase flow in a small, horizontal, rectangular channel
Cai, Y.; Wambsganss, M.W.; Jendrzejczyk, J.A.
1995-07-01
Various measurement tools that are used in chaos theory were applied to analyze two-phase pressure signals with the objective of identifying and interpreting flow pattern transitions for two-phase flows in a small, horizontal rectangular channel. These measurement tools included power spectral density function, autocorrelation function, pseudo-phase-plane trajectory, Lyapunov exponents, and fractal dimensions. It was demonstrated that the randomlike pressure fluctuations characteristic of two-phase flow in small rectangular channels are chaotic. As such, they are governed by a high-order deterministic system. The correlation dimension is potentially a new approach for identifying certain two-phase flow patterns and transitions.
Ahmad, Israr Saaban, Azizan Bin Ibrahim, Adyda Binti; Shahzad, Mohammad
2015-12-11
This paper addresses a comparative computational study on the synchronization quality, cost and converging speed for two pairs of identical chaotic and hyperchaotic systems with unknown time-varying parameters. It is assumed that the unknown time-varying parameters are bounded. Based on the Lyapunov stability theory and using the adaptive control method, a single proportional controller is proposed to achieve the goal of complete synchronizations. Accordingly, appropriate adaptive laws are designed to identify the unknown time-varying parameters. The designed control strategy is easy to implement in practice. Numerical simulations results are provided to verify the effectiveness of the proposed synchronization scheme.
The Modeling of Fuzzy Systems Based on Lee-Oscillatory Chaotic Fuzzy Model (LoCFM)
NASA Astrophysics Data System (ADS)
Wong, Max H. Y.; Liu, James N. K.; Shum, Dennis T. F.; Lee, Raymond S. T.
This paper introduces a new fuzzy membership function — LEE-oscillatory Chaotic Fuzzy Model (LoCFM). The development of this model is based on fuzzy logic and the incorporation of chaos theory — LEE Oscillator. Prototype systems are being developed for handling imprecise problems, typically involving linguistic expression and fuzzy semantic meaning. In addition, the paper also examines the mechanism of the LEE Oscillator through analyzing its structure and neural dynamics. It demonstrates the potential application of the model in future development.
NASA Astrophysics Data System (ADS)
Hamel, Sarah; Boulkroune, Abdesselem
2016-08-01
In this paper, a modified generalized function projective synchronization scheme for a class of master-slave chaotic systems subject to dynamic disturbances and input nonlinearities (dead-zone and sector nonlinearities) is investigated. This synchronization system can be seen as a generalization of many existing projective synchronization schemes (namely the function projective synchronization, the modified projective synchronization and so on), in the sense that the master system has a scaling function matrix and the slave system has a scaling factor matrix. To practically achieve this generalized function synchronization, an adaptive fuzzy variable-structure control system is designed. The fuzzy systems are used to appropriately approximate the uncertain nonlinear functions. A Lyapunov approach is employed to prove the boundedness of all signals of the closed-loop control system as well as the exponential convergence of the synchronization errors to an adjustable region. Simulations results are presented to illustrate the effectiveness of the proposed generalized function PS scheme.
Fundamental concepts of quantum chaos
NASA Astrophysics Data System (ADS)
Robnik, M.
2016-09-01
We review the fundamental concepts of quantum chaos in Hamiltonian systems. The quantum evolution of bound systems does not possess the sensitive dependence on initial conditions, and thus no chaotic behaviour occurs, whereas the study of the stationary solutions of the Schrödinger equation in the quantum phase space (Wigner functions) reveals precise analogy of the structure of the classical phase portrait. We analyze the regular eigenstates associated with invariant tori in the classical phase space, and the chaotic eigenstates associated with the classically chaotic regions, and the corresponding energy spectra. The effects of quantum localization of the chaotic eigenstates are treated phenomenologically, resulting in Brody-like level statistics, which can be found also at very high-lying levels, while the coupling between the regular and the irregular eigenstates due to tunneling, and of the corresponding levels, manifests itself only in low-lying levels.
NASA Astrophysics Data System (ADS)
He, Jianbin; Yu, Simin; Cai, Jianping
2016-12-01
Lyapunov exponent is an important index for describing chaotic systems behavior, and the largest Lyapunov exponent can be used to determine whether a system is chaotic or not. For discrete-time dynamical systems, the Lyapunov exponents are calculated by an eigenvalue method. In theory, according to eigenvalue method, the more accurate calculations of Lyapunov exponent can be obtained with the increment of iterations, and the limits also exist. However, due to the finite precision of computer and other reasons, the results will be numeric overflow, unrecognized, or inaccurate, which can be stated as follows: (1) The iterations cannot be too large, otherwise, the simulation result will appear as an error message of NaN or Inf; (2) If the error message of NaN or Inf does not appear, then with the increment of iterations, all Lyapunov exponents will get close to the largest Lyapunov exponent, which leads to inaccurate calculation results; (3) From the viewpoint of numerical calculation, obviously, if the iterations are too small, then the results are also inaccurate. Based on the analysis of Lyapunov-exponent calculation in discrete-time systems, this paper investigates two improved algorithms via QR orthogonal decomposition and SVD orthogonal decomposition approaches so as to solve the above-mentioned problems. Finally, some examples are given to illustrate the feasibility and effectiveness of the improved algorithms.
Bodruzzaman, M.; Essawy, M.A.
1996-02-27
Pressurized fluidized-bed combustors (FBC) are becoming very popular, efficient, and environmentally acceptable replica for conventional boilers in Coal-fired and chemical plants. In this paper, we present neural network-based methods for chaotic behavior monitoring and control in FBC systems, in addition to chaos analysis of FBC data, in order to localize chaotic modes in them. Both of the normal and abnormal mixing processes in FBC systems are known to undergo chaotic behavior. Even though, this type of behavior is not always undesirable, it is a challenge to most types of conventional control methods, due to its unpredictable nature. The performance, reliability, availability and operating cost of an FBC system will be significantly improved, if an appropriate control method is available to control its abnormal operation and switch it to normal when exists. Since this abnormal operation develops only at certain times due to a sequence of transient behavior, then an appropriate abnormal behavior monitoring method is also necessary. Those methods has to be fast enough for on-line operation, such that the control methods would be applied before the system reaches a non-return point in its transients. It was found that both normal and abnormal behavior of FBC systems are chaotic. However, the abnormal behavior has a higher order chaos. Hence, the appropriate control system should be capable of switching the system behavior from its high order chaos condition to low order chaos. It is to mention that most conventional chaos control methods are designed to switch a chaotic behavior to a periodic orbit. Since this is not the goal for the FBC case, further developments are needed. We propose neural network-based control methods which are known for their flexibility and capability to control both non-linear and chaotic systems. A special type of recurrent neural network, known as Dynamic System Imitator (DSI), will be used for the monitoring and control purposes.
Quantum walk public-key cryptographic system
NASA Astrophysics Data System (ADS)
Vlachou, C.; Rodrigues, J.; Mateus, P.; Paunković, N.; Souto, A.
2015-12-01
Quantum Cryptography is a rapidly developing field of research that benefits from the properties of Quantum Mechanics in performing cryptographic tasks. Quantum walks are a powerful model for quantum computation and very promising for quantum information processing. In this paper, we present a quantum public-key cryptographic system based on quantum walks. In particular, in the proposed protocol the public-key is given by a quantum state generated by performing a quantum walk. We show that the protocol is secure and analyze the complexity of public key generation and encryption/decryption procedures.
Duality quantum algorithm efficiently simulates open quantum systems
NASA Astrophysics Data System (ADS)
Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu
2016-07-01
Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d3) in contrast to O(d4) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm.
Duality quantum algorithm efficiently simulates open quantum systems.
Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu
2016-07-28
Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d(3)) in contrast to O(d(4)) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm.
NASA Astrophysics Data System (ADS)
Suzuki, Hideyuki; Imura, Jun-Ichi; Horio, Yoshihiko; Aihara, Kazuyuki
2013-04-01
The chaotic Boltzmann machine proposed in this paper is a chaotic pseudo-billiard system that works as a Boltzmann machine. Chaotic Boltzmann machines are shown numerically to have computing abilities comparable to conventional (stochastic) Boltzmann machines. Since no randomness is required, efficient hardware implementation is expected. Moreover, the ferromagnetic phase transition of the Ising model is shown to be characterised by the largest Lyapunov exponent of the proposed system. In general, a method to relate probabilistic models to nonlinear dynamics by derandomising Gibbs sampling is presented.
Suzuki, Hideyuki; Imura, Jun-ichi; Horio, Yoshihiko; Aihara, Kazuyuki
2013-01-01
The chaotic Boltzmann machine proposed in this paper is a chaotic pseudo-billiard system that works as a Boltzmann machine. Chaotic Boltzmann machines are shown numerically to have computing abilities comparable to conventional (stochastic) Boltzmann machines. Since no randomness is required, efficient hardware implementation is expected. Moreover, the ferromagnetic phase transition of the Ising model is shown to be characterised by the largest Lyapunov exponent of the proposed system. In general, a method to relate probabilistic models to nonlinear dynamics by derandomising Gibbs sampling is presented.
NASA Astrophysics Data System (ADS)
Yang, Dixiong; Zhou, Jilei
2014-11-01
This study reveals the essential connections among several popular chaos feedback control approaches, such as delayed feedback control (DFC), stability transformation method (STM), adaptive adjustment method (AAM), parameter adjustment method, relaxed Newton method, and speed feedback control method (SFCM), etc. Meanwhile, the generality and practical applicability of these approaches are evaluated and compared. It is shown that for discrete chaotic maps, STM can be regarded as a kind of predictive feedback control, and AAM is actually a special case of STM which is merely effective for a particular dynamical system. The parameter adjustment method is only a different expression of the relaxed Newton method, and both of them represent just one search direction of STM, i.e., the gradient direction. Moreover, the intrinsic relation between the STM and SFCM for controlling the equilibrium of continuous autonomous systems is investigated, indicating that STM can be viewed as a special form of the SFCM. Finally, both the STM and SFCM are extended to control the chaotic vibrations of non-autonomous mechanical systems effectively.
A novel adaptive-impulsive synchronization of fractional-order chaotic systems
NASA Astrophysics Data System (ADS)
Leung, Y. T. Andrew; Li, Xian-Feng; Chu, Yan-Dong; Zhang, Hui
2015-10-01
A novel adaptive-impulsive scheme is proposed for synchronizing fractional-order chaotic systems without the necessity of knowing the attractors’ bounds in priori. The nonlinear functions in these systems are supposed to satisfy local Lipschitz conditions but which are estimated with adaptive laws. The novelty is that the combination of adaptive control and impulsive control offers a control strategy gathering the advantages of both. In order to guarantee the convergence is no less than an expected exponential rate, a combined feedback strength design is created such that the symmetric axis can shift freely according to the updated transient feedback strength. All of the unknown Lipschitz constants are also updated exponentially in the meantime of achieving synchronization. Two different fractional-order chaotic systems are employed to demonstrate the effectiveness of the novel adaptive-impulsive control scheme. Project supported by the National Natural Science Foundations of China (Grant Nos. 11161027 and 11262009), the Key Natural Science Foundation of Gansu Province, China (Grant No. 1104WCGA195), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20136204110001).
The role of model dynamics in ensemble Kalman filter performance for chaotic systems
Ng, G.-H.C.; McLaughlin, D.; Entekhabi, D.; Ahanin, A.
2011-01-01
The ensemble Kalman filter (EnKF) is susceptible to losing track of observations, or 'diverging', when applied to large chaotic systems such as atmospheric and ocean models. Past studies have demonstrated the adverse impact of sampling error during the filter's update step. We examine how system dynamics affect EnKF performance, and whether the absence of certain dynamic features in the ensemble may lead to divergence. The EnKF is applied to a simple chaotic model, and ensembles are checked against singular vectors of the tangent linear model, corresponding to short-term growth and Lyapunov vectors, corresponding to long-term growth. Results show that the ensemble strongly aligns itself with the subspace spanned by unstable Lyapunov vectors. Furthermore, the filter avoids divergence only if the full linearized long-term unstable subspace is spanned. However, short-term dynamics also become important as non-linearity in the system increases. Non-linear movement prevents errors in the long-term stable subspace from decaying indefinitely. If these errors then undergo linear intermittent growth, a small ensemble may fail to properly represent all important modes, causing filter divergence. A combination of long and short-term growth dynamics are thus critical to EnKF performance. These findings can help in developing practical robust filters based on model dynamics. ?? 2011 The Authors Tellus A ?? 2011 John Wiley & Sons A/S.
Chaotic Motions in the Real Fuzzy Electronic Circuits (Preprint)
2012-12-01
sources to be applied to encrypt high confidential signals, because of its high complexity, sensitiveness of initial conditions and unpredictability...Fuzzy Modeling and Synchronization of Chaotic Quantum Cellular Neural Networks Nano System via A Novel Fuzzy Model and Its Implementation on
Quantum dynamics in open quantum-classical systems.
Kapral, Raymond
2015-02-25
Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence on the properties of the quantum system. In many instances the environment is well-approximated by classical mechanics, so that one is led to consider the dynamics of open quantum-classical systems. Since a full quantum dynamical description of large many-body systems is not currently feasible, mixed quantum-classical methods can provide accurate and computationally tractable ways to follow the dynamics of both the system and its environment. This review focuses on quantum-classical Liouville dynamics, one of several quantum-classical descriptions, and discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantum-classical systems, nonadiabatic dynamics, surface-hopping and mean-field theories and their relation to quantum-classical Liouville dynamics, as well as methods for simulating the dynamics.
Quantum energy teleportation in a quantum Hall system
Yusa, Go; Izumida, Wataru; Hotta, Masahiro
2011-09-15
We propose an experimental method for a quantum protocol termed quantum energy teleportation (QET), which allows energy transportation to a remote location without physical carriers. Using a quantum Hall system as a realistic model, we discuss the physical significance of QET and estimate the order of energy gain using reasonable experimental parameters.
On control and synchronization in chaotic and hyperchaotic systems via linear feedback control
NASA Astrophysics Data System (ADS)
Rafikov, Marat; Balthazar, José Manoel
2008-09-01
This paper presents the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems has been formulated under optimal control theory viewpoint. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations were provided in order to show the effectiveness of this method for the control of the chaotic Rössler system and synchronization of the hyperchaotic Rössler system.
Mariño, Inés P; Míguez, Joaquín
2005-11-01
We introduce a numerical approximation method for estimating an unknown parameter of a (primary) chaotic system which is partially observed through a scalar time series. Specifically, we show that the recursive minimization of a suitably designed cost function that involves the dynamic state of a fully observed (secondary) system and the observed time series can lead to the identical synchronization of the two systems and the accurate estimation of the unknown parameter. The salient feature of the proposed technique is that the only external input to the secondary system is the unknown parameter which needs to be adjusted. We present numerical examples for the Lorenz system which show how our algorithm can be considerably faster than some previously proposed methods.
Quantum variance: A measure of quantum coherence and quantum correlations for many-body systems
NASA Astrophysics Data System (ADS)
Frérot, Irénée; Roscilde, Tommaso
2016-08-01
Quantum coherence is a fundamental common trait of quantum phenomena, from the interference of matter waves to quantum degeneracy of identical particles. Despite its importance, estimating and measuring quantum coherence in generic, mixed many-body quantum states remains a formidable challenge, with fundamental implications in areas as broad as quantum condensed matter, quantum information, quantum metrology, and quantum biology. Here, we provide a quantitative definition of the variance of quantum coherent fluctuations (the quantum variance) of any observable on generic quantum states. The quantum variance generalizes the concept of thermal de Broglie wavelength (for the position of a free quantum particle) to the space of eigenvalues of any observable, quantifying the degree of coherent delocalization in that space. The quantum variance is generically measurable and computable as the difference between the static fluctuations and the static susceptibility of the observable; despite its simplicity, it is found to provide a tight lower bound to most widely accepted estimators of "quantumness" of observables (both as a feature as well as a resource), such as the Wigner-Yanase skew information and the quantum Fisher information. When considering bipartite fluctuations in an extended quantum system, the quantum variance expresses genuine quantum correlations among the two parts. In the case of many-body systems, it is found to obey an area law at finite temperature, extending therefore area laws of entanglement and quantum fluctuations of pure states to the mixed-state context. Hence the quantum variance paves the way to the measurement of macroscopic quantum coherence and quantum correlations in most complex quantum systems.
A New Color Image Encryption Scheme Using CML and a Fractional-Order Chaotic System
Wu, Xiangjun; Li, Yang; Kurths, Jürgen
2015-01-01
The chaos-based image cryptosystems have been widely investigated in recent years to provide real-time encryption and transmission. In this paper, a novel color image encryption algorithm by using coupled-map lattices (CML) and a fractional-order chaotic system is proposed to enhance the security and robustness of the encryption algorithms with a permutation-diffusion structure. To make the encryption procedure more confusing and complex, an image division-shuffling process is put forward, where the plain-image is first divided into four sub-images, and then the position of the pixels in the whole image is shuffled. In order to generate initial conditions and parameters of two chaotic systems, a 280-bit long external secret key is employed. The key space analysis, various statistical analysis, information entropy analysis, differential analysis and key sensitivity analysis are introduced to test the security of the new image encryption algorithm. The cryptosystem speed is analyzed and tested as well. Experimental results confirm that, in comparison to other image encryption schemes, the new algorithm has higher security and is fast for practical image encryption. Moreover, an extensive tolerance analysis of some common image processing operations such as noise adding, cropping, JPEG compression, rotation, brightening and darkening, has been performed on the proposed image encryption technique. Corresponding results reveal that the proposed image encryption method has good robustness against some image processing operations and geometric attacks. PMID:25826602
Generalized correlation integral vectors: A distance concept for chaotic dynamical systems
Haario, Heikki; Kalachev, Leonid; Hakkarainen, Janne
2015-06-15
Several concepts of fractal dimension have been developed to characterise properties of attractors of chaotic dynamical systems. Numerical approximations of them must be calculated by finite samples of simulated trajectories. In principle, the quantities should not depend on the choice of the trajectory, as long as it provides properly distributed samples of the underlying attractor. In practice, however, the trajectories are sensitive with respect to varying initial values, small changes of the model parameters, to the choice of a solver, numeric tolerances, etc. The purpose of this paper is to present a statistically sound approach to quantify this variability. We modify the concept of correlation integral to produce a vector that summarises the variability at all selected scales. The distribution of this stochastic vector can be estimated, and it provides a statistical distance concept between trajectories. Here, we demonstrate the use of the distance for the purpose of estimating model parameters of a chaotic dynamic model. The methodology is illustrated using computational examples for the Lorenz 63 and Lorenz 95 systems, together with a framework for Markov chain Monte Carlo sampling to produce posterior distributions of model parameters.
A new color image encryption scheme using CML and a fractional-order chaotic system.
Wu, Xiangjun; Li, Yang; Kurths, Jürgen
2015-01-01
The chaos-based image cryptosystems have been widely investigated in recent years to provide real-time encryption and transmission. In this paper, a novel color image encryption algorithm by using coupled-map lattices (CML) and a fractional-order chaotic system is proposed to enhance the security and robustness of the encryption algorithms with a permutation-diffusion structure. To make the encryption procedure more confusing and complex, an image division-shuffling process is put forward, where the plain-image is first divided into four sub-images, and then the position of the pixels in the whole image is shuffled. In order to generate initial conditions and parameters of two chaotic systems, a 280-bit long external secret key is employed. The key space analysis, various statistical analysis, information entropy analysis, differential analysis and key sensitivity analysis are introduced to test the security of the new image encryption algorithm. The cryptosystem speed is analyzed and tested as well. Experimental results confirm that, in comparison to other image encryption schemes, the new algorithm has higher security and is fast for practical image encryption. Moreover, an extensive tolerance analysis of some common image processing operations such as noise adding, cropping, JPEG compression, rotation, brightening and darkening, has been performed on the proposed image encryption technique. Corresponding results reveal that the proposed image encryption method has good robustness against some image processing operations and geometric attacks.
Sheng, Zheng; Wang, Jun; Zhou, Shudao; Zhou, Bihua
2014-03-01
This paper introduces a novel hybrid optimization algorithm to establish the parameters of chaotic systems. In order to deal with the weaknesses of the traditional cuckoo search algorithm, the proposed adaptive cuckoo search with simulated annealing algorithm is presented, which incorporates the adaptive parameters adjusting operation and the simulated annealing operation in the cuckoo search algorithm. Normally, the parameters of the cuckoo search algorithm are kept constant that may result in decreasing the efficiency of the algorithm. For the purpose of balancing and enhancing the accuracy and convergence rate of the cuckoo search algorithm, the adaptive operation is presented to tune the parameters properly. Besides, the local search capability of cuckoo search algorithm is relatively weak that may decrease the quality of optimization. So the simulated annealing operation is merged into the cuckoo search algorithm to enhance the local search ability and improve the accuracy and reliability of the results. The functionality of the proposed hybrid algorithm is investigated through the Lorenz chaotic system under the noiseless and noise condition, respectively. The numerical results demonstrate that the method can estimate parameters efficiently and accurately in the noiseless and noise condition. Finally, the results are compared with the traditional cuckoo search algorithm, genetic algorithm, and particle swarm optimization algorithm. Simulation results demonstrate the effectiveness and superior performance of the proposed algorithm.
NASA Astrophysics Data System (ADS)
Sheng, Zheng; Wang, Jun; Zhou, Shudao; Zhou, Bihua
2014-03-01
This paper introduces a novel hybrid optimization algorithm to establish the parameters of chaotic systems. In order to deal with the weaknesses of the traditional cuckoo search algorithm, the proposed adaptive cuckoo search with simulated annealing algorithm is presented, which incorporates the adaptive parameters adjusting operation and the simulated annealing operation in the cuckoo search algorithm. Normally, the parameters of the cuckoo search algorithm are kept constant that may result in decreasing the efficiency of the algorithm. For the purpose of balancing and enhancing the accuracy and convergence rate of the cuckoo search algorithm, the adaptive operation is presented to tune the parameters properly. Besides, the local search capability of cuckoo search algorithm is relatively weak that may decrease the quality of optimization. So the simulated annealing operation is merged into the cuckoo search algorithm to enhance the local search ability and improve the accuracy and reliability of the results. The functionality of the proposed hybrid algorithm is investigated through the Lorenz chaotic system under the noiseless and noise condition, respectively. The numerical results demonstrate that the method can estimate parameters efficiently and accurately in the noiseless and noise condition. Finally, the results are compared with the traditional cuckoo search algorithm, genetic algorithm, and particle swarm optimization algorithm. Simulation results demonstrate the effectiveness and superior performance of the proposed algorithm.
Sheng, Zheng; Wang, Jun; Zhou, Bihua; Zhou, Shudao
2014-03-15
This paper introduces a novel hybrid optimization algorithm to establish the parameters of chaotic systems. In order to deal with the weaknesses of the traditional cuckoo search algorithm, the proposed adaptive cuckoo search with simulated annealing algorithm is presented, which incorporates the adaptive parameters adjusting operation and the simulated annealing operation in the cuckoo search algorithm. Normally, the parameters of the cuckoo search algorithm are kept constant that may result in decreasing the efficiency of the algorithm. For the purpose of balancing and enhancing the accuracy and convergence rate of the cuckoo search algorithm, the adaptive operation is presented to tune the parameters properly. Besides, the local search capability of cuckoo search algorithm is relatively weak that may decrease the quality of optimization. So the simulated annealing operation is merged into the cuckoo search algorithm to enhance the local search ability and improve the accuracy and reliability of the results. The functionality of the proposed hybrid algorithm is investigated through the Lorenz chaotic system under the noiseless and noise condition, respectively. The numerical results demonstrate that the method can estimate parameters efficiently and accurately in the noiseless and noise condition. Finally, the results are compared with the traditional cuckoo search algorithm, genetic algorithm, and particle swarm optimization algorithm. Simulation results demonstrate the effectiveness and superior performance of the proposed algorithm.
Quantum systems under frequency modulation.
Silveri, M P; Tuorila, J A; Thuneberg, E V; Paraoanu, G S
2017-05-01
We review the physical phenomena that arise when quantum mechanical energy levels are modulated in time. The dynamics resulting from changes in the transition frequency is a problem studied since the early days of quantum mechanics. It has been of constant interest both experimentally and theoretically since, with the simple two-state model providing an inexhaustible source of novel concepts. When the transition frequency of a quantum system is modulated, several phenomena can be observed, such as Landau-Zener-Stückelberg-Majorana interference, motional averaging and narrowing, and the formation of dressed states with the appearance of sidebands in the spectrum. Adiabatic changes result in the accumulation of geometric phases, which can be used to create topological states. In recent years, an exquisite experimental control in the time domain was gained through the parameters entering the Hamiltonian, and high-fidelity readout schemes allowed the state of the system to be monitored non-destructively. These developments were made in the field of quantum devices, especially in superconducting qubits, as a well as in atomic physics, in particular in ultracold gases. As a result of these advances, it became possible to demonstrate many of the fundamental effects that arise in a quantum system when its transition frequencies are modulated. The purpose of this review is to present some of these developments, from two-state atoms and harmonic oscillators to multilevel and many-particle systems.
NASA Astrophysics Data System (ADS)
Zhou, Ke; Wang, Zhi-Hui; Gao, Li-Ke; Sun, Yue; Ma, Tie-Dong
2015-03-01
This paper presents a modified sliding mode control for fractional-order chaotic economical systems with parameter uncertainty and external disturbance. By constructing the suitable sliding mode surface with fractional-order integral, the effective sliding mode controller is designed to realize the asymptotical stability of fractional-order chaotic economical systems. Comparing with the existing results, the main results in this paper are more practical and rigorous. Simulation results show the effectiveness and feasibility of the proposed sliding mode control method. Project supported by the National Natural Science Foundation of China (Grant Nos. 51207173 and 51277192).
Simple Autonomous Chaotic Circuits
NASA Astrophysics Data System (ADS)
Piper, Jessica; Sprott, J.
2010-03-01
Over the last several decades, numerous electronic circuits exhibiting chaos have been proposed. Non-autonomous circuits with as few as two components have been developed. However, the operation of such circuits relies on the non-ideal behavior of the devices used, and therefore the circuit equations can be quite complex. In this paper, we present two simple autonomous chaotic circuits using only opamps and linear passive components. The circuits each use one opamp as a comparator, to provide a signum nonlinearity. The chaotic behavior is robust, and independent of nonlinearities in the passive components. Moreover, the circuit equations are among the algebraically simplest chaotic systems yet constructed.
Quantum Entanglement and Quantum Discord in Gaussian Open Systems
Isar, Aurelian
2011-10-03
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable quantum entanglement and quantum discord for a system consisting of two noninteracting modes embedded in a thermal environment. Entanglement and discord are used to quantify the quantum correlations of the system. For all values of the temperature of the thermal reservoir, an initial separable Gaussian state remains separable for all times. In the case of an entangled initial Gaussian state, entanglement suppression (entanglement sudden death) takes place for non-zero temperatures of the environment. Only for a zero temperature of the thermal bath the initial entangled state remains entangled for finite times. We analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that quantum discord decays asymptotically in time under the effect of the thermal bath.
Quantum cloning attacks against PUF-based quantum authentication systems
NASA Astrophysics Data System (ADS)
Yao, Yao; Gao, Ming; Li, Mo; Zhang, Jian
2016-08-01
With the advent of physical unclonable functions (PUFs), PUF-based quantum authentication systems have been proposed for security purposes, and recently, proof-of-principle experiment has been demonstrated. As a further step toward completing the security analysis, we investigate quantum cloning attacks against PUF-based quantum authentication systems and prove that quantum cloning attacks outperform the so-called challenge-estimation attacks. We present the analytical expression of the false-accept probability by use of the corresponding optimal quantum cloning machines and extend the previous results in the literature. In light of these findings, an explicit comparison is made between PUF-based quantum authentication systems and quantum key distribution protocols in the context of cloning attacks. Moreover, from an experimental perspective, a trade-off between the average photon number and the detection efficiency is discussed in detail.
Chaotic transport in Hamiltonian systems perturbed by a weak turbulent wave field
Abdullaev, S. S.
2011-08-15
Chaotic transport in a Hamiltonian system perturbed by a weak turbulent wave field is studied. It is assumed that a turbulent wave field has a wide spectrum containing up to thousands of modes whose phases are fluctuating in time with a finite correlation time. To integrate the Hamiltonian equations a fast symplectic mapping is derived. It has a large time-step equal to one full turn in angle variable. It is found that the chaotic transport across tori caused by the interactions of small-scale resonances have a fractal-like structure with the reduced or zero values of diffusion coefficients near low-order rational tori thereby forming transport barriers there. The density of rational tori is numerically calculated and its properties are investigated. It is shown that the transport barriers are formed in the gaps of the density of rational tori near the low-order rational tori. The dependencies of the depth and width of transport barriers on the wave field spectrum and the correlation time of fluctuating turbulent field (or the Kubo number) are studied. These numerical findings may have importance in understanding the mechanisms of transport barrier formation in fusion plasmas.
Quantum Entanglement in Open Systems
Isar, Aurelian
2008-01-24
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, the master equation for two independent harmonic oscillators interacting with an environment is solved in the asymptotic long-time regime. Using the Peres-Simon necessary and sufficient condition for separability of two-mode Gaussian states, we show that the two non-interacting systems become asymptotically entangled for certain environments, so that in the long-time regime they manifest non-local quantum correlations. We calculate also the logarithmic negativity characterizing the degree of entanglement of the asymptotic state.
NASA Astrophysics Data System (ADS)
Bruzzone, Agostino G.; Revetria, Roberto; Simeoni, Simone; Viazzo, Simone; Orsoni, Alessandra
2004-08-01
In logistics and industrial production managers must deal with the impact of stochastic events to improve performances and reduce costs. In fact, production and logistics systems are generally designed considering some parameters as deterministically distributed. While this assumption is mostly used for preliminary prototyping, it is sometimes also retained during the final design stage, and especially for estimated parameters (i.e. Market Request). The proposed methodology can determine the impact of stochastic events in the system by evaluating the chaotic threshold level. Such an approach, based on the application of a new and innovative methodology, can be implemented to find the condition under which chaos makes the system become uncontrollable. Starting from problem identification and risk assessment, several classification techniques are used to carry out an effect analysis and contingency plan estimation. In this paper the authors illustrate the methodology with respect to a real industrial case: a production problem related to the logistics of distributed chemical processing.
NASA Astrophysics Data System (ADS)
He, Shaobo; Sun, Kehui; Mei, Xiaoyong; Yan, Bo; Xu, Siwei
2017-01-01
In this paper, the numerical solutions of conformable fractional-order linear and nonlinear equations are obtained by employing the constructed conformable Adomian decomposition method (CADM). We found that CADM is an effective method for numerical solution of conformable fractional-order differential equations. Taking the conformable fractional-order simplified Lorenz system as an example, the numerical solution and chaotic behaviors of the conformable fractional-order simplified Lorenz system are investigated. It is found that rich dynamics exist in the conformable fractional-order simplified Lorenz system, and the minimum order for chaos is even less than 2. The results are validated by means of bifurcation diagram, Lyapunov characteristic exponents and phase portraits.
NASA Astrophysics Data System (ADS)
Sivaganesh, G.; Daniel Sweetlin, M.; Arulgnanam, A.
2016-07-01
In this paper, we present a numerical investigation on the robust synchronization phenomenon observed in a unidirectionally-coupled quasiperiodically-forced simple nonlinear electronic circuit system exhibiting strange non-chaotic attractors (SNAs) in its dynamics. The SNA obtained in the simple quasiperiodic system is characterized for its SNA behavior. Then, we studied the nature of the synchronized state in unidirectionally coupled SNAs by using the Master-Slave approach. The stability of the synchronized state is studied through the master stability functions (MSF) obtained for coupling different state variables of the drive and response system. The property of robust synchronization is analyzed for one type of coupling of the state variables through phase portraits, conditional lyapunov exponents and the Kaplan-Yorke dimension. The phenomenon of complete synchronization of SNAs via a unidirectional coupling scheme is reported for the first time.
Piecewise affine models of chaotic attractors: The Rössler and Lorenz systems
NASA Astrophysics Data System (ADS)
Amaral, Gleison F. V.; Letellier, Christophe; Aguirre, Luis Antonio
2006-03-01
This paper proposes a procedure by which it is possible to synthesize Rössler [Phys. Lett. A 57, 397-398 (1976)] and Lorenz [J. Atmos. Sci. 20, 130-141 (1963)] dynamics by means of only two affine linear systems and an abrupt switching law. Comparison of different (valid) switching laws suggests that parameters of such a law behave as codimension one bifurcation parameters that can be changed to produce various dynamical regimes equivalent to those observed with the original systems. Topological analysis is used to characterize the resulting attractors and to compare them with the original attractors. The paper provides guidelines that are helpful to synthesize other chaotic dynamics by means of switching affine linear systems.
Disturbance observer based active and adaptive synchronization of energy resource chaotic system.
Wei, Wei; Wang, Meng; Li, Donghai; Zuo, Min; Wang, Xiaoyi
2016-11-01
In this paper, synchronization of a three-dimensional energy resource chaotic system is considered. For the sake of achieving the synchronization between the drive and response systems, two different nonlinear control approaches, i.e. active control with known parameters and adaptive control with unknown parameters, have been designed. In order to guarantee the transient performance, finite-time boundedness (FTB) and finite-time stability (FTS) are introduced in the design of active control and adaptive control, respectively. Simultaneously, in view of the existence of disturbances, a new disturbance observer is proposed to estimate the disturbance. The conditions of the asymptotic stability for the closed-loop system are obtained. Numerical simulations are provided to illustrate the proposed approaches.
Turek, Marko; Spehner, Dominique; Müller, Sebastian; Richter, Klaus
2005-01-01
We present a semiclassical calculation of the generalized form factor Kab(tau) which characterizes the fluctuations of matrix elements of the operators a and b in the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on some recently developed techniques for the spectral form factor of systems with hyperbolic and ergodic underlying classical dynamics and f = 2 degrees of freedom, that allow us to go beyond the diagonal approximation. First we extend these techniques to systems with f > 2. Then we use these results to calculate Kab(tau). We show that the dependence on the rescaled time tau (time in units of the Heisenberg time) is universal for both the spectral and the generalized form factor. Furthermore, we derive a relation between Kab(tau) and the classical time-correlation function of the Weyl symbols of a and b.
Parameter estimation of Lorenz chaotic system using a hybrid swarm intelligence algorithm
NASA Astrophysics Data System (ADS)
Lazzús, Juan A.; Rivera, Marco; López-Caraballo, Carlos H.
2016-03-01
A novel hybrid swarm intelligence algorithm for chaotic system parameter estimation is present. For this purpose, the parameters estimation on Lorenz systems is formulated as a multidimensional problem, and a hybrid approach based on particle swarm optimization with ant colony optimization (PSO-ACO) is implemented to solve this problem. Firstly, the performance of the proposed PSO-ACO algorithm is tested on a set of three representative benchmark functions, and the impact of the parameter settings on PSO-ACO efficiency is studied. Secondly, the parameter estimation is converted into an optimization problem on a three-dimensional Lorenz system. Numerical simulations on Lorenz model and comparisons with results obtained by other algorithms showed that PSO-ACO is a very powerful tool for parameter estimation with high accuracy and low deviations.
Effective time-independent analysis for quantum kicked systems
NASA Astrophysics Data System (ADS)
Bandyopadhyay, Jayendra N.; Guha Sarkar, Tapomoy
2015-03-01
We present a mapping of potentially chaotic time-dependent quantum kicked systems to an equivalent approximate effective time-independent scenario, whereby the system is rendered integrable. The time evolution is factorized into an initial kick, followed by an evolution dictated by a time-independent Hamiltonian and a final kick. This method is applied to the kicked top model. The effective time-independent Hamiltonian thus obtained does not suffer from spurious divergences encountered if the traditional Baker-Cambell-Hausdorff treatment is used. The quasienergy spectrum of the Floquet operator is found to be in excellent agreement with the energy levels of the effective Hamiltonian for a wide range of system parameters. The density of states for the effective system exhibits sharp peaklike features, pointing towards quantum criticality. The dynamics in the classical limit of the integrable effective Hamiltonian shows remarkable agreement with the nonintegrable map corresponding to the actual time-dependent system in the nonchaotic regime. This suggests that the effective Hamiltonian serves as a substitute for the actual system in the nonchaotic regime at both the quantum and classical level.
Effective time-independent analysis for quantum kicked systems.
Bandyopadhyay, Jayendra N; Guha Sarkar, Tapomoy
2015-03-01
We present a mapping of potentially chaotic time-dependent quantum kicked systems to an equivalent approximate effective time-independent scenario, whereby the system is rendered integrable. The time evolution is factorized into an initial kick, followed by an evolution dictated by a time-independent Hamiltonian and a final kick. This method is applied to the kicked top model. The effective time-independent Hamiltonian thus obtained does not suffer from spurious divergences encountered if the traditional Baker-Cambell-Hausdorff treatment is used. The quasienergy spectrum of the Floquet operator is found to be in excellent agreement with the energy levels of the effective Hamiltonian for a wide range of system parameters. The density of states for the effective system exhibits sharp peaklike features, pointing towards quantum criticality. The dynamics in the classical limit of the integrable effective Hamiltonian shows remarkable agreement with the nonintegrable map corresponding to the actual time-dependent system in the nonchaotic regime. This suggests that the effective Hamiltonian serves as a substitute for the actual system in the nonchaotic regime at both the quantum and classical level.
NASA Technical Reports Server (NTRS)
Touma, Jihad; Wisdom, Jack
1993-01-01
The discovery (by Laskar, 1989, 1990) that the evolution of the solar system is chaotic, made in a numerical integration of the averaged secular approximation of the equations of motions for the planets, was confirmed by Sussman and Wisdom (1992) by direct numerical integration of the whole solar system. This paper presents results of direct integrations of the rotation of Mars in the chaotically evolved planetary system, made using the same model as that used by Sussman and Wisdom. The numerical integration shows that the obliquity of Mars undergoes large chaotic variations, which occur as the system evolves in the chaotic zone associated with a secular spin-orbit resonance.
Chaotic laser based physical random bit streaming system with a computer application interface
NASA Astrophysics Data System (ADS)
Shinohara, Susumu; Arai, Kenichi; Davis, Peter; Sunada, Satoshi; Harayama, Takahisa
2017-03-01
We demonstrate a random bit streaming system that uses a chaotic laser as its physical entropy source. By performing real-time bit manipulation for bias reduction, we were able to provide the memory of a personal computer with a constant supply of ready-to-use physical random bits at a throughput of up to 4 Gbps. We pay special attention to the end-to-end entropy source model describing how the entropy from physical sources is converted into bit entropy. We confirmed the statistical quality of the generated random bits by revealing the pass rate of the NIST SP800-22 test suite to be 65 % to 75 %, which is commonly considered acceptable for a reliable random bit generator. We also confirmed the stable operation of our random bit steaming system with long-term bias monitoring.
NASA Astrophysics Data System (ADS)
Alhaidari, A. D.; Taiwo, T. J.
2017-02-01
Using a recent formulation of quantum mechanics without a potential function, we present a four-parameter system associated with the Wilson and Racah polynomials. The continuum scattering states are written in terms of the Wilson polynomials whose asymptotics give the scattering amplitude and phase shift. On the other hand, the finite number of discrete bound states are associated with the Racah polynomials.
Quantum Indeterminacy of Cosmic Systems
Hogan, Craig J.
2013-12-30
It is shown that quantum uncertainty of motion in systems controlled mainly by gravity generally grows with orbital timescale $H^{-1}$, and dominates classical motion for trajectories separated by distances less than $\\approx H^{-3/5}$ in Planck units. For example, the cosmological metric today becomes indeterminate at macroscopic separations, $H_0^{-3/5}\\approx 60$ meters. Estimates suggest that entangled non-localized quantum states of geometry and matter may significantly affect fluctuations during inflation, and connect the scale of dark energy to that of strong interactions.
NASA Astrophysics Data System (ADS)
Fuh, Chyun-Chau; Tsai, Hsun-Heng; Yao, Wei-Hann
2012-03-01
This paper proposes a robust controller which combines a feedback linearization controller with a disturbance observer. This controller can suppress the chaotic motion of an unknown nonlinear system even though it receives an unknown external force. Two numerical simulations are performed to demonstrate the feasibility of the proposed method.
Highly Stable Evolution of Earth's Future Orbit despite Chaotic Behavior of the Solar System
NASA Astrophysics Data System (ADS)
Zeebe, Richard E.
2015-09-01
Due to the chaotic nature of the solar system, the question of its dynamic long-term stability can only be answered in a statistical sense, for instance, based on numerical ensemble integrations of nearby orbits. Destabilization of the inner planets, including catastrophic encounters and/or collisions involving the Earth, has been suggested to be initiated through a large increase in Mercury’s eccentricity ({e}{M}), with an estimated probability of ˜1%. However, it has recently been shown that the statistics of numerical solar system integrations are sensitive to the accuracy and type of numerical algorithm. Here, I report results from computationally demanding ensemble integrations (N = 1600 with slightly different initial conditions) at unprecedented accuracy based on the full equations of motion of the eight planets and Pluto over 5 Gyr, including contributions from general relativity. The standard symplectic algorithm used for long-term integrations produced spurious results for highly eccentric orbits and during close encounters, which were hence integrated with a suitable Bulirsch-Stoer algorithm, specifically designed for these situations. The present study yields odds for a large increase in Mercury’s eccentricity that are less than previous estimates. Strikingly, in two solutions, Mercury continued on highly eccentric orbits (after reaching {e}{M} values >0.93) for 80-100 Myr before colliding with Venus or the Sun. Most importantly, none of the 1600 solutions led to a close encounter involving the Earth or a destabilization of Earth’s orbit in the future. I conclude that Earth’s orbit will be dynamically highly stable for billions of years in the future, despite the chaotic behavior of the solar system.
Energy-dependent correlations in the S-matrix of chaotic systems
NASA Astrophysics Data System (ADS)
Novaes, Marcel
2016-12-01
The M-dimensional unitary matrix S(E), which describes scattering of waves, is a strongly fluctuating function of the energy for complex systems such as ballistic cavities, whose geometry induces chaotic ray dynamics. Its statistical behaviour can be expressed by means of correlation functions of the kind <" separators=" S i j ( E + ɛ ) Sp q † ( E - ɛ ) > , which have been much studied within the random matrix approach. In this work, we consider correlations involving an arbitrary number of matrix elements and express them as infinite series in 1/M, whose coefficients are rational functions of ɛ. From a mathematical point of view, this may be seen as a generalization of the Weingarten functions of circular ensembles.
Polygamy of entanglement in multipartite quantum systems
NASA Astrophysics Data System (ADS)
Kim, Jeong San
2009-08-01
We show that bipartite entanglement distribution (or entanglement of assistance) in multipartite quantum systems is by nature polygamous. We first provide an analytical upper bound for the concurrence of assistance in bipartite quantum systems and derive a polygamy inequality of multipartite entanglement in arbitrary-dimensional quantum systems.
Localization in Open Quantum Systems
NASA Astrophysics Data System (ADS)
Yusipov, I.; Laptyeva, T.; Denisov, S.; Ivanchenko, M.
2017-02-01
In an isolated single-particle quantum system, a spatial disorder can induce Anderson localization. Being a result of interference, this phenomenon is expected to be fragile in the face of dissipation. Here we show that a proper dissipation can drive a disordered system into a steady state with tunable localization properties. This can be achieved with a set of identical dissipative operators, each one acting nontrivially on a pair of sites. Operators are parametrized by a uniform phase, which controls the selection of Anderson modes contributing to the state. On the microscopic level, quantum trajectories of a system in the asymptotic regime exhibit intermittent dynamics consisting of long-time sticking events near selected modes interrupted by intermode jumps.
Bodruzzaman, M.
1996-10-30
We have developed techniques to control the chaotic behavior in Fluidized Bed Systems (FBC) systems using recurrent neural networks. For the sake of comparison of the techniques we have developed with the traditional chaotic system control methods, in the past three months we have been investigating the most popular and first known chaotic system control technique known as the OGY method. This method was developed by Edward Ott, Celso Grebogi and James York in 1990. In the past few years this method was further developed and applied by many researchers in the field. It was shown that this method has potential applications to a large cross section of problems in many fields. The only remaining question is whether it will prove possible to move from laboratory demonstrations on model systems to real world situations of engineering importance. We have developed computer programs to compute the OGY parameters from a chaotic time series, to control a chaotic system to a desired periodic orbit, using small perturbations to an accessible system parameter. We have tested those programs on the logistic map and the Henon map. We were able to control the chaotic behavior in such typical chaotic systems to period 1, 2, 3, 5..., as shown in some sample results below. In the following sections a brief discussion for the OGY method will be introduced, followed by results for the logistic map and Henon map control.
Perturbative approach to Markovian open quantum systems
Li, Andy C. Y.; Petruccione, F.; Koch, Jens
2014-01-01
The exact treatment of Markovian open quantum systems, when based on numerical diagonalization of the Liouville super-operator or averaging over quantum trajectories, is severely limited by Hilbert space size. Perturbation theory, standard in the investigation of closed quantum systems, has remained much less developed for open quantum systems where a direct application to the Lindblad master equation is desirable. We present such a perturbative treatment which will be useful for an analytical understanding of open quantum systems and for numerical calculation of system observables which would otherwise be impractical. PMID:24811607
NASA Astrophysics Data System (ADS)
Wei, Qing-Lai; Song, Rui-Zhuo; Sun, Qiu-Ye; Xiao, Wen-Dong
2015-09-01
This paper estimates an off-policy integral reinforcement learning (IRL) algorithm to obtain the optimal tracking control of unknown chaotic systems. Off-policy IRL can learn the solution of the HJB equation from the system data generated by an arbitrary control. Moreover, off-policy IRL can be regarded as a direct learning method, which avoids the identification of system dynamics. In this paper, the performance index function is first given based on the system tracking error and control error. For solving the Hamilton-Jacobi-Bellman (HJB) equation, an off-policy IRL algorithm is proposed. It is proven that the iterative control makes the tracking error system asymptotically stable, and the iterative performance index function is convergent. Simulation study demonstrates the effectiveness of the developed tracking control method. Project supported by the National Natural Science Foundation of China (Grant Nos. 61304079 and 61374105), the Beijing Natural Science Foundation, China (Grant Nos. 4132078 and 4143065), the China Postdoctoral Science Foundation (Grant No. 2013M530527), the Fundamental Research Funds for the Central Universities, China (Grant No. FRF-TP-14-119A2), and the Open Research Project from State Key Laboratory of Management and Control for Complex Systems, China (Grant No. 20150104).
Resonances in open quantum systems
NASA Astrophysics Data System (ADS)
Eleuch, Hichem; Rotter, Ingrid
2017-02-01
The Hamilton operator of an open quantum system is non-Hermitian. Its eigenvalues are generally complex and provide not only the energies but also the lifetimes of the states of the system. The states may couple via the common environment of scattering wave functions into which the system is embedded. This causes an external mixing (EM) of the states. Mathematically, EM is related to the existence of singular (the so-called exceptional) points. The eigenfunctions of a non-Hermitian operator are biorthogonal, in contrast to the orthogonal eigenfunctions of a Hermitian operator. A quantitative measure for the ratio between biorthogonality and orthogonality is the phase rigidity of the wave functions. At and near an exceptional point (EP), the phase rigidity takes its minimum value. The lifetimes of two nearby eigenstates of a quantum system bifurcate under the influence of an EP. At the parameter value of maximum width bifurcation, the phase rigidity approaches the value one, meaning that the two eigenfunctions become orthogonal. However, the eigenfunctions are externally mixed at this parameter value. The S matrix and therewith the cross section do contain, in the one-channel case, almost no information on the EM of the states. The situation is completely different in the case with two (or more) channels where the resonance structure is strongly influenced by the EM of the states and interesting features of non-Hermitian quantum physics are revealed. We provide numerical results for two and three nearby eigenstates of a non-Hermitian Hamilton operator that are embedded in one common continuum and are influenced by two adjoining EPs. The results are discussed. They are of interest for an experimental test of the non-Hermitian quantum physics as well as for applications.
Yau, Wei-Chuen; Phan, Raphael C-W
2013-12-01
Many authentication schemes have been proposed for telecare medicine information systems (TMIS) to ensure the privacy, integrity, and availability of patient records. These schemes are crucial for TMIS systems because otherwise patients' medical records become susceptible to tampering thus hampering diagnosis or private medical conditions of patients could be disclosed to parties who do not have a right to access such information. Very recently, Hao et al. proposed a chaotic map-based authentication scheme for telecare medicine information systems in a recent issue of Journal of Medical Systems. They claimed that the authentication scheme can withstand various attacks and it is secure to be used in TMIS. In this paper, we show that this authentication scheme is vulnerable to key-compromise impersonation attacks, off-line password guessing attacks upon compromising of a smart card, and parallel session attacks. We also exploit weaknesses in the password change phase of the scheme to mount a denial-of-service attack. Our results show that this scheme cannot be used to provide security in a telecare medicine information system.
Testing the Predictions of Random Matrix Theory in Low Loss Wave Chaotic Scattering Systems
NASA Astrophysics Data System (ADS)
Yeh, Jen-Hao; Antonsen, Thomas; Ott, Edward; Anlage, Steven
2013-03-01
Wave chaos is a field where researchers apply random matrix theory (RMT) to predict the statistics of wave properties in complicated wave scattering systems. The RMT predictions have successfully demonstrated universality of the distributions of these wave properties, which only depend on the loss parameter of the system and the physical symmetry. Examination of these predictions in very low loss systems is interesting because extreme limits for the distribution functions and other predictions are encountered. Therefore, we use a wave-chaotic superconducting cavity to establish a low loss environment and test RMT predictions, including the statistics of the scattering (S) matrix and the impedance (Z) matrix, the universality (or lack thereof) of the Z- and S-variance ratios, and the statistics of the proper delay times of the Wigner-Smith time-delay matrix. We have applied an in-situ microwave calibration method (Thru-Reflection-Line method) to calibrate the cryostat system, and we also applied the random coupling model to remove the system-specific features. Our experimental results of different properties agree with the RMT predictions. This work is funded by the ONR/Maryland AppEl Center Task A2 (contract No. N000140911190), the AFOSR under grant FA95500710049, and Center for Nanophysics and Advanced Materials.
Fractional order fuzzy control of hybrid power system with renewable generation using chaotic PSO.
Pan, Indranil; Das, Saptarshi
2016-05-01
This paper investigates the operation of a hybrid power system through a novel fuzzy control scheme. The hybrid power system employs various autonomous generation systems like wind turbine, solar photovoltaic, diesel engine, fuel-cell, aqua electrolyzer etc. Other energy storage devices like the battery, flywheel and ultra-capacitor are also present in the network. A novel fractional order (FO) fuzzy control scheme is employed and its parameters are tuned with a particle swarm optimization (PSO) algorithm augmented with two chaotic maps for achieving an improved performance. This FO fuzzy controller shows better performance over the classical PID, and the integer order fuzzy PID controller in both linear and nonlinear operating regimes. The FO fuzzy controller also shows stronger robustness properties against system parameter variation and rate constraint nonlinearity, than that with the other controller structures. The robustness is a highly desirable property in such a scenario since many components of the hybrid power system may be switched on/off or may run at lower/higher power output, at different time instants.
Optimal protocols for slowly driven quantum systems
NASA Astrophysics Data System (ADS)
Zulkowski, Patrick R.; DeWeese, Michael R.
2015-09-01
The design of efficient quantum information processing will rely on optimal nonequilibrium transitions of driven quantum systems. Building on a recently developed geometric framework for computing optimal protocols for classical systems driven in finite time, we construct a general framework for optimizing the average information entropy for driven quantum systems. Geodesics on the parameter manifold endowed with a positive semidefinite metric correspond to protocols that minimize the average information entropy production in finite time. We use this framework to explicitly compute the optimal entropy production for a simple two-state quantum system coupled to a heat bath of bosonic oscillators, which has applications to quantum annealing.
Repeated interactions in open quantum systems
Bruneau, Laurent; Joye, Alain; Merkli, Marco
2014-07-15
Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the dynamics of quantum coherences (decoherence) and quantum correlations (entanglement), or the emergence of heat and particle fluxes in non-equilibrium situations. From the mathematical physics perspective, one of the main challenges is to derive the irreversible dynamics of the open system, starting from a unitary dynamics of the system and its environment. The repeated interactions systems considered in these notes are models of non-equilibrium quantum statistical mechanics. They are relevant in quantum optics, and more generally, serve as a relatively well treatable approximation of a more difficult quantum dynamics. In particular, the repeated interaction models allow to determine the large time (stationary) asymptotics of quantum systems out of equilibrium.
Experimental observation of the Poincaré-Birkhoff scenario in a driven many-body quantum system
NASA Astrophysics Data System (ADS)
Tomkovič, J.; Muessel, W.; Strobel, H.; Löck, S.; Schlagheck, P.; Ketzmerick, R.; Oberthaler, M. K.
2017-01-01
Accessing the connection between classical chaos and quantum many-body systems has been a long-standing experimental challenge. Here, we investigate the onset of chaos in periodically driven two-component Bose-Einstein condensates, whose small quantum uncertainties allow for exploring the phase space with high resolution. By analyzing the uncertainties of time-evolved many-body states, we find signatures of elliptic and hyperbolic periodic orbits generated according to the Poincaré-Birkhoff theorem, and the formation of a chaotic region at increasing driving strengths. The employed fluctuation analysis allows for probing the phase-space structure by use of only short-time quantum dynamics.
Quantum correlation of an optically controlled open quantum system
NASA Astrophysics Data System (ADS)
Chan, Ching-Kit; Sham, L. J.
2012-02-01
A precise time-dependent optical control of an open quantum system relies on an accurate account of the quantum interference among the system, the photon control and the dissipative environment. In the spirit of the Keldysh non-equilibrium Green's function approach, we develop a diagrammatic technique to precisely calculate this quantum correlation for a fast multimode coherent photon control against slow relaxation, valid for both Markovian and non-Markovian systems. We demonstrate how this novel formalism can lead to a better accuracy than existing approximations of the master equation. We also describe extensions to cases with controls by photon state other than the coherent Glauber state.
Topological degree in analysis of chaotic behavior in singularly perturbed systems.
Pokrovskii, A; Zhezherun, A
2008-06-01
A scheme of applying topological degree theory to the analysis of chaotic behavior in singularly perturbed systems is suggested. The scheme combines one introduced by Zgliczynski [Topol. Methods Nonlinear Anal. 8, 169 (1996)] with the method of topological shadowing, but does not rely on computer based proofs. It is illustrated by a three-dimensional system with piecewise linear slow surface. This approach, when applicable, guarantees abundance of periodic orbits with arbitrarily large periods, each of which is a canard-type trajectory: at first it passes along, and close to, an attractive part of the slow surface of the singularly perturbed system and then continues for a while along the repulsive part of the slow surface. These periodic trajectories are robust in a topological sense with respect to small disturbances in the right-hand sides of the system under consideration, but typically not stable in the Lyapunov sense. Methods of localization of such periodic trajectories are briefly discussed, and numerical examples of localizations are given. The periodic trajectories that are useful from the applications point of view can be stabilized via an appropriate feedback control, for instance, the Pyragas control.
Benet, L.; Chadderton, L. T.; Kun, S. Yu.; Qi Wang
2007-06-15
We study coherent superpositions of clockwise and anticlockwise rotating intermediate complexes with overlapping resonances formed in bimolecular chemical reactions. Disintegration of such complexes represents an analog of a famous double-slit experiment. The time for disappearance of the interference fringes is estimated from heuristic arguments related to fingerprints of chaotic dynamics of a classical counterpart of the coherently rotating complex. Validity of this estimate is confirmed numerically for the H+D{sub 2} chemical reaction. Thus we demonstrate the quantum-classical transition in temporal behavior of highly excited quantum many-body systems in the absence of external noise and coupling to an environment.
Simulation of n-qubit quantum systems. III. Quantum operations
NASA Astrophysics Data System (ADS)
Radtke, T.; Fritzsche, S.
2007-05-01
During the last decade, several quantum information protocols, such as quantum key distribution, teleportation or quantum computation, have attracted a lot of interest. Despite the recent success and research efforts in quantum information processing, however, we are just at the beginning of understanding the role of entanglement and the behavior of quantum systems in noisy environments, i.e. for nonideal implementations. Therefore, in order to facilitate the investigation of entanglement and decoherence in n-qubit quantum registers, here we present a revised version of the FEYNMAN program for working with quantum operations and their associated (Jamiołkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. Apart from the implementation of different noise models, the current program extension may help investigate the fragility of many quantum states, one of the main obstacles in realizing quantum information protocols today. Program summaryTitle of program: Feynman Catalogue identifier: ADWE_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE_v3_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: None Operating systems: Any system that supports MAPLE; tested under Microsoft Windows XP, SuSe Linux 10 Program language used:MAPLE 10 Typical time and memory requirements: Most commands that act upon quantum registers with five or less qubits take ⩽10 seconds of processor time (on a Pentium 4 processor with ⩾2 GHz or equivalent) and 5-20 MB of memory. Especially when working with symbolic expressions, however, the memory and time requirements critically depend on the number of qubits in the quantum registers, owing to the exponential dimension growth of the associated Hilbert space. For example, complex (symbolic) noise models (with several Kraus operators) for multi-qubit systems
NASA Astrophysics Data System (ADS)
Zhang, Fangfang; Liu, Shutang
2014-10-01
Considering the time lag produced by the transmission in chaos-communication, we present self-time-delay synchronization (STDS) of complex chaotic systems. STDS implies that the synchronization between the time-delay system (the receiver) and the original system (the transmitter) while maintaining the structure and parameters of systems unchanged, thus these various problems produced by time-delay in practice are avoided. It is more suitable to simulate real communication situation. Aimed to time-delay coupled complex chaotic systems, the control law is derived by active control technique. Based on STDS, a novel communication scheme is further designed according to chaotic masking. In simulation, we take time-delay coupled complex Lorenz system transmitting actual speech signal (analog signal) and binary signal as examples. The speech signal contains two components, which are transmitted by the real part and imaginary part of one complex state variable. Two sequences of binary bits are converted into analog signals by 2M-ary and zero-order holder, then added into the real part and imaginary part of one complex state variable. Therefore, the STDS controller is realized by one critical state variable. It is simple in principle and easy to implement in engineering. Moreover, the communication system is robust to noise. It is possible to adopt cheap circuits with time-delay, which is economical and practical for communication.
Global quantum discord in multipartite systems
Rulli, C. C.; Sarandy, M. S.
2011-10-15
We propose a global measure for quantum correlations in multipartite systems, which is obtained by suitably recasting the quantum discord in terms of relative entropy and local von Neumann measurements. The measure is symmetric with respect to subsystem exchange and is shown to be nonnegative for an arbitrary state. As an illustration, we consider tripartite correlations in the Werner-GHZ (Greenberger-Horne-Zeilinger) state and multipartite correlations at quantum criticality. In particular, in contrast with the pairwise quantum discord, we show that the global quantum discord is able to characterize the infinite-order quantum phase transition in the Ashkin-Teller spin chain.
Mixed coherent states in coupled chaotic systems: Design of secure wireless communication
NASA Astrophysics Data System (ADS)
Vigneshwaran, M.; Dana, S. K.; Padmanaban, E.
2016-12-01
A general coupling design is proposed to realize a mixed coherent (MC) state: coexistence of complete synchronization, antisynchronization, and amplitude death in different pairs of similar state variables of the coupled chaotic system. The stability of coupled system is ensured by the Lyapunov function and a scaling of each variable is also separately taken care of. When heterogeneity as a parameter mismatch is introduced in the coupled system, the coupling function facilitates to retain its coherence and displays the global stability with renewed scaling factor. Robust synchronization features facilitated by a MC state enable to design a dual modulation scheme: binary phase shift key (BPSK) and parameter mismatch shift key (PMSK), for secure data transmission. Two classes of decoders (coherent and noncoherent) are discussed, the noncoherent decoder shows better performance over the coherent decoder, mostly a noncoherent demodulator is preferred in biological implant applications. Both the modulation schemes are demonstrated numerically by using the Lorenz oscillator and the BPSK scheme is demonstrated experimentally using radio signals.
QUANTUM MECHANICS WITHOUT STATISTICAL POSTULATES
G. GEIGER; ET AL
2000-11-01
The Bohmian formulation of quantum mechanics describes the measurement process in an intuitive way without a reduction postulate. Due to the chaotic motion of the hidden classical particle all statistical features of quantum mechanics during a sequence of repeated measurements can be derived in the framework of a deterministic single system theory.
The Role of Chaotic Dynamics in the Cooling of Magmatic Systems in Subduction Related Environment
NASA Astrophysics Data System (ADS)
Petrelli, M.; El Omari, K.; Le Guer, Y.; Perugini, D.
2015-12-01
Understanding the dynamics occurring during the thermo-chemical evolution of igneous bodies is of crucial importance in both petrology and volcanology. This is particularly true in subduction related systems where large amount of magmas start, and sometime end, their differentiation histories at mid and lower crust levels. These magmas play a fundamental role in the evolution of both plutonic and volcanic systems but several key questions are still open about their thermal and chemical evolution: 1) what are the dynamics governing the development of these magmatic systems, 2) what are the timescales of cooling, crystallization and chemical differentiation; 4) how these systems contribute to the evolution of shallower magmatic systems? Recent works shed light on the mechanisms acting during the growing of new magmatic bodies and it is now accepted that large crustal igneous bodies result from the accretion and/or amalgamation of smaller ones. What is lacking now is how fluid dynamics of magma bodies can influence the evolution of these igneous systems. In this contribution we focus on the thermo-chemical evolution of a subduction related magmatic system at pressure conditions corresponding to mid-crustal levels (0.7 GPa, 20-25 km). In order to develop a robust model and address the Non-Newtonian behavior of crystal bearing magmas, we link the numerical formulation of the problem to experimental results and rheological modeling. We define quantitatively the thermo-chemical evolution of the system and address the timing required to reach the maximum packing fraction. We will shows that the development of chaotic dynamics significantly speed up the crystallization process decreasing the time needed to reach the maximum packing fraction. Our results have important implications for both the rheological history of the magmatic body and the refilling of shallower magmatic systems.
Robust quantum correlations in out-of-equilibrium matter-light systems
NASA Astrophysics Data System (ADS)
Acevedo, O. L.; Quiroga, L.; Rodríguez, F. J.; Johnson, N. F.
2015-09-01
High precision macroscopic quantum control in interacting light-matter systems remains a significant goal toward novel information processing and ultra-precise metrology. We show that the out-of-equilibrium behavior of a paradigmatic light-matter system (Dicke model) reveals two successive stages of enhanced quantum correlations beyond the traditional schemes of near-adiabatic and sudden quenches. The first stage features magnification of matter-only and light-only entanglement and squeezing due to effective nonlinear self-interactions. The second stage results from a highly entangled light-matter state, with enhanced superradiance and signatures of chaotic and highly quantum states. We show that these new effects scale up consistently with matter system size, and are reliable even in dissipative environments.
Thermodynamics of Weakly Measured Quantum Systems
NASA Astrophysics Data System (ADS)
Alonso, Jose Joaquin; Lutz, Eric; Romito, Alessandro
2016-02-01
We consider continuously monitored quantum systems and introduce definitions of work and heat along individual quantum trajectories that are valid for coherent superposition of energy eigenstates. We use these quantities to extend the first and second laws of stochastic thermodynamics to the quantum domain. We illustrate our results with the case of a weakly measured driven two-level system and show how to distinguish between quantum work and heat contributions. We finally employ quantum feedback control to suppress detector backaction and determine the work statistics.
Thermodynamics of Weakly Measured Quantum Systems.
Alonso, Jose Joaquin; Lutz, Eric; Romito, Alessandro
2016-02-26
We consider continuously monitored quantum systems and introduce definitions of work and heat along individual quantum trajectories that are valid for coherent superposition of energy eigenstates. We use these quantities to extend the first and second laws of stochastic thermodynamics to the quantum domain. We illustrate our results with the case of a weakly measured driven two-level system and show how to distinguish between quantum work and heat contributions. We finally employ quantum feedback control to suppress detector backaction and determine the work statistics.
NASA Astrophysics Data System (ADS)
He, Yaoyao; Yang, Shanlin; Xu, Qifa
2013-07-01
In order to solve the model of short-term cascaded hydroelectric system scheduling, a novel chaotic particle swarm optimization (CPSO) algorithm using improved logistic map is introduced, which uses the water discharge as the decision variables combined with the death penalty function. According to the principle of maximum power generation, the proposed approach makes use of the ergodicity, symmetry and stochastic property of improved logistic chaotic map for enhancing the performance of particle swarm optimization (PSO) algorithm. The new hybrid method has been examined and tested on two test functions and a practical cascaded hydroelectric system. The experimental results show that the effectiveness and robustness of the proposed CPSO algorithm in comparison with other traditional algorithms.
NASA Astrophysics Data System (ADS)
Bonenberger, Theresa S.; Baumgart, Jörg; Neumann, Cornelius
2016-04-01
For mixing light from different colored LEDs, an optical color mixing system is required to avoid colored shadows and color fringes. Concerning the different color mixing systems, mixing rods are widespread as they provide very good spatial color mixing with high efficiency. The essential disadvantage of mixing rods, so far, is the lack of angular color mixing. The solution presented in this publication is the application of a chaotic-dispersive billiard's geometry on the cross section of the mixing rod. To show both the spatial and the angular mixing properties of a square and a chaotic-dispersive mixing rod, simulations generated by the raytracing software ASAP are provided. All results are validated with prototype measurements.
Zeno dynamics in quantum open systems
Zhang, Yu-Ran; Fan, Heng
2015-01-01
Quantum Zeno effect shows that frequent observations can slow down or even stop the unitary time evolution of an unstable quantum system. This effect can also be regarded as a physical consequence of the statistical indistinguishability of neighboring quantum states. The accessibility of quantum Zeno dynamics under unitary time evolution can be quantitatively estimated by quantum Zeno time in terms of Fisher information. In this work, we investigate the accessibility of quantum Zeno dynamics in quantum open systems by calculating noisy Fisher information when a trace preserving and completely positive map is assumed. We firstly study the consequences of non-Markovian noise on quantum Zeno effect and give the exact forms of the dissipative Fisher information and the quantum Zeno time. Then, for the operator-sum representation, an achievable upper bound of the quantum Zeno time is given with the help of the results in noisy quantum metrology. It is of significance that the noise reducing the accuracy in the entanglement-enhanced parameter estimation can conversely be favorable for the accessibility of quantum Zeno dynamics of entangled states. PMID:26099840
Li, Xuejun; Xu, Jia; Yang, Yun
2015-01-01
Cloud workflow system is a kind of platform service based on cloud computing. It facilitates the automation of workflow applications. Between cloud workflow system and its counterparts, market-oriented business model is one of the most prominent factors. The optimization of task-level scheduling in cloud workflow system is a hot topic. As the scheduling is a NP problem, Ant Colony Optimization (ACO) and Particle Swarm Optimization (PSO) have been proposed to optimize the cost. However, they have the characteristic of premature convergence in optimization process and therefore cannot effectively reduce the cost. To solve these problems, Chaotic Particle Swarm Optimization (CPSO) algorithm with chaotic sequence and adaptive inertia weight factor is applied to present the task-level scheduling. Chaotic sequence with high randomness improves the diversity of solutions, and its regularity assures a good global convergence. Adaptive inertia weight factor depends on the estimate value of cost. It makes the scheduling avoid premature convergence by properly balancing between global and local exploration. The experimental simulation shows that the cost obtained by our scheduling is always lower than the other two representative counterparts.
An enhanced mobile-healthcare emergency system based on extended chaotic maps.
Lee, Cheng-Chi; Hsu, Che-Wei; Lai, Yan-Ming; Vasilakos, Athanasios
2013-10-01
Mobile Healthcare (m-Healthcare) systems, namely smartphone applications of pervasive computing that utilize wireless body sensor networks (BSNs), have recently been proposed to provide smartphone users with health monitoring services and received great attentions. An m-Healthcare system with flaws, however, may leak out the smartphone user's personal information and cause security, privacy preservation, or user anonymity problems. In 2012, Lu et al. proposed a secure and privacy-preserving opportunistic computing (SPOC) framework for mobile-Healthcare emergency. The brilliant SPOC framework can opportunistically gather resources on the smartphone such as computing power and energy to process the computing-intensive personal health information (PHI) in case of an m-Healthcare emergency with minimal privacy disclosure. To balance between the hazard of PHI privacy disclosure and the necessity of PHI processing and transmission in m-Healthcare emergency, in their SPOC framework, Lu et al. introduced an efficient user-centric privacy access control system which they built on the basis of an attribute-based access control mechanism and a new privacy-preserving scalar product computation (PPSPC) technique. However, we found out that Lu et al.'s protocol still has some secure flaws such as user anonymity and mutual authentication. To fix those problems and further enhance the computation efficiency of Lu et al.'s protocol, in this article, the authors will present an improved mobile-Healthcare emergency system based on extended chaotic maps. The new system is capable of not only providing flawless user anonymity and mutual authentication but also reducing the computation cost.
Orbital stability analysis and chaotic dynamics of exoplanets in multi-stellar systems
NASA Astrophysics Data System (ADS)
Satyal, Suman
The advancement in detection technology has substantially increased the discovery rate of exoplanets in the last two decades. The confirmation of thousands of exoplanets orbiting the solar type stars has raised new astrophysical challenges, including the studies of orbital dynamics and long-term stability of such planets. Continuous orbital stability of the planet in stellar habitable zone is considered vital for life to develop. Hence, these studies furthers one self-evident aim of mankind to find an answer to the century old question: Are we alone?. This dissertation investigates the planetary orbits in single and binary star systems. Within binaries, a planet could orbit either one or both stars as S-type or P-type, respectively. I have considered S-type planets in two binaries, gamma Cephei and HD 196885, and compute their orbits by using various numerical techniques to assess their periodic, quasi-periodic or chaotic nature. The Hill stability (HS) function, which measures the orbital perturbation induced by the nearby companion, is calculated for each system and then its efficacy as a new chaos indicator is tested against Maximum Lyapunov Exponents (MLE) and Mean Exponential Growth factor of Nearby Orbits (MEGNO). The dynamics of HD 196885 AB is further explored with an emphasis on the planet's higher orbital inclination relative to the binary plane. I have quantitatively mapped out the chaotic and quasi-periodic regions of the system's phase space, which indicates a likely regime of the planet's inclination. In, addition, the resonant angle is inspected to determine whether alternation between libration and circulation occurs as a consequence of Kozai oscillations, a probable mechanism that can drive the planetary orbit to a large inclination. The studies of planetary system in GJ 832 shows potential of hosting multiple planets in close orbits. The phase space of GJ 832c (inner planet) and the Earth-mass test planet(s) are analyzed for periodic
Das, Ashok Kumar; Goswami, Adrijit
2014-06-01
Recently, Awasthi and Srivastava proposed a novel biometric remote user authentication scheme for the telecare medicine information system (TMIS) with nonce. Their scheme is very efficient as it is based on efficient chaotic one-way hash function and bitwise XOR operations. In this paper, we first analyze Awasthi-Srivastava's scheme and then show that their scheme has several drawbacks: (1) incorrect password change phase, (2) fails to preserve user anonymity property, (3) fails to establish a secret session key beween a legal user and the server, (4) fails to protect strong replay attack, and (5) lacks rigorous formal security analysis. We then a propose a novel and secure biometric-based remote user authentication scheme in order to withstand the security flaw found in Awasthi-Srivastava's scheme and enhance the features required for an idle user authentication scheme. Through the rigorous informal and formal security analysis, we show that our scheme is secure against possible known attacks. In addition, we simulate our scheme for the formal security verification using the widely-accepted AVISPA (Automated Validation of Internet Security Protocols and Applications) tool and show that our scheme is secure against passive and active attacks, including the replay and man-in-the-middle attacks. Our scheme is also efficient as compared to Awasthi-Srivastava's scheme.
Quantum criticality in a double-quantum-dot system.
Zaránd, Gergely; Chung, Chung-Hou; Simon, Pascal; Vojta, Matthias
2006-10-20
We discuss the realization of the quantum-critical non-Fermi-liquid state, originally discovered within the two-impurity Kondo model, in double-quantum-dot systems. Contrary to common belief, the corresponding fixed point is robust against particle-hole and various other asymmetries and is unstable only to charge transfer between the two dots. We propose an experimental setup where such charge transfer processes are suppressed, allowing a controlled approach to the quantum-critical state. We also discuss transport and scaling properties in the vicinity of the critical point.
Quantum mechanics in complex systems
NASA Astrophysics Data System (ADS)
Hoehn, Ross Douglas
This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantum mechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantum mechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown
Chaotic dynamics and thermodynamics of periodic systems with long-range forces
NASA Astrophysics Data System (ADS)
Kumar, Pankaj
-body molecular-dynamics approach. The simulation results for the three-body systems show that the motion exhibits chaotic, quasiperiodic, and periodic behaviors in segmented regions of the phase space. The results for the large versions of the single-component and two-component Coulombic systems show no clear-cut indication of a phase transition. However, as predicted by the theoretical treatment, the simulated temperature dependencies of energy, pressure as well as Lyapunov exponent for the gravitational system indicate a phase transition and the critical temperature obtained in simulation agrees well with that from the theory.
Quantum speed limits in open system dynamics.
del Campo, A; Egusquiza, I L; Plenio, M B; Huelga, S F
2013-02-01
Bounds to the speed of evolution of a quantum system are of fundamental interest in quantum metrology, quantum chemical dynamics, and quantum computation. We derive a time-energy uncertainty relation for open quantum systems undergoing a general, completely positive, and trace preserving evolution which provides a bound to the quantum speed limit. When the evolution is of the Lindblad form, the bound is analogous to the Mandelstam-Tamm relation which applies in the unitary case, with the role of the Hamiltonian being played by the adjoint of the generator of the dynamical semigroup. The utility of the new bound is exemplified in different scenarios, ranging from the estimation of the passage time to the determination of precision limits for quantum metrology in the presence of dephasing noise.
Mohammadzadeh, Ardashir; Ghaemi, Sehraneh
2015-09-01
This paper proposes a novel approach for training of proposed recurrent hierarchical interval type-2 fuzzy neural networks (RHT2FNN) based on the square-root cubature Kalman filters (SCKF). The SCKF algorithm is used to adjust the premise part of the type-2 FNN and the weights of defuzzification and the feedback weights. The recurrence property in the proposed network is the output feeding of each membership function to itself. The proposed RHT2FNN is employed in the sliding mode control scheme for the synchronization of chaotic systems. Unknown functions in the sliding mode control approach are estimated by RHT2FNN. Another application of the proposed RHT2FNN is the identification of dynamic nonlinear systems. The effectiveness of the proposed network and its learning algorithm is verified by several simulation examples. Furthermore, the universal approximation of RHT2FNNs is also shown.
Quantum chaos meets coherent control.
Gong, Jiangbin; Brumer, Paul
2005-01-01
Coherent control of atomic and molecular processes has been a rapidly developing field. Applications of coherent control to large and complex molecular systems are expected to encounter the effects of chaos in the underlying classical dynamics, i.e., quantum chaos. Hence, recent work has focused on examining control in model chaotic systems. This work is reviewed, with an emphasis on a variety of new quantum phenomena that are of interest to both areas of quantum chaos and coherent control.
Quantum interference between independent reservoirs in open quantum systems
NASA Astrophysics Data System (ADS)
Chan, Ching-Kit; Lin, Guin-Dar; Yelin, Susanne F.; Lukin, Mikhail D.
2014-04-01
When a quantum system interacts with multiple reservoirs, the environmental effects are usually treated in an additive manner. We show that this assumption breaks down for non-Markovian environments that have finite memory times. Specifically, we demonstrate that quantum interferences between independent environments can qualitatively modify the dynamics of the physical system. We illustrate this effect with a two-level system coupled to two structured photonic reservoirs, discuss its origin using a nonequilibrium diagrammatic technique, and show an example when the application of this interference can result in an improved dark state preparation in a Λ system.
Quantum Q systems: from cluster algebras to quantum current algebras
NASA Astrophysics Data System (ADS)
Di Francesco, Philippe; Kedem, Rinat
2017-02-01
This paper gives a new algebraic interpretation for the algebra generated by the quantum cluster variables of the A_r quantum Q-system (Di Francesco and Kedem in Int Math Res Not IMRN 10:2593-2642, 2014). We show that the algebra can be described as a quotient of the localization of the quantum algebra U_{√{q}}({n}[u,u^{-1}])subset U_{√{q}}(widehat{{sl}}_2), in the Drinfeld presentation. The generating current is made up of a subset of the cluster variables which satisfy the Q-system, which we call fundamental. The other cluster variables are given by a quantum determinant-type formula, and are polynomials in the fundamental generators. The conserved quantities of the discrete evolution (Di Francesco and Kedem in Adv Math 228(1):97-152, 2011) described by quantum Q-system generate the Cartan currents at level 0, in a non-standard polarization. The rest of the quantum affine algebra is also described in terms of cluster variables.
NASA Astrophysics Data System (ADS)
Cook, Darcy; Ferens, Ken; Kinsner, Witold
Simulated Annealing (SA) has shown to be a successful technique in optimization problems. It has been applied to both continuous function optimization problems, and combinatorial optimization problems. There has been some work in modifying the SA algorithm to apply properties of chaotic processes with the goal of reducing the time to converge to an optimal or a good solution. There are several variations of these chaotic simulated annealing (CSA) algorithms. In this paper a new variation of chaotic simulated annealing is proposed and is applied in solving a combinatorial optimization problem in multiprocessor task allocation. The experiments show the CSA algorithms reach a good solution faster than traditional SA algorithms in many cases because of a wider initial solution search.
Response of a two-level quantum system to a class of time-dependent quasiperiodic perturbations
Luck, J.M.; Orland, H.; Smilansky, U.
1988-11-01
We study analytically the response of a two-level quantum system to a certain class of time-dependent quasiperiodic perturbations generated by a Fibonacci sequence. We show that the quasi-energy spectrum (Fourier transform of the evolution operator) generically is not a denumerable sum of delta functions. Hence the response is not quasiperiodic. Several numerical investigations (Poincare sections, polarization fluctuations, etc.) suggest an intermediate kind of behavior between quasiperiodic and chaotic.
Quasi-Periodically Driven Quantum Systems
NASA Astrophysics Data System (ADS)
Verdeny, Albert; Puig, Joaquim; Mintert, Florian
2016-10-01
Floquet theory provides rigorous foundations for the theory of periodically driven quantum systems. In the case of non-periodic driving, however, the situation is not so well understood. Here, we provide a critical review of the theoretical framework developed for quasi-periodically driven quantum systems. Although the theoretical footing is still under development, we argue that quasi-periodically driven quantum systems can be treated with generalisations of Floquet theory in suitable parameter regimes. Moreover, we provide a generalisation of the Floquet-Magnus expansion and argue that quasi-periodic driving offers a promising route for quantum simulations.
My chaotic trajectory: A brief (personalized) history of solar-system dynamics.
NASA Astrophysics Data System (ADS)
Burns, Joseph A.
2014-05-01
I will use this opportunity to recall my professional career. Like many, I was drawn into the space program during the mid-60s and early 70s when the solar system’s true nature was being revealed. Previously, dynamical astronomy discussed the short-term, predictable motions of point masses; simultaneously, small objects (e.g., satellites, asteroids, dust) were thought boring rather than dynamically rich. Many of today’s most active research subjects were unknown: TNOs, planetary rings, exoplanets and debris disks. The continuing stream of startling findings by spacecraft, ground-based surveys and numerical simulations forced a renaissance in celestial mechanics, incorporating new dynamical paradigms and additional physics (e.g., energy loss, catastrophic events, radiation forces). My interests evolved as the space program expanded outward: dust, asteroids, natural satellites, rings; rotations, orbital evolution, origins. Fortunately for me, in the early days, elementary models with simple solutions were often adequate to gain a first-order explanation of many puzzles. One could be a generalist, always learning new things.My choice of research subjects was influenced greatly by: i) Cornell colleagues involved in space missions who shared results: the surprising diversity of planetary satellites, the unanticipated orbital and rotational dynamics of asteroids, the chaotic histories of solar system bodies, the non-intuitive behavior of dust and planetary rings, irregular satellites. ii) Teaching introductory courses in applied math, dynamics and planetary science encouraged understandable models. iii) The stimulation of new ideas owing to service at Icarus and on space policy forums. iv) Most importantly, excellent students and colleagues who pushed me into new research directions, and who then stimulated and educated me about those topics.If time allows, I will describe some of today’s puzzles for me and point out similarities between the past development in our
Lu, Yanrong; Li, Lixiang; Peng, Haipeng; Xie, Dong; Yang, Yixian
2015-06-01
The Telecare Medicine Information Systems (TMISs) provide an efficient communicating platform supporting the patients access health-care delivery services via internet or mobile networks. Authentication becomes an essential need when a remote patient logins into the telecare server. Recently, many extended chaotic maps based authentication schemes using smart cards for TMISs have been proposed. Li et al. proposed a secure smart cards based authentication scheme for TMISs using extended chaotic maps based on Lee's and Jiang et al.'s scheme. In this study, we show that Li et al.'s scheme has still some weaknesses such as violation the session key security, vulnerability to user impersonation attack and lack of local verification. To conquer these flaws, we propose a chaotic maps and smart cards based password authentication scheme by applying biometrics technique and hash function operations. Through the informal and formal security analyses, we demonstrate that our scheme is resilient possible known attacks including the attacks found in Li et al.'s scheme. As compared with the previous authentication schemes, the proposed scheme is more secure and efficient and hence more practical for telemedical environments.
Moon, Jongho; Choi, Younsung; Kim, Jiye; Won, Dongho
2016-03-01
Recently, numerous extended chaotic map-based password authentication schemes that employ smart card technology were proposed for Telecare Medical Information Systems (TMISs). In 2015, Lu et al. used Li et al.'s scheme as a basis to propose a password authentication scheme for TMISs that is based on biometrics and smart card technology and employs extended chaotic maps. Lu et al. demonstrated that Li et al.'s scheme comprises some weaknesses such as those regarding a violation of the session-key security, a vulnerability to the user impersonation attack, and a lack of local verification. In this paper, however, we show that Lu et al.'s scheme is still insecure with respect to issues such as a violation of the session-key security, and that it is vulnerable to both the outsider attack and the impersonation attack. To overcome these drawbacks, we retain the useful properties of Lu et al.'s scheme to propose a new password authentication scheme that is based on smart card technology and requires the use of chaotic maps. Then, we show that our proposed scheme is more secure and efficient and supports security properties.
Adiabatic Quantum Search in Open Systems.
Wild, Dominik S; Gopalakrishnan, Sarang; Knap, Michael; Yao, Norman Y; Lukin, Mikhail D
2016-10-07
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.
Adiabatic Quantum Search in Open Systems
NASA Astrophysics Data System (ADS)
Wild, Dominik S.; Gopalakrishnan, Sarang; Knap, Michael; Yao, Norman Y.; Lukin, Mikhail D.
2016-10-01
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.
Tailoring superradiance to design artificial quantum systems.
Longo, Paolo; Keitel, Christoph H; Evers, Jörg
2016-03-24
Cooperative phenomena arising due to the coupling of individual atoms via the radiation field are a cornerstone of modern quantum and optical physics. Recent experiments on x-ray quantum optics added a new twist to this line of research by exploiting superradiance in order to construct artificial quantum systems. However, so far, systematic approaches to deliberately design superradiance properties are lacking, impeding the desired implementation of more advanced quantum optical schemes. Here, we develop an analytical framework for the engineering of single-photon superradiance in extended media applicable across the entire electromagnetic spectrum, and show how it can be used to tailor the properties of an artificial quantum system. This "reverse engineering" of superradiance not only provides an avenue towards non-linear and quantum mechanical phenomena at x-ray energies, but also leads to a unified view on and a better understanding of superradiance across different physical systems.
Tailoring superradiance to design artificial quantum systems
NASA Astrophysics Data System (ADS)
Longo, Paolo; Keitel, Christoph H.; Evers, Jörg
2016-03-01
Cooperative phenomena arising due to the coupling of individual atoms via the radiation field are a cornerstone of modern quantum and optical physics. Recent experiments on x-ray quantum optics added a new twist to this line of research by exploiting superradiance in order to construct artificial quantum systems. However, so far, systematic approaches to deliberately design superradiance properties are lacking, impeding the desired implementation of more advanced quantum optical schemes. Here, we develop an analytical framework for the engineering of single-photon superradiance in extended media applicable across the entire electromagnetic spectrum, and show how it can be used to tailor the properties of an artificial quantum system. This “reverse engineering” of superradiance not only provides an avenue towards non-linear and quantum mechanical phenomena at x-ray energies, but also leads to a unified view on and a better understanding of superradiance across different physical systems.
Quantum Interference between independent environments in open quantum systems
NASA Astrophysics Data System (ADS)
Chan, Ching-Kit; Lin, Guin-Dar; Yelin, Susanne; Lukin, Mikhail
2014-03-01
When a general quantum system interacts with multiple environments, the environmental effects are usually treated in an additive manner in the master equation. This assumption becomes questionable for non-Markovian environments that have finite memory times. Here, we show that quantum interferences between independent environments exist and can qualitatively modify the dynamics of the reduced physical system. We illustrate this effect with examples of atomic systems coupled to structured reservoirs, and discuss its origin in general using a non-equilibrium diagrammatic technique. The consequential decoherence dynamics cannot be captured by an additive master equation.
NASA Astrophysics Data System (ADS)
Yadmellat, Peyman; Nikravesh, S. Kamaleddin Yadavar
2011-01-01
In this paper, a recursive delayed output-feedback control strategy is considered for stabilizing unstable periodic orbit of unknown nonlinear chaotic systems. An unknown nonlinearity is directly estimated by a linear-in-parameter neural network which is then used in an observer structure. An on-line modified back propagation algorithm with e-modification is used to update the weights of the network. The globally uniformly ultimately boundedness of overall closed-loop system response is analytically ensured using Razumikhin lemma. To verify the effectiveness of the proposed observer-based controller, a set of simulations is performed on a Rossler system in comparison with several previous methods.
Virtual Libraries: Interactive Support Software and an Application in Chaotic Models.
ERIC Educational Resources Information Center
Katsirikou, Anthi; Skiadas, Christos; Apostolou, Apostolos; Rompogiannakis, Giannis
This paper begins with a discussion of the characteristics and the singularity of chaotic systems, including dynamic systems theory, chaotic orbit, fractals, chaotic attractors, and characteristics of chaotic systems. The second section addresses the digital libraries (DL) concept and the appropriateness of chaotic models, including definition and…
Controlling the shannon entropy of quantum systems.
Xing, Yifan; Wu, Jun
2013-01-01
This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.
Quantum signatures of chaos or quantum chaos?
NASA Astrophysics Data System (ADS)
Bunakov, V. E.
2016-11-01
A critical analysis of the present-day concept of chaos in quantum systems as nothing but a "quantum signature" of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville-Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stability parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.
Slightly anharmonic systems in quantum optics
NASA Technical Reports Server (NTRS)
Klimov, Andrey B.; Chumakov, Sergey M.
1995-01-01
We consider an arbitrary atomic system (n-level atom or many such atoms) interacting with a strong resonant quantum field. The approximate evolution operator for a quantum field case can be produced from the atomic evolution operator in an external classical field by a 'quantization prescription', passing the operator arguments to Wigner D-functions. Many important phenomena arising from the quantum nature of the field can be described by such a way.
NASA Astrophysics Data System (ADS)
Li, Yuan; Lv, Hui; Jiao, Dongxiu
2017-03-01
In this study, an adaptive neural network synchronization (NNS) approach, capable of guaranteeing prescribed performance (PP), is designed for non-identical fractional-order chaotic systems (FOCSs). For PP synchronization, we mean that the synchronization error converges to an arbitrary small region of the origin with convergence rate greater than some function given in advance. Neural networks are utilized to estimate unknown nonlinear functions in the closed-loop system. Based on the integer-order Lyapunov stability theorem, a fractional-order adaptive NNS controller is designed, and the PP can be guaranteed. Finally, simulation results are presented to confirm our results.
NASA Astrophysics Data System (ADS)
Liu, Dan-Feng; Wu, Zhao-Yan; Ye, Qing-Ling
2014-04-01
In this paper, structure identification of an uncertain network coupled with complex-variable chaotic systems is investigated. Both the topological structure and the system parameters can be unknown and need to be identified. Based on impulsive stability theory and the Lyapunov function method, an impulsive control scheme combined with an adaptive strategy is adopted to design effective and universal network estimators. The restriction on the impulsive interval is relaxed by adopting an adaptive strategy. Further, the proposed method can monitor the online switching topology effectively. Several numerical simulations are provided to illustrate the effectiveness of the theoretical results.
Simulation of n-qubit quantum systems. V. Quantum measurements
NASA Astrophysics Data System (ADS)
Radtke, T.; Fritzsche, S.
2010-02-01
The FEYNMAN program has been developed during the last years to support case studies on the dynamics and entanglement of n-qubit quantum registers. Apart from basic transformations and (gate) operations, it currently supports a good number of separability criteria and entanglement measures, quantum channels as well as the parametrizations of various frequently applied objects in quantum information theory, such as (pure and mixed) quantum states, hermitian and unitary matrices or classical probability distributions. With the present update of the FEYNMAN program, we provide a simple access to (the simulation of) quantum measurements. This includes not only the widely-applied projective measurements upon the eigenspaces of some given operator but also single-qubit measurements in various pre- and user-defined bases as well as the support for two-qubit Bell measurements. In addition, we help perform generalized and POVM measurements. Knowing the importance of measurements for many quantum information protocols, e.g., one-way computing, we hope that this update makes the FEYNMAN code an attractive and versatile tool for both, research and education. New version program summaryProgram title: FEYNMAN Catalogue identifier: ADWE_v5_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE_v5_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 27 210 No. of bytes in distributed program, including test data, etc.: 1 960 471 Distribution format: tar.gz Programming language: Maple 12 Computer: Any computer with Maple software installed Operating system: Any system that supports Maple; the program has been tested under Microsoft Windows XP and Linux Classification: 4.15 Catalogue identifier of previous version: ADWE_v4_0 Journal reference of previous version: Comput. Phys. Commun
Accidental degeneracies in nonlinear quantum deformed systems
NASA Astrophysics Data System (ADS)
Aleixo, A. N. F.; Balantekin, A. B.
2011-09-01
We construct a multi-parameter nonlinear deformed algebra for quantum confined systems that includes many other deformed models as particular cases. We demonstrate that such systems exhibit the property of accidental pairwise energy level degeneracies. We also study, as a special case of our multi-parameter deformation formalism, the extension of the Tamm-Dancoff cutoff deformed oscillator and the occurrence of accidental pairwise degeneracy in the energy levels of the deformed system. As an application, we discuss the case of a trigonometric Rosen-Morse potential, which is successfully used in models for quantum confined systems, ranging from electrons in quantum dots to quarks in hadrons.
Quantum Simulation of Tunneling in Small Systems
Sornborger, Andrew T.
2012-01-01
A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because of the number of gates and qubits necessary, however, digital quantum particle simulations remain untested. A contributing factor to the system size required is the number of ancillary qubits needed to implement matrix exponentials of the potential operator. Here, we show that a set of tunneling problems may be investigated with no ancillary qubits and a cost of one single-qubit operator per time step for the potential evolution, eliminating at least half of the quantum gates required for the algorithm and more than that in the general case. Such simulations are within reach of current quantum computer architectures. PMID:22916333
Cryptosystems based on chaotic dynamics
McNees, R.A.; Protopopescu, V.; Santoro, R.T.; Tolliver, J.S.
1993-08-01
An encryption scheme based on chaotic dynamics is presented. This scheme makes use of the efficient and reproducible generation of cryptographically secure pseudo random numbers from chaotic maps. The result is a system which encrypts quickly and possesses a large keyspace, even in small precision implementations. This system offers an excellent solution to several problems including the dissemination of key material, over the air rekeying, and other situations requiring the secure management of information.
Lee, Tian-Fu
2013-12-01
A smartcard-based authentication and key agreement scheme for telecare medicine information systems enables patients, doctors, nurses and health visitors to use smartcards for secure login to medical information systems. Authorized users can then efficiently access remote services provided by the medicine information systems through public networks. Guo and Chang recently improved the efficiency of a smartcard authentication and key agreement scheme by using chaotic maps. Later, Hao et al. reported that the scheme developed by Guo and Chang had two weaknesses: inability to provide anonymity and inefficient double secrets. Therefore, Hao et al. proposed an authentication scheme for telecare medicine information systems that solved these weaknesses and improved performance. However, a limitation in both schemes is their violation of the contributory property of key agreements. This investigation discusses these weaknesses and proposes a new smartcard-based authentication and key agreement scheme that uses chaotic maps for telecare medicine information systems. Compared to conventional schemes, the proposed scheme provides fewer weaknesses, better security, and more efficiency.
NASA Astrophysics Data System (ADS)
Casati, Giulio; Chirikov, Boris
1995-04-01
Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos
NASA Astrophysics Data System (ADS)
Casati, Giulio; Chirikov, Boris
2006-11-01
Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos
Tahoun, A H
2017-01-01
In this paper, the stabilization problem of actuators saturation in uncertain chaotic systems is investigated via an adaptive PID control method. The PID control parameters are auto-tuned adaptively via adaptive control laws. A multi-level augmented error is designed to account for the extra terms appearing due to the use of PID and saturation. The proposed control technique uses both the state-feedback and the output-feedback methodologies. Based on Lyapunov׳s stability theory, new anti-windup adaptive controllers are proposed. Demonstrative examples with MATLAB simulations are studied. The simulation results show the efficiency of the proposed adaptive PID controllers.
Galilei invariant technique for quantum system description
Kamuntavičius, Gintautas P.
2014-04-15
Problems with quantum systems models, violating Galilei invariance are examined. The method for arbitrary non-relativistic quantum system Galilei invariant wave function construction, applying a modified basis where center-of-mass excitations have been removed before Hamiltonian matrix diagonalization, is developed. For identical fermion system, the Galilei invariant wave function can be obtained while applying conventional antisymmetrization methods of wave functions, dependent on single particle spatial variables.
NASA Astrophysics Data System (ADS)
Chao-Xia, Zhang; Si-Min, Yu
2016-05-01
This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively adjusting multiple parameters of conventional multi-parameter control, this paper introduces a unified step function controlled by a single parameter for constructing various multi-wing chaotic and hyperchaotic systems. In particular, to the best of the authors’ knowledge, this is also the first time to find a non-equilibrium multi-wing hyperchaotic system by means of the unified step function control. According to the heteroclinic loop Shilnikov theorem, some properties for multi-wing attractors and its chaos mechanism are further discussed and analyzed. A circuit for multi-wing systems is designed and implemented for demonstration, which verifies the effectiveness of the proposed approach. Project supported by the National Natural Science Foundation of China (Grant No. 61403143), the Natural Science Foundation of Guangdong Province, China (Grant No. 2014A030313739), the Science and Technology Foundation Program of Guangzhou City, China (Grant No. 201510010124), and the Excellent Doctorial Dissertation Foundation of Guangdong Province, China (Grant No. XM080054).
Zaher, Ashraf A
2008-06-01
A simple technique is introduced to build fast state observers for chaotic systems when only a scalar time series of the output is available. This technique relies on using a backstepping-like approach via introducing new virtual states that can be observed using the drive-response synchronization mechanism. The proposed dynamic structure of the virtual states allows for employing control parameters that can adjust the convergence rate of the observed states. In addition, these control parameters can be used to improve the transient performance of the response system to accommodate small and large variations of the initial conditions, thus achieving superior performance to conventional synchronization techniques. Simple Lyapunov functions are used to estimate the range of the control parameters that guarantees stable operation of the proposed technique. Three benchmark chaotic systems are considered for illustration; namely, the Lorenz, Chua, and Rossler systems. The conflict between stability and agility of the states observer is analyzed and a simple tuning mechanism is introduced. Implementation of the proposed technique in both analog and digital forms is also addressed and experimental results are reported ensuring feasibility and real-time applicability. Finally, advantages and limitations are discussed and a comparison with conventional synchronization methods is investigated.
NASA Astrophysics Data System (ADS)
Chedjou, J. C.; Dada, J. P.; Moussa, I.; Takenga, C.; Anne, R.; Kyamakya, K.
This paper studies synchronization transitions in a system of coupled non-identical self-sustained chaotic oscillators of the Rössler type. The interest devoted to the Rössler oscillators is motivated by their capability to behave chaotically at very high frequencies. Both phase synchronization and lag synchronization are analyzed in terms of a coupling parameter. It is shown that both types of synchronization can be achieved when monitoring a coupling parameter. The advantage of using one parameter to insure both types of synchronization is found in practical realizations. Indeed one should monitor only one resistor to predict the boundaries of the control resistor for the occurrence of each type of synchronization. Another advantage of monitoring only one resistor is found in the accuracy of results. An experimental study of the synchronization is carried out. Experimental waveforms in the drive and response systems are obtained. The waveforms are compared to confirm the achievement of sync hronization experimentally. One of the advantages of using analog simulation in this work is the possibility to analyze the behaviour of the coupled system at very high frequencies by performing an appropriate time scaling. This offers the possibility of using our coupled system for Ultra-wideband (UWB) applications.
Inhibition of quantum transport due to 'scars' of unstable periodic orbits
NASA Technical Reports Server (NTRS)
Jensen, R. V.; Sanders, M. M.; Saraceno, M.; Sundaram, B.
1989-01-01
A new quantum mechanism for the suppression of chaotic ionization of highly excited hydrogen atoms explains the appearance of anomalously stable states in the microwave ionization experiments of Koch et al. A novel phase-space representation of the perturbed wave functions reveals that the inhibition of quantum transport is due to the selective excitation of wave functions that are highly localized near unstable periodic orbits in the chaotic classical phase space. The 'scarred' wave functions provide a new basis for the quantum description of a variety of classically chaotic systems.
Quantum Simulation for Open-System Dynamics
NASA Astrophysics Data System (ADS)
Wang, Dong-Sheng; de Oliveira, Marcos Cesar; Berry, Dominic; Sanders, Barry
2013-03-01
Simulations are essential for predicting and explaining properties of physical and mathematical systems yet so far have been restricted to classical and closed quantum systems. Although forays have been made into open-system quantum simulation, the strict algorithmic aspect has not been explored yet is necessary to account fully for resource consumption to deliver bounded-error answers to computational questions. An open-system quantum simulator would encompass classical and closed-system simulation and also solve outstanding problems concerning, e.g. dynamical phase transitions in non-equilibrium systems, establishing long-range order via dissipation, verifying the simulatability of open-system dynamics on a quantum Turing machine. We construct an efficient autonomous algorithm for designing an efficient quantum circuit to simulate many-body open-system dynamics described by a local Hamiltonian plus decoherence due to separate baths for each particle. The execution time and number of gates for the quantum simulator both scale polynomially with the system size. DSW funded by USARO. MCO funded by AITF and Brazilian agencies CNPq and FAPESP through Instituto Nacional de Ciencia e Tecnologia-Informacao Quantica (INCT-IQ). DWB funded by ARC Future Fellowship (FT100100761). BCS funded by AITF, CIFAR, NSERC and USARO.
Sun, Yeong-Jeu; Wu, Yu-Biaw; Wang, Ching-Cheng
2013-06-01
In this study, the concept of global exponential ε-stabilization is introduced and the robust stabilization for a class of nonlinear systems with single input is investigated. Based on Lyapunov-like Theorem with differential and integral inequalities, a feedback control is proposed to realize the global stabilization of such nonlinear systems with any pre-specified exponential convergence rate. The guaranteed exponential convergence rate can be also correctly estimated. This result can be straightforwardly applicable to some famous chaotic systems. Besides, it will be proven that a single and linear control, with lower dimensions than that of the states, can realize the global exponential stability of some famous chaotic systems. Finally, comparisons of our main results with recently published results as well as numerical examples with circuit realization are provided to show the effectiveness and superiority of the obtained results.
NASA Astrophysics Data System (ADS)
Sun, Yeong-Jeu; Wu, Yu-Biaw; Wang, Ching-Cheng
2013-06-01
In this study, the concept of global exponential ɛ-stabilization is introduced and the robust stabilization for a class of nonlinear systems with single input is investigated. Based on Lyapunov-like Theorem with differential and integral inequalities, a feedback control is proposed to realize the global stabilization of such nonlinear systems with any pre-specified exponential convergence rate. The guaranteed exponential convergence rate can be also correctly estimated. This result can be straightforwardly applicable to some famous chaotic systems. Besides, it will be proven that a single and linear control, with lower dimensions than that of the states, can realize the global exponential stability of some famous chaotic systems. Finally, comparisons of our main results with recently published results as well as numerical examples with circuit realization are provided to show the effectiveness and superiority of the obtained results.
Farivar, Faezeh; Shoorehdeli, Mahdi Aliyari
2012-01-01
In this paper, fault tolerant synchronization of chaotic gyroscope systems versus external disturbances via Lyapunov rule-based fuzzy control is investigated. Taking the general nature of faults in the slave system into account, a new synchronization scheme, namely, fault tolerant synchronization, is proposed, by which the synchronization can be achieved no matter whether the faults and disturbances occur or not. By making use of a slave observer and a Lyapunov rule-based fuzzy control, fault tolerant synchronization can be achieved. Two techniques are considered as control methods: classic Lyapunov-based control and Lyapunov rule-based fuzzy control. On the basis of Lyapunov stability theory and fuzzy rules, the nonlinear controller and some generic sufficient conditions for global asymptotic synchronization are obtained. The fuzzy rules are directly constructed subject to a common Lyapunov function such that the error dynamics of two identical chaotic motions of symmetric gyros satisfy stability in the Lyapunov sense. Two proposed methods are compared. The Lyapunov rule-based fuzzy control can compensate for the actuator faults and disturbances occurring in the slave system. Numerical simulation results demonstrate the validity and feasibility of the proposed method for fault tolerant synchronization.
Quantum entanglement in condensed matter systems
NASA Astrophysics Data System (ADS)
Laflorencie, Nicolas
2016-08-01
This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of correlated quantum systems, useful and non-trivial information can be obtained through the study of the reduced density matrix, whose eigenvalue spectrum (the entanglement spectrum) and the associated Rényi entropies are now well recognized to contain key features. In particular, the celebrated area law for the entanglement entropy of ground-states will be discussed from the perspective of its subleading corrections which encode universal details of various quantum states of matter, e.g. symmetry breaking states or topological order. Going beyond entropies, the study of the low-lying part of the entanglement spectrum also allows to diagnose topological properties or give a direct access to the excitation spectrum of the edges, and may also raise significant questions about the underlying entanglement Hamiltonian. All these powerful tools can be further applied to shed some light on disordered quantum systems where impurity/disorder can conspire with quantum fluctuations to induce non-trivial effects. Disordered quantum spin systems, the Kondo effect, or the many-body localization problem, which have all been successfully (re)visited through the prism of quantum entanglement, will be discussed in detail. Finally, the issue of experimental access to entanglement measurement will be addressed, together with its most recent developments.
Characteristic Energy Scales of Quantum Systems.
ERIC Educational Resources Information Center
Morgan, Michael J.; Jakovidis, Greg
1994-01-01
Provides a particle-in-a-box model to help students understand and estimate the magnitude of the characteristic energy scales of a number of quantum systems. Also discusses the mathematics involved with general computations. (MVL)
Software-defined Quantum Communication Systems
Humble, Travis S; Sadlier, Ronald J
2013-01-01
We show how to extend the paradigm of software-defined communication to include quantum communication systems. We introduce the decomposition of a quantum communication terminal into layers separating the concerns of the hardware, software, and middleware. We provide detailed descriptions of how each component operates and we include results of an implementation of the super-dense coding protocol. We argue that the versatility of software-defined quantum communication test beds can be useful for exploring new regimes in communication and rapidly prototyping new systems.
NASA Astrophysics Data System (ADS)
Khanzadeh, Alireza; Pourgholi, Mahdi
2016-08-01
In the conventional chaos synchronization methods, the time at which two chaotic systems are synchronized, is usually unknown and depends on initial conditions. In this work based on Lyapunov stability theory a sliding mode controller with time-varying switching surfaces is proposed to achieve chaos synchronization at a pre-specified time for the first time. The proposed controller is able to synchronize chaotic systems precisely at any time when we want. Moreover, by choosing the time-varying switching surfaces in a way that the reaching phase is eliminated, the synchronization becomes robust to uncertainties and exogenous disturbances. Simulation results are presented to show the effectiveness of the proposed method of stabilizing and synchronizing chaotic systems with complete robustness to uncertainty and disturbances exactly at a pre-specified time.
NASA Astrophysics Data System (ADS)
Gu, Huaguang
2013-06-01
The transition from chaotic bursting to chaotic spiking has been simulated and analyzed in theoretical neuronal models. In the present study, we report experimental observations in a neural pacemaker of a transition from chaotic bursting to chaotic spiking within a bifurcation scenario from period-1 bursting to period-1 spiking. This was induced by adjusting extracellular calcium or potassium concentrations. The bifurcation scenario began from period-doubling bifurcations or period-adding sequences of bursting pattern. This chaotic bursting is characterized by alternations between multiple continuous spikes and a long duration of quiescence, whereas chaotic spiking is comprised of fast, continuous spikes without periods of quiescence. Chaotic bursting changed to chaotic spiking as long interspike intervals (ISIs) of quiescence disappeared within bursting patterns, drastically decreasing both ISIs and the magnitude of the chaotic attractors. Deterministic structures of the chaotic bursting and spiking patterns are also identified by a short-term prediction. The experimental observations, which agree with published findings in theoretical neuronal models, demonstrate the existence and reveal the dynamics of a neuronal transition from chaotic bursting to chaotic spiking in the nervous system.
The Optical Response of Strongly Coupled Quantum Dot- Metal Nanoparticle Hybrid Systems
NASA Astrophysics Data System (ADS)
Artuso, Ryan Domenick
In this thesis, we study, theoretically, hybrid systems composed of semiconducting quantum dots (SQDs) and metallic nanoparticles (MNPs) which are coupled by means of an applied optical field. Systems composed of SQDs and MNPs have recently been a very active area of research. Such structures are considered to be viable candidates for use in nanodevices in quantum information and nanoscale excitation transfer. The goal of this thesis is to investigate the interactions of the constituent particles and predict the hybrid response of SQD/MNP systems. We first study a single SQD coupled to a spherical MNP, and explore the relationship between the size of the constituents and the response of the system. We identify four distinct regimes of behavior in the strong field limit that each exhibit novel properties, namely, the Fano regime, exciton induced transparency, suppression and bistability. In chapter 3, we will explore these four regimes in detail and set bounds on each. In chapter 4, we then show that the response of the system can be tailored by engineering metal nanoparticle shape and the exciton resonance of SQDs to control the local-fields that couple the MNPs and SQDs. We identify regimes where dark modes and higher order multipolar modes can influence hybrid response. External fields do not directly drive MNP dark modes, so SQD/MNP coupling is dominated by the local induced coupling, providing a situation in which the induced self-interaction could be probed using near field techniques. Finally, we consider a system of two SQDs coupled to a MNP. In particular, we identify and address issues in modeling the system using a semiclassical approach, which can lead to unstable and chaotic behavior in a strong SQD-SQD coupling regime. When we model the system using a more quantum mechanical approach, this chaotic regime is absent. Finally, we compare the two models on a system with a strong plasmon-mediated interaction between the SQDs and a weak direct interaction
Software-defined Quantum Communication Systems
Humble, Travis S; Sadlier, Ronald J
2014-01-01
Quantum communication systems harness modern physics through state-of-the-art optical engineering to provide revolutionary capabilities. An important concern for quantum communication engineering is designing and prototyping these systems to prototype proposed capabilities. We apply the paradigm of software-defined communica- tion for engineering quantum communication systems to facilitate rapid prototyping and prototype comparisons. We detail how to decompose quantum communication terminals into functional layers defining hardware, software, and middleware concerns, and we describe how each layer behaves. Using the super-dense coding protocol as a test case, we describe implementations of both the transmitter and receiver, and we present results from numerical simulations of the behavior. We find that while the theoretical benefits of super dense coding are maintained, there is a classical overhead associated with the full implementation.
NASA Astrophysics Data System (ADS)
Welch, Kyle; Liebman-Pelaez, Alexander; Corwin, Eric
Equilibrium statistical mechanics is traditionally limited to thermal systems. Can it be applied to athermal, non-equilibrium systems that nonetheless satisfy the basic criteria of steady-state chaos and isotropy? We answer this question using a macroscopic system of chaotic surface waves which is, by all measures, non-equilibrium. The waves are generated in a dish of water that is vertically oscillated above a critical amplitude. We have constructed a rheometer that actively measures the drag imparted by the waves on a buoyant particle, a quantity entirely divorced in origin from the drag imparted by the fluid in which the particle floats. We also perform a separate, passive measurement, extracting a diffusion constant and effective temperature. Having directly measured all three properties (temperature, diffusion constant, and drag coefficient) we go on to show that our macroscopic, non-equilibrium case is wholly consistent with the Einstein relation, a classic result for equilibrium thermal systems.
Novaes, Marcel
2015-06-15
We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = − iħS{sup †}dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches.
Isoperiodic classical systems and their quantum counterparts
NASA Astrophysics Data System (ADS)
Asorey, M.; Cariñena, J. F.; Marmo, G.; Perelomov, A.
2007-06-01
One-dimensional isoperiodic classical systems have been first analyzed by Abel. Abel's characterization can be extended for singular potentials and potentials which are not defined on the whole real line. The standard shear equivalence of isoperiodic potentials can also be extended by using reflection and inversion transformations. We provide a full characterization of isoperiodic rational potentials showing that they are connected by translations, reflections or Joukowski transformations. Upon quantization many of these isoperiodic systems fail to exhibit identical quantum energy spectra. This anomaly occurs at order O( ℏ2) because semiclassical corrections of energy levels of order O( ℏ) are identical for all isoperiodic systems. We analyze families of systems where this quantum anomaly occurs and some special systems where the spectral identity is preserved by quantization. Conversely, we point out the existence of isospectral quantum systems which do not correspond to isoperiodic classical systems.
Robust observer for uncertain linear quantum systems
Yamamoto, Naoki
2006-09-15
In the theory of quantum dynamical filtering, one of the biggest issues is that the underlying system dynamics represented by a quantum stochastic differential equation must be known exactly in order that the corresponding filter provides an optimal performance; however, this assumption is generally unrealistic. Therefore, in this paper, we consider a class of linear quantum systems subjected to time-varying norm-bounded parametric uncertainties and then propose a robust observer such that the variance of the estimation error is guaranteed to be within a certain bound. Although in the linear case much of classical control theory can be applied to quantum systems, the quantum robust observer obtained in this paper does not have a classical analog due to the system's specific structure with respect to the uncertainties. Moreover, by considering a typical quantum control problem, we show that the proposed robust observer is fairly robust against a parametric uncertainty of the system even when the other estimators--the optimal Kalman filter and risk-sensitive observer--fail in the estimation.
Dissipation in deforming chaotic billiards
NASA Astrophysics Data System (ADS)
Barnett, Alexander Harvey
Chaotic billiards (hard-walled cavities) in two or more dimensions are paradigm systems in the fields of classical and quantum chaos. We study the dissipation (irreversible heating) rate in such billiard systems due to general shape deformations which are periodic in time. We are motivated by older studies of one-body nuclear dissipation and by anticipated mesoscopic applications. We review the classical and quantum linear response theories of dissipation rate and demonstrate their correspondence in the semiclassical limit. In both pictures, heating is a result of stochastic energy spreading. The heating rate can be expressed as a frequency-dependent friction coefficient μ(ω), which depends on billiard shape and deformation choice. We show that there is a special class of deformations for which μ vanishes as like a power law in the small- ω limit. Namely, for deformations which cause translations and dilations μ ~ ω4 whereas for those which cause rotations μ ~ ω2. This contrasts the generic case for which μ ~ ω4 We show how a systematic treatment of this special class leads to an improved version of the `wall formula' estimate for μ(0). We show that the special nature of dilation (a new result) is semiclassically equivalent to a quasi- orthogonality relation between the (undeformed) billiard quantum eigenstates on the boundary. This quasi- orthogonality forms the heart of a `scaling method' for the numerical calculation of quantum eigenstates, invented recently by Vergini and Saraceno. The scaling method is orders of magnitude more efficient than any other known billiard quantization method, however an adequate explanation for its success has been lacking until now. We explain the scaling method, its errors, and applications. We also present improvements to Heller's plane wave method. Two smaller projects conclude the thesis. Firstly, we give a new formalism for quantum point contact (QPC) conductance in terms of scattering cross-section in the half
Second-order superintegrable quantum systems
Miller, W.; Kalnins, E. G.; Kress, J. M.
2007-03-15
A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n - 1 functionally independent constants of the motion that are polynomial in the momenta, the maximum number possible. If these constants of the motion are all quadratic, then the system is second-order superintegrable, the most tractable case and the one we study here. Such systems have remarkable properties: multi-integrability and separability, a quadratic algebra of symmetries whose representation theory yields spectral information about the Schroedinger operator, and deep connections with expansion formulas relating classes of special functions. For n = 2 and for conformally flat spaces when n = 3, we have worked out the structure of the classical systems and shown that the quadratic algebra always closes at order 6. Here, we describe the quantum analogs of these results. We show that, for nondegenerate potentials, each classical system has a unique quantum extension.
Chuang, Chun-Fu; Sun, Yeong-Jeu; Wang, Wen-June
2012-12-01
In this study, exponential finite-time synchronization for generalized Lorenz chaotic systems is investigated. The significant contribution of this paper is that master-slave synchronization is achieved within a pre-specified convergence time and with a simple linear control. The designed linear control consists of two parts: one achieves exponential synchronization, and the other realizes finite-time synchronization within a guaranteed convergence time. Furthermore, the control gain depends on the parameters of the exponential convergence rate, the finite-time convergence rate, the bound of the initial states of the master system, and the system parameter. In addition, the proposed approach can be directly and efficiently applied to secure communication. Finally, four numerical examples are provided to demonstrate the feasibility and correctness of the obtained results.
Hybrid quantum systems with trapped charged particles
NASA Astrophysics Data System (ADS)
Kotler, Shlomi; Simmonds, Raymond W.; Leibfried, Dietrich; Wineland, David J.
2017-02-01
Trapped charged particles have been at the forefront of quantum information processing (QIP) for a few decades now, with deterministic two-qubit logic gates reaching record fidelities of 99.9 % and single-qubit operations of much higher fidelity. In a hybrid system involving trapped charges, quantum degrees of freedom of macroscopic objects such as bulk acoustic resonators, superconducting circuits, or nanomechanical membranes, couple to the trapped charges and ideally inherit the coherent properties of the charges. The hybrid system therefore implements a "quantum transducer," where the quantum reality (i.e., superpositions and entanglement) of small objects is extended to include the larger object. Although a hybrid quantum system with trapped charges could be valuable both for fundamental research and for QIP applications, no such system exists today. Here we study theoretically the possibilities of coupling the quantum-mechanical motion of a trapped charged particle (e.g., an ion or electron) to the quantum degrees of freedom of superconducting devices, nanomechanical resonators, and quartz bulk acoustic wave resonators. For each case, we estimate the coupling rate between the charged particle and its macroscopic counterpart and compare it to the decoherence rate, i.e., the rate at which quantum superposition decays. A hybrid system can only be considered quantum if the coupling rate significantly exceeds all decoherence rates. Our approach is to examine specific examples by using parameters that are experimentally attainable in the foreseeable future. We conclude that hybrid quantum systems involving a single atomic ion are unfavorable compared with the use of a single electron because the coupling rates between the ion and its counterpart are slower than the expected decoherence rates. A system based on trapped electrons, on the other hand, might have coupling rates that significantly exceed decoherence rates. Moreover, it might have appealing properties such
Color image encryption based on hybrid hyper-chaotic system and cellular automata
NASA Astrophysics Data System (ADS)
Yaghouti Niyat, Abolfazl; Moattar, Mohammad Hossein; Niazi Torshiz, Masood
2017-03-01
This paper proposes an image encryption scheme based on Cellular Automata (CA). CA is a self-organizing structure with a set of cells in which each cell is updated by certain rules that are dependent on a limited number of neighboring cells. The major disadvantages of cellular automata in cryptography include limited number of reversal rules and inability to produce long sequences of states by these rules. In this paper, a non-uniform cellular automata framework is proposed to solve this problem. This proposed scheme consists of confusion and diffusion steps. In confusion step, the positions of the original image pixels are replaced by chaos mapping. Key image is created using non-uniform cellular automata and then the hyper-chaotic mapping is used to select random numbers from the image key for encryption. The main contribution of the paper is the application of hyper chaotic functions and non-uniform CA for robust key image generation. Security analysis and experimental results show that the proposed method has a very large key space and is resistive against noise and attacks. The correlation between adjacent pixels in the encrypted image is reduced and the amount of entropy is equal to 7.9991 which is very close to 8 which is ideal.
Quantum optical properties in plasmonic systems
NASA Astrophysics Data System (ADS)
Ooi, C. H. Raymond
2015-04-01
Plasmonic metallic particle (MP) can affect the optical properties of a quantum system (QS) in a remarkable way. We develop a general quantum nonlinear formalism with exact vectorial description for the scattered photons by the QS. The formalism enables us to study the variations of the dielectric function and photon spectrum of the QS with the particle distance between QS and MP, exciting laser direction, polarization and phase in the presence of surface plasmon resonance (SPR) in the MP. The quantum formalism also serves as a powerful tool for studying the effects of these parameters on the nonclassical properties of the scattered photons. The plasmonic effect of nanoparticles has promising possibilities as it provides a new way for manipulating quantum optical properties of light in nanophotonic systems.
Note on quantum groups and integrable systems
NASA Astrophysics Data System (ADS)
Popolitov, A.
2016-01-01
The free-field formalism for quantum groups [preprint ITEP-M3/94, CRM-2202 hep-th/9409093] provides a special choice of coordinates on a quantum group. In these coordinates the construction of associated integrable system [arXiv:1207.1869] is especially simple. This choice also fits into general framework of cluster varieties [math.AG/0311245]—natural changes in coordinates are cluster mutations.
Intermittent chaotic chimeras for coupled rotators
NASA Astrophysics Data System (ADS)
Olmi, Simona; Martens, Erik A.; Thutupalli, Shashi; Torcini, Alessandro
2015-09-01
Two symmetrically coupled populations of N oscillators with inertia m display chaotic solutions with broken symmetry similar to experimental observations with mechanical pendulums. In particular, we report evidence of intermittent chaotic chimeras, where one population is synchronized and the other jumps erratically between laminar and turbulent phases. These states have finite lifetimes diverging as a power law with N and m . Lyapunov analyses reveal chaotic properties in quantitative agreement with theoretical predictions for globally coupled dissipative systems.
Toward simulating complex systems with quantum effects
NASA Astrophysics Data System (ADS)
Kenion-Hanrath, Rachel Lynn
Quantum effects like tunneling, coherence, and zero point energy often play a significant role in phenomena on the scales of atoms and molecules. However, the exact quantum treatment of a system scales exponentially with dimensionality, making it impractical for characterizing reaction rates and mechanisms in complex systems. An ongoing effort in the field of theoretical chemistry and physics is extending scalable, classical trajectory-based simulation methods capable of capturing quantum effects to describe dynamic processes in many-body systems; in the work presented here we explore two such techniques. First, we detail an explicit electron, path integral (PI)-based simulation protocol for predicting the rate of electron transfer in condensed-phase transition metal complex systems. Using a PI representation of the transferring electron and a classical representation of the transition metal complex and solvent atoms, we compute the outer sphere free energy barrier and dynamical recrossing factor of the electron transfer rate while accounting for quantum tunneling and zero point energy effects. We are able to achieve this employing only a single set of force field parameters to describe the system rather than parameterizing along the reaction coordinate. Following our success in describing a simple model system, we discuss our next steps in extending our protocol to technologically relevant materials systems. The latter half focuses on the Mixed Quantum-Classical Initial Value Representation (MQC-IVR) of real-time correlation functions, a semiclassical method which has demonstrated its ability to "tune'' between quantum- and classical-limit correlation functions while maintaining dynamic consistency. Specifically, this is achieved through a parameter that determines the quantumness of individual degrees of freedom. Here, we derive a semiclassical correction term for the MQC-IVR to systematically characterize the error introduced by different choices of simulation
Tunable entanglement resource in elastic electron-exchange collisions out of chaotic spin systems
NASA Astrophysics Data System (ADS)
Lohmann, B.; Blum, K.; Langer, B.
2016-09-01
Elastic collisions between initially unpolarized electrons and hydrogenlike atoms are discussed aiming to analyze the entanglement properties of the correlated final spin system. Explicit spin-dependent interactions are neglected and electron exchange only is taken into account. We show the final spin system to be completely characterized by a single spin correlation parameter depending on scattering angle and energy. Its numerical value identifies the final spins of the collision partners to be either in the separable, entangled, or Bell correlated regions. The symmetry of the scattering process allows for the construction of explicit examples applying methods of classical communication and local operations for illustrating the concepts of nonlocality versus separability. It is shown that strong correlations can be produced violating Bell's inequalities significantly. Furthermore, the degree of entanglement can be continuously varied simply by changing either the scattering angle and/or energy. This allows for the generation of tunable spin pairs with any desired degree of entanglement. It is suggested to use such nonlocally entangled spin pairs as a resource for further experiments, for example in quantum information processes.
Semiclassical matrix elements for a chaotic propagator in the scar function basis
NASA Astrophysics Data System (ADS)
Rivas, Alejandro M. F.
2013-04-01
A semiclassical approximation for the matrix elements of a quantum chaotic propagator in the scar function basis has been derived. The obtained expression is solely expressed in terms of canonical invariant objects. For our purpose, we have used the recently developed, semiclassical matrix elements of the propagator in coherent states, together with the linearization of the flux in the neighborhood of a classically unstable periodic orbit of chaotic two-dimensional systems. The expression derived here is successfully verified to be exact for a (linear) cat map, after the theory is adapted to a discrete phase space appropriate to a quantized torus.
Revealing Open Quantum Systems with Subsystem DFT
NASA Astrophysics Data System (ADS)
Krishtal, Alisa; Pavanello, Michele
The traditional quantum chemical methods, wave function or density based, are designed to solve for a closed system, where the Hamiltonian contains all relevant interactions. The closed system is, however, not realistic, as in real life the system is embedded in an environment with which it interacts to some degree. Including the description of the environment at the full quantum mechanical level leads to the Open Quantum Systems (OQS) theory: the only theory which can describe non-Markovian dynamics between the system and the environment. By allowing the flow of information in both directions phenomena such as quantum entanglement, relevant for the design of quantum computers, become available. While most OQS theories rely on the density matrix to describe the system-bath interaction, time-dependent subsystem DFT allows to approach the problem using the electron density. Through Dyson-like equations connecting the density-density response kernels of the OQS and its environment, the extent to which non-Markovian dynamics is present can be revealed. We illustrate this for the process of excitation energy transfer in coupled chromophores embedded in explicit solvent.
Quantum hacking: attacking practical quantum key distribution systems
NASA Astrophysics Data System (ADS)
Qi, Bing; Fung, Chi-Hang Fred; Zhao, Yi; Ma, Xiongfeng; Tamaki, Kiyoshi; Chen, Christine; Lo, Hoi-Kwong
2007-09-01
Quantum key distribution (QKD) can, in principle, provide unconditional security based on the fundamental laws of physics. Unfortunately, a practical QKD system may contain overlooked imperfections and violate some of the assumptions in a security proof. Here, we report two types of eavesdropping attacks against a practical QKD system. The first one is "time-shift" attack, which is applicable to QKD systems with gated single photon detectors (SPDs). In this attack, the eavesdropper, Eve, exploits the time mismatch between the open windows of the two SPDs. She can acquire a significant amount of information on the final key by simply shifting the quantum signals forwards or backwards in time domain. Our experimental results in [9] with a commercial QKD system demonstrate that, under this attack, the original QKD system is breakable. This is the first experimental demonstration of a feasible attack against a commercial QKD system. This is a surprising result. The second one is "phase-remapping" attack [10]. Here, Eve exploits the fact that a practical phase modulator has a finite response time. In principle, Eve could change the encoded phase value by time-shifting the signal pulse relative to the reference pulse.
Lee, Sang-Bong
1993-09-01
Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantum mechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantum mechanics is more fundamental than classical mechanics, the quantum description of classically chaotic nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover`s and Kubo-Fox-Keizer`s approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty.
Characterizing chaotic melodies in automatic music composition
NASA Astrophysics Data System (ADS)
Coca, Andrés E.; Tost, Gerard O.; Zhao, Liang
2010-09-01
In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests.
Quantum dynamics of nonlinear cavity systems
NASA Astrophysics Data System (ADS)
Nation, Paul David
In this work we investigate the quantum dynamics of three different configurations of nonlinear cavity systems. We begin by carrying out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector comprising a SQUID with a mechanically compliant loop segment. The SQUID is approximated by a nonlinear current-dependent inductor, inducing an external flux tunable nonlinear Duffing term in the cavity equation of motion. Expressions are derived for the detector signal and noise response where it is found that a soft-spring Duffing self-interaction enables a closer approach to the displacement detection standard quantum limit, as well as cooling closer to the ground state. Next, we consider the use of a superconducting transmission line formed from an array of dc-SQUIDs for investigating analogue Hawking radiation. We will show that biasing the array with a space-time varying flux modifies the propagation velocity of the transmission line, leading to an effective metric with a horizon. As a fundamentally quantum mechanical device, this setup allows for investigations of quantum effects such as backreaction and analogue space-time fluctuations on the Hawking process. Finally, we investigate a quantum parametric amplifier with dynamical pump mode, viewed as a zero-dimensional model of Hawking radiation from an evaporating black hole. The conditions are derived under which the spectrum of particles generated from vacuum fluctuations deviates from the thermal spectrum predicted for the conventional parametric amplifier. We find that significant deviation occurs once the pump mode (black hole) has released nearly half of its initial energy in the signal (Hawking radiation) and idler (in-falling particle) modes. As a model of black hole dynamics, this finding lends support to the view that late-time Hawking radiation contains information about the quantum state of the black hole and is entangled with the black hole's quantum
The path integral picture of quantum systems
NASA Astrophysics Data System (ADS)
Ceperley, David
2011-03-01
The imaginary time path integral ``formalism'' was introduced in 1953 by Feynman to understand the superfluid transition in liquid helium. The equilibrium properties of quantum many body systems is isomorphic to the classical statistical mechanics of cross-linking polymer-like objects. With the Markov Chain Monte Carlo method, invented by Metropolis et al., also in 1953, a potential way of calculating properties of correlated quantum systems was in place. But calculations for many-body quantum systems did not become routine until computers and algorithms had become sufficiently powerful three decades later. Once such simulations could happen, it was realized that simulations provided a deeper insight into boson superfluids, in particular the relation of bose condensation to the polymer end-to-end distance, and the superfluid density to the polymer ``winding number.'' Some recent developments and applications to supersolids, and helium droplets will be given. Finally, limitations of the methodology e.g. to fermion systems are discussed.
Multimode optomechanical system in the quantum regime.
Nielsen, William Hvidtfelt Padkær; Tsaturyan, Yeghishe; Møller, Christoffer Bo; Polzik, Eugene S; Schliesser, Albert
2017-01-03
We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 10(7)) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry-Perot resonator detects these modes' motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to -2.4 dB (-3.6 dB if corrected for detection losses) and bandwidths ≲90 kHz. The multimode nature of the membrane and Fabry-Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom.
Multimode optomechanical system in the quantum regime
NASA Astrophysics Data System (ADS)
Hvidtfelt Padkær Nielsen, William; Tsaturyan, Yeghishe; Møller, Christoffer Bo; Polzik, Eugene S.; Schliesser, Albert
2017-01-01
We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 107) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry–Perot resonator detects these modes’ motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to ‑2.4 dB (‑3.6 dB if corrected for detection losses) and bandwidths ≲90 kHz. The multimode nature of the membrane and Fabry–Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom.
Novaes, Marcel
2015-06-15
We consider S-matrix correlation functions for a chaotic cavity having M open channels, in the absence of time-reversal invariance. Relying on a semiclassical approximation, we compute the average over E of the quantities Tr[S{sup †}(E − ϵ) S(E + ϵ)]{sup n}, for general positive integer n. Our result is an infinite series in ϵ, whose coefficients are rational functions of M. From this, we extract moments of the time delay matrix Q = − iħS{sup †}dS/dE and check that the first 8 of them agree with the random matrix theory prediction from our previous paper [M. Novaes, J. Math. Phys. 56, 062110 (2015)].
NASA Astrophysics Data System (ADS)
Li, Wenlin; Li, Chong; Song, Heshan
2015-02-01
We propose a quantitative criterion to determine whether the coupled quantum systems can achieve complete synchronization or phase synchronization in the process of analyzing quantum synchronization. Adopting the criterion, we discuss the quantum synchronization effects between optomechanical systems and find that the error between the systems and the fluctuation of error is sensitive to coupling intensity by calculating the largest Lyapunov exponent of the model and quantum fluctuation, respectively. By taking the appropriate coupling intensity, we can control quantum synchronization even under different logical relationships between switches. Finally, we simulate the dynamical evolution of the system to verify the quantum synchronization criterion and to show the ability of synchronization control.
Nonequilibrium Quantum Systems: Fluctuations and Interactions
NASA Astrophysics Data System (ADS)
Subasi, Yigit
We explore some aspects of nonequilibrium statistical mechanics of classical and quantum systems. Two chapters are devoted to fluctuation theorems which were originally derived for classical systems. The main challenge in formulating them in quantum mechanics is the fact that fundamental quantities of interest, like work, are defined via the classical concept of a phase space trajectory. We utilize the decoherent histories conceptual framework, in which classical trajectories emerge in quantum mechanics as a result of coarse graining, and provide a first-principles analysis of the nonequilibrium work relation of Jarzynski and Crooks's fluctuation theorem for a quantum system interacting with a general environment based on the quantum Brownian motion (QBM) model. We indicate a parameter range at low temperatures where the theorems might fail in their original form. Fluctuation theorems of Jarzynski and Crooks for systems obeying classical Hamiltonian dynamics are derived under the assumption that the initial conditions are sampled from a canonical ensemble, even though the equilibrium state of an isolated system is typically associated with the microcanonical ensemble. We address this issue through an exact analysis of the classical Brownian motion model. We argue that a stronger form of ensemble equivalence than usually discussed in equilibrium statistical mechanics is required for these theorems to hold in the infinite environment limit irrespective of the ensemble used, and proceed to prove it for this model. An exact expression for the probability distribution of work is obtained for finite environments. Intuitively one expects a system to relax to an equilibrium state when brought into contact with a thermal environment. Yet it is important to have rigorous results that provide conditions for equilibration and characterize the equilibrium state. We consider the dynamics of open quantum systems using the Langevin and master equations and rigorously show that
Heisenberg picture approach to the stability of quantum Markov systems
Pan, Yu E-mail: zibo.miao@anu.edu.au; Miao, Zibo E-mail: zibo.miao@anu.edu.au; Amini, Hadis; Gough, John; Ugrinovskii, Valery; James, Matthew R.
2014-06-15
Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.
Simulation of n-qubit quantum systems. I. Quantum registers and quantum gates
NASA Astrophysics Data System (ADS)
Radtke, T.; Fritzsche, S.
2005-12-01
During recent years, quantum computations and the study of n-qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing quantum computations, however, these investigations also revealed a great deal of difficulties which still need to be solved in practice. In quantum computing, unitary and non-unitary quantum operations act on a given set of qubits to form (entangled) states, in which the information is encoded by the overall system often referred to as quantum registers. To facilitate the simulation of such n-qubit quantum systems, we present the FEYNMAN program to provide all necessary tools in order to define and to deal with quantum registers and quantum operations. Although the present version of the program is restricted to unitary transformations, it equally supports—whenever possible—the representation of the quantum registers both, in terms of their state vectors and density matrices. In addition to the composition of two or more quantum registers, moreover, the program also supports their decomposition into various parts by applying the partial trace operation and the concept of the reduced density matrix. Using an interactive design within the framework of MAPLE, therefore, we expect the FEYNMAN program to be helpful not only for teaching the basic elements of quantum computing but also for studying their physical realization in the future. Program summaryTitle of program:FEYNMAN Catalogue number:ADWE Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:None Computers for which the program is designed:All computers with a license of the computer algebra system MAPLE [Maple is a registered trademark of Waterlo Maple Inc.] Operating systems or monitors under which the program has been tested:Linux, MS Windows XP Programming language used:MAPLE 9.5 (but should be compatible
Quantum Hall effect in semiconductor systems with quantum dots and antidots
Beltukov, Ya. M.; Greshnov, A. A.
2015-04-15
The integer quantum Hall effect in systems of semiconductor quantum dots and antidots is studied theoretically as a factor of temperature. It is established that the conditions for carrier localization in quantum-dot systems favor the observation of the quantum Hall effect at higher temperatures than in quantum-well systems. The obtained numerical results show that the fundamental plateau corresponding to the transition between the ground and first excited Landau levels can be retained up to a temperature of T ∼ 50 K, which is an order of magnitude higher than in the case of quantum wells. Implementation of the quantum Hall effect at such temperatures requires quantum-dot systems with controllable characteristics, including the optimal size and concentration and moderate geometrical and composition fluctuations. In addition, ordered arrangement is desirable, hence quantum antidots are preferable.
Time dilation in quantum systems and decoherence
NASA Astrophysics Data System (ADS)
Pikovski, Igor; Zych, Magdalena; Costa, Fabio; Brukner, Časlav
2017-02-01
Both quantum mechanics and general relativity are based on principles that defy our daily intuitions, such as time dilation, quantum interference and entanglement. Because the regimes where the two theories are typically tested are widely separated, their foundational principles are rarely jointly studied. Recent works have found that novel phenomena appear for quantum particles with an internal structure in the presence of time dilation, which can take place at low energies and in weak gravitational fields. Here we briefly review the effects of time dilation on quantum interference and generalize the results to a variety of systems. In addition, we provide an extended study of the basic principles of quantum theory and relativity that are of relevance for the effects and also address several questions that have been raised, such as the description in different reference frames, the role of the equivalence principle and the effective irreversibility of the decoherence. The manuscript clarifies some of the counterintuitive aspects arising when quantum phenomena and general relativistic effects are jointly considered.
Relativistic quantum metrology in open system dynamics.
Tian, Zehua; Wang, Jieci; Fan, Heng; Jing, Jiliang
2015-01-22
Quantum metrology studies the ultimate limit of precision in estimating a physical quantity if quantum strategies are exploited. Here we investigate the evolution of a two-level atom as a detector which interacts with a massless scalar field using the master equation approach for open quantum system. We employ local quantum estimation theory to estimate the Unruh temperature when probed by a uniformly accelerated detector in the Minkowski vacuum. In particular, we evaluate the Fisher information (FI) for population measurement, maximize its value over all possible detector preparations and evolution times, and compare its behavior with that of the quantum Fisher information (QFI). We find that the optimal precision of estimation is achieved when the detector evolves for a long enough time. Furthermore, we find that in this case the FI for population measurement is independent of initial preparations of the detector and is exactly equal to the QFI, which means that population measurement is optimal. This result demonstrates that the achievement of the ultimate bound of precision imposed by quantum mechanics is possible. Finally, we note that the same configuration is also available to the maximum of the QFI itself.
Quantum Control in an Atomic Spin System
NASA Astrophysics Data System (ADS)
Phillips, C. S.; Woods, W.; Potts, J. R.; Ponsor, S.; Gardner, J. R.
1998-11-01
The experimental work described here investigates the physics of coherent quantum control in an atomic spin system. This type of system is very attractive for precision studies of coherent control for a number of reasons, including the ease with which it may be manipulated experimentally and the relative simplicity of its theoretical description. To this end, we are studying quantum control of the spin wavefunction of ground state (F=3) ^85Rb atoms confined in a vapor-cell MOT. Application of uniform magnetic and optical fields to this system results in an anharmonic ladder of seven levels whose state can be manipulated arbitrarily using radio-frequency rotating magnetic fields. Using the optimal control formalism of Shi and Rabitz, we have developed a numerical model of this system which predicts the appropriate control pulse shape given the initial and desired final state of the system. As predicted, we find that the control pulse which causes a given system evolution is not unique, allowing the construction of control pulses with multiple goals, such as evolution through specified intermediate states. This freedom should allow for the construction of control pulses that both produce the desired final state and are robust to decoherence effects. This type of precise control may find application in the development of quantum computation devices as well as in other types of nano-technology. An experimental implementation of quantum control in this system, already underway in our lab, will be presented.
Network realization of triplet-type quantum stochastic systems
NASA Astrophysics Data System (ADS)
Zhou, Shaosheng; Fu, Shizhou; Chen, Yuping
2017-01-01
This paper focuses on a problem of network synthesis for a class of quantum stochastic systems. The systems under consideration are of triplet-type form and stem from linear quantum optics and linear quantum circuits. A new quantum network realization approach is proposed by generalizing the scattering operator from the scalar form to a unitary matrix in network components. It shows that the triplet-type quantum stochastic system can be approximated by a quantum network which consists of some one-degree-of-freedom generalized open-quantum harmonic oscillators (1DGQHOs) via series, concatenation and feedback connections.
Constraint algebra for interacting quantum systems
NASA Astrophysics Data System (ADS)
Fubini, S.; Roncadelli, M.
1988-04-01
We consider relativistic constrained systems interacting with external fields. We provide physical arguments to support the idea that the quantum constraint algebra should be the same as in the free quantum case. For systems with ordering ambiguities this principle is essential to obtain a unique quantization. This is shown explicitly in the case of a relativistic spinning particle, where our assumption about the constraint algebra plus invariance under general coordinate transformations leads to a unique S-matrix. On leave from Dipartimento di Fisica Nucleare e Teorica, Università di Pavia and INFN, I-27100 Pavia, Italy.
Quons in a quantum dissipative system
NASA Astrophysics Data System (ADS)
Lee, Taejin
2016-03-01
String theory proves to be an imperative tool to explore the critical behavior of the quantum dissipative system. We discuss the quantum particles moving in two dimensions, in the presence of a uniform magnetic field, subject to a periodic potential and a dissipative force, which are described by the dissipative Wannier-Azbel-Hofstadter (DWAH) model. Using string theory formulation of the model, we find that the elementary excitations of the system at the generic points of the off-critical regions, in the zero temperature limit are quons, which satisfy q-deformed statistics.
Exponential quantum spreading in a class of kicked rotor systems near high-order resonances
NASA Astrophysics Data System (ADS)
Wang, Hailong; Wang, Jiao; Guarneri, Italo; Casati, Giulio; Gong, Jiangbin
2013-11-01
Long-lasting exponential quantum spreading was recently found in a simple but very rich dynamical model, namely, an on-resonance double-kicked rotor model [J. Wang, I. Guarneri, G. Casati, and J. B. Gong, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.234104 107, 234104 (2011)]. The underlying mechanism, unrelated to the chaotic motion in the classical limit but resting on quasi-integrable motion in a pseudoclassical limit, is identified for one special case. By presenting a detailed study of the same model, this work offers a framework to explain long-lasting exponential quantum spreading under much more general conditions. In particular, we adopt the so-called “spinor” representation to treat the kicked-rotor dynamics under high-order resonance conditions and then exploit the Born-Oppenheimer approximation to understand the dynamical evolution. It is found that the existence of a flat band (or an effectively flat band) is one important feature behind why and how the exponential dynamics emerges. It is also found that a quantitative prediction of the exponential spreading rate based on an interesting and simple pseudoclassical map may be inaccurate. In addition to general interests regarding the question of how exponential behavior in quantum systems may persist for a long time scale, our results should motivate further studies toward a better understanding of high-order resonance behavior in δ-kicked quantum systems.
Role of the Initial State in the Nonequilibrium Quantum Dynamics of Many-Body Systems
NASA Astrophysics Data System (ADS)
Santos, Lea F.; Torres-Herrera, Eduardo J.
2014-03-01
We show that the dynamics of isolated many-body quantum systems after a quench depends on the interplay between the initial state and the Hamiltonian dictating the evolution. The systems considered are in the nonperturbative regime. The relaxation process is controlled by the width of the energy distribution of the initial state and may be very similar for both chaotic and integrable Hamiltonians. Our analytical expression for the fidelity decay displays excellent agreement with our numerical results. This decay is Gaussian and may persist until saturation. We also provide analytical expressions that describe very well the initial evolution of the Shannon entropy and of few-body observables. The analyses are developed for deterministic one-dimensional systems and initial states of interest to current experiments with cold atoms in optical lattices. This work was supported by the NSF grant No. DMR-1147430. E.J.T.H. acknowledges partial support by CONACyT, México.
NASA Astrophysics Data System (ADS)
Li, Wenlin; Li, Chong; Song, Heshan
2016-12-01
In the framework of superconducting hybrid systems, we construct a star quantum network in which a superconducting transmission line resonator as a quantum bus and multiple units constituted by transmission line resonator and superconducting qubits as the carriers of quantum information. We further propose and analyze a theoretical scheme to realize quantum information processing in the quantum network. The coupling between the bus and any two superconducting qubits can be selectively implemented based on the dark state resonances of the highly dissipative transmission line resonators, and it can be found that quantum information processing between any two units can be completed in one step. As examples, the transmission of unknown quantum states and the preparation of quantum entanglement in this quantum network are investigated. At last, we exhibit our simulation results and complete the relevant discussions in order to show the advantages of this kind of quantum network.
Lyapunov Control of Quantum Systems with Impulsive Control Fields
Yang, Wei; Sun, Jitao
2013-01-01
We investigate the Lyapunov control of finite-dimensional quantum systems with impulsive control fields, where the studied quantum systems are governed by the Schrödinger equation. By three different Lyapunov functions and the invariant principle of impulsive systems, we study the convergence of quantum systems with impulsive control fields and propose new results for the mentioned quantum systems in the form of sufficient conditions. Two numerical simulations are presented to illustrate the effectiveness of the proposed control method. PMID:23766712
Quantum emulation of quasiperiodic systems
NASA Astrophysics Data System (ADS)
Senaratne, Ruwan; Geiger, Zachary; Fujiwara, Kurt; Singh, Kevin; Rajagopal, Shankari; Weld, David
2016-05-01
Tunable quasiperiodic optical traps can enable quantum emulation of electronic phenomena in quasicrystals. A 1D bichromatic lattice or a Gaussian beam intersecting a 2D square lattice in a direct analogy of the ``cut-and-project'' construction can be used to create tunable 1D quasiperiodic potentials for cold neutral atoms. We report on progress towards the observation of singular continuous diffraction patterns, fractal energy spectra, and Bloch oscillations in these synthetic quasicrystals. We will also discuss the existence of edge states which can be topologically pumped across the lattice by varying a phasonic parameter. We acknowledge support from the ONR, the ARO and the PECASE and DURIP programs, the AFOSR, the Alfred P. Sloan foundation and the President's Research Catalyst Award from the University of California Office of the President.
EDITORIAL: CAMOP: Quantum Non-Stationary Systems CAMOP: Quantum Non-Stationary Systems
NASA Astrophysics Data System (ADS)
Dodonov, Victor V.; Man'ko, Margarita A.
2010-09-01
Although time-dependent quantum systems have been studied since the very beginning of quantum mechanics, they continue to attract the attention of many researchers, and almost every decade new important discoveries or new fields of application are made. Among the impressive results or by-products of these studies, one should note the discovery of the path integral method in the 1940s, coherent and squeezed states in the 1960-70s, quantum tunneling in Josephson contacts and SQUIDs in the 1960s, the theory of time-dependent quantum invariants in the 1960-70s, different forms of quantum master equations in the 1960-70s, the Zeno effect in the 1970s, the concept of geometric phase in the 1980s, decoherence of macroscopic superpositions in the 1980s, quantum non-demolition measurements in the 1980s, dynamics of particles in quantum traps and cavity QED in the 1980-90s, and time-dependent processes in mesoscopic quantum devices in the 1990s. All these topics continue to be the subject of many publications. Now we are witnessing a new wave of interest in quantum non-stationary systems in different areas, from cosmology (the very first moments of the Universe) and quantum field theory (particle pair creation in ultra-strong fields) to elementary particle physics (neutrino oscillations). A rapid increase in the number of theoretical and experimental works on time-dependent phenomena is also observed in quantum optics, quantum information theory and condensed matter physics. Time-dependent tunneling and time-dependent transport in nano-structures are examples of such phenomena. Another emerging direction of study, stimulated by impressive progress in experimental techniques, is related to attempts to observe the quantum behavior of macroscopic objects, such as mirrors interacting with quantum fields in nano-resonators. Quantum effects manifest themselves in the dynamics of nano-electromechanical systems; they are dominant in the quite new and very promising field of circuit
Classical system boundaries cannot be determined within quantum Darwinism
NASA Astrophysics Data System (ADS)
Fields, Chris
Multiple observers who interact with environmental encodings of the states of a macroscopic quantum system S as required by quantum Darwinism cannot demonstrate that they are jointly observing S without a joint a priori assumption of a classical boundary separating S from its environment E. Quantum Darwinism cannot, therefore, be regarded as providing a purely quantum-mechanical explanation of the "emergence" of classicality.
CHAOTIC ZONES AROUND GRAVITATING BINARIES
Shevchenko, Ivan I.
2015-01-20
The extent of the continuous zone of chaotic orbits of a small-mass tertiary around a system of two gravitationally bound primaries of comparable masses (a binary star, a binary black hole, a binary asteroid, etc.) is estimated analytically, as a function of the tertiary's orbital eccentricity. The separatrix map theory is used to demonstrate that the central continuous chaos zone emerges (above a threshold in the primaries' mass ratio) due to overlapping of the orbital resonances corresponding to the integer ratios p:1 between the tertiary and the central binary periods. In this zone, the unlimited chaotic orbital diffusion of the tertiary takes place, up to its ejection from the system. The primaries' mass ratio, above which such a chaotic zone is universally present at all initial eccentricities of the tertiary, is estimated. The diversity of the observed orbital configurations of biplanetary and circumbinary exosystems is shown to be in accord with the existence of the primaries' mass parameter threshold.
NASA Astrophysics Data System (ADS)
Cui, Ping
The thesis comprises two major themes of quantum statistical dynamics. One is the development of quantum dissipation theory (QDT). It covers the establishment of some basic relations of quantum statistical dynamics, the construction of several nonequivalent complete second-order formulations, and the development of exact QDT. Another is related to the applications of quantum statistical dynamics to a variety of research fields. In particular, unconventional but novel theories of the electron transfer in Debye solvents, quantum transport, and quantum measurement are developed on the basis of QDT formulations. The thesis is organized as follows. In Chapter 1, we present some background knowledge in relation to the aforementioned two themes of this thesis. The key quantity in QDT is the reduced density operator rho(t) ≡ trBrho T(t); i.e., the partial trace of the total system and bath composite rhoT(t) over the bath degrees of freedom. QDT governs the evolution of reduced density operator, where the effects of bath are treated in a quantum statistical manner. In principle, the reduced density operator contains all dynamics information of interest. However, the conventional quantum transport theory is formulated in terms of nonequilibrium Green's function. The newly emerging field of quantum measurement in relation to quantum information and quantum computing does exploit a sort of QDT formalism. Besides the background of the relevant theoretical development, some representative experiments on molecular nanojunctions are also briefly discussed. In chapter 2, we outline some basic (including new) relations that highlight several important issues on QDT. The content includes the background of nonequilibrium quantum statistical mechanics, the general description of the total composite Hamiltonian with stochastic system-bath interaction, a novel parameterization scheme for bath correlation functions, a newly developed exact theory of driven Brownian oscillator (DBO
Lithography system using quantum entangled photons
NASA Technical Reports Server (NTRS)
Williams, Colin (Inventor); Dowling, Jonathan (Inventor); della Rossa, Giovanni (Inventor)
2002-01-01
A system of etching using quantum entangled particles to get shorter interference fringes. An interferometer is used to obtain an interference fringe. N entangled photons are input to the interferometer. This reduces the distance between interference fringes by n, where again n is the number of entangled photons.
Optimal control of complex atomic quantum systems
van Frank, S.; Bonneau, M.; Schmiedmayer, J.; Hild, S.; Gross, C.; Cheneau, M.; Bloch, I.; Pichler, T.; Negretti, A.; Calarco, T.; Montangero, S.
2016-01-01
Quantum technologies will ultimately require manipulating many-body quantum systems with high precision. Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing complexity. However, this control is still sub-optimal. In many scenarios, achieving a fast transformation is crucial to fight against decoherence and imperfection effects. Optimal control theory is believed to be the ideal candidate to bridge the gap between early stage proof-of-principle demonstrations and experimental protocols suitable for practical applications. Indeed, it can engineer protocols at the quantum speed limit – the fastest achievable timescale of the transformation. Here, we demonstrate such potential by computing theoretically and verifying experimentally the optimal transformations in two very different interacting systems: the coherent manipulation of motional states of an atomic Bose-Einstein condensate and the crossing of a quantum phase transition in small systems of cold atoms in optical lattices. We also show that such processes are robust with respect to perturbations, including temperature and atom number fluctuations. PMID:27725688
Optimal control of complex atomic quantum systems
NASA Astrophysics Data System (ADS)
van Frank, S.; Bonneau, M.; Schmiedmayer, J.; Hild, S.; Gross, C.; Cheneau, M.; Bloch, I.; Pichler, T.; Negretti, A.; Calarco, T.; Montangero, S.
2016-10-01
Quantum technologies will ultimately require manipulating many-body quantum systems with high precision. Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing complexity. However, this control is still sub-optimal. In many scenarios, achieving a fast transformation is crucial to fight against decoherence and imperfection effects. Optimal control theory is believed to be the ideal candidate to bridge the gap between early stage proof-of-principle demonstrations and experimental protocols suitable for practical applications. Indeed, it can engineer protocols at the quantum speed limit – the fastest achievable timescale of the transformation. Here, we demonstrate such potential by computing theoretically and verifying experimentally the optimal transformations in two very different interacting systems: the coherent manipulation of motional states of an atomic Bose-Einstein condensate and the crossing of a quantum phase transition in small systems of cold atoms in optical lattices. We also show that such processes are robust with respect to perturbations, including temperature and atom number fluctuations.
Hidden supersymmetry in quantum bosonic systems
Correa, Francisco Plyushchay, Mikhail S.
2007-10-15
We show that some simple well-studied quantum mechanical systems without fermion (spin) degrees of freedom display, surprisingly, a hidden supersymmetry. The list includes the bound state Aharonov-Bohm, the Dirac delta and the Poeschl-Teller potential problems, in which the unbroken and broken N = 2 supersymmetry of linear and nonlinear (polynomial) forms is revealed.
Coherent control in simple quantum systems
NASA Technical Reports Server (NTRS)
Prants, Sergey V.
1995-01-01
Coherent dynamics of two, three, and four-level quantum systems, simultaneously driven by concurrent laser pulses of arbitrary and different forms, is treated by using a nonperturbative, group-theoretical approach. The respective evolution matrices are calculated in an explicit form. General aspects of controllability of few-level atoms by using laser fields are treated analytically.
Open quantum systems approach to atomtronics
Pepino, R. A.; Cooper, J.; Meiser, D.; Anderson, D. Z.; Holland, M. J.
2010-07-15
We derive a quantum master equation to treat quantum systems interacting with multiple reservoirs. The formalism is used to investigate the atomic transport of bosons across a variety of lattice configurations. We demonstrate how the behavior of an electronic diode, a field-effect transistor, and a bipolar junction transistor can be realized with neutral, ultracold atoms trapped in optical lattices. An analysis of the current fluctuations is provided for the case of the atomtronic diode. Finally, we show that it is possible to demonstrate and logic gate behavior in an optical lattice.
Duality in the quantum Hall system
NASA Astrophysics Data System (ADS)
Lütken, C. A.; Ross, G. G.
1992-05-01
We suggest that a unified description of the integer and fractional phases of the quantum Hall system may be possible if the scaling diagram of transport coefficients is invariant under linear fractional (modular) transformations. In this model the hierarchy of states, as well as the observed universality of critical exponents, are consequences of a discrete SL(2,openZ) symmetry acting on the parameter space of an effective quantum-field theory. Available scaling data on the position of delocalization fixed points in the integer case and the position of mobility fixed points in the fractional case agree with the model within experimental accuracy.
Noise suppression of on-chip mechanical resonators by chaotic coherent feedback
NASA Astrophysics Data System (ADS)
Yang, Nan; Zhang, Jing; Wang, Hui; Liu, Yu-xi; Wu, Re-Bing; Liu, Lian-qing; Li, Chun-Wen; Nori, Franco
2015-09-01
We propose a method to decouple the nanomechanical resonator in optomechanical systems from the environmental noise by introducing a chaotic coherent feedback loop. We find that the chaotic controller in the feedback loop can modulate the dynamics of the controlled optomechanical system and induce a broadband response of the mechanical mode. This broadband response of the mechanical mode will cut off the coupling between the mechanical mode and the environment and thus suppress the environmental noise of the mechanical modes. As an application, we use the protected optomechanical system to act as a quantum memory. It is shown that the noise-decoupled optomechanical quantum memory is efficient for storing information transferred from coherent or squeezed light.
An impurity-induced gap system as a quantum data bus for quantum state transfer
Chen, Bing; Li, Yong; Song, Z.; Sun, C.-P.
2014-09-15
We introduce a tight-binding chain with a single impurity to act as a quantum data bus for perfect quantum state transfer. Our proposal is based on the weak coupling limit of the two outermost quantum dots to the data bus, which is a gapped system induced by the impurity. By connecting two quantum dots to two sites of the data bus, the system can accomplish a high-fidelity and long-distance quantum state transfer. Numerical simulations for finite system show that the numerical and analytical results of the effective coupling strength agree well with each other. Moreover, we study the robustness of this quantum communication protocol in the presence of disorder in the couplings between the nearest-neighbor quantum dots. We find that the gap of the system plays an important role in robust quantum state transfer.
Quantum cryptographic system with reduced data loss
Lo, Hoi-Kwong; Chau, Hoi Fung
1998-01-01
A secure method for distributing a random cryptographic key with reduced data loss. Traditional quantum key distribution systems employ similar probabilities for the different communication modes and thus reject at least half of the transmitted data. The invention substantially reduces the amount of discarded data (those that are encoded and decoded in different communication modes e.g. using different operators) in quantum key distribution without compromising security by using significantly different probabilities for the different communication modes. Data is separated into various sets according to the actual operators used in the encoding and decoding process and the error rate for each set is determined individually. The invention increases the key distribution rate of the BB84 key distribution scheme proposed by Bennett and Brassard in 1984. Using the invention, the key distribution rate increases with the number of quantum signals transmitted and can be doubled asymptotically.
Quantum cryptographic system with reduced data loss
Lo, H.K.; Chau, H.F.
1998-03-24
A secure method for distributing a random cryptographic key with reduced data loss is disclosed. Traditional quantum key distribution systems employ similar probabilities for the different communication modes and thus reject at least half of the transmitted data. The invention substantially reduces the amount of discarded data (those that are encoded and decoded in different communication modes e.g. using different operators) in quantum key distribution without compromising security by using significantly different probabilities for the different communication modes. Data is separated into various sets according to the actual operators used in the encoding and decoding process and the error rate for each set is determined individually. The invention increases the key distribution rate of the BB84 key distribution scheme proposed by Bennett and Brassard in 1984. Using the invention, the key distribution rate increases with the number of quantum signals transmitted and can be doubled asymptotically. 23 figs.
Heat exchange mediated by a quantum system
NASA Astrophysics Data System (ADS)
Panasyuk, George Y.; Levin, George A.; Yerkes, Kirk L.
2012-08-01
We consider heat transfer between two thermal reservoirs mediated by a quantum system using the generalized quantum Langevin equation. The thermal reservoirs are treated as ensembles of oscillators within the framework of the Drude-Ullersma model. General expressions for the heat current and thermal conductance are obtained for arbitrary coupling strength between the reservoirs and the mediator and for different temperature regimes. As an application of these results we discuss the origin of Fourier's law in a chain of large but finite subsystems coupled to each other by the quantum mediators. We also address a question of anomalously large heat current between the scanning tunneling microscope (STM) tip and substrate found in a recent experiment. The question of minimum thermal conductivity is revisited in the framework of scaling theory as a potential application of the developed approach.
Heat exchange mediated by a quantum system.
Panasyuk, George Y; Levin, George A; Yerkes, Kirk L
2012-08-01
We consider heat transfer between two thermal reservoirs mediated by a quantum system using the generalized quantum Langevin equation. The thermal reservoirs are treated as ensembles of oscillators within the framework of the Drude-Ullersma model. General expressions for the heat current and thermal conductance are obtained for arbitrary coupling strength between the reservoirs and the mediator and for different temperature regimes. As an application of these results we discuss the origin of Fourier's law in a chain of large but finite subsystems coupled to each other by the quantum mediators. We also address a question of anomalously large heat current between the scanning tunneling microscope (STM) tip and substrate found in a recent experiment. The question of minimum thermal conductivity is revisited in the framework of scaling theory as a potential application of the developed approach.
Identification of open quantum systems from observable time traces
Zhang, Jun; Sarovar, Mohan
2015-05-27
Estimating the parameters that dictate the dynamics of a quantum system is an important task for quantum information processing and quantum metrology, as well as fundamental physics. In our paper we develop a method for parameter estimation for Markovian open quantum systems using a temporal record of measurements on the system. Furthermore, the method is based on system realization theory and is a generalization of our previous work on identification of Hamiltonian parameters.
Sabavath, Gopi Kishan; Banerjee, I.; Mahapatra, S. K.; Shaw, Pankaj Kumar; Sekar Iyengar, A. N.
2015-08-15
Floating potential fluctuations from a direct current magnetron sputtering plasma have been analysed using time series analysis techniques like phase space plots, power spectra, frequency bifurcation plot, etc. The system exhibits quasiperiodic-chaotic-quasiperiodic-chaotic transitions as the discharge voltage was increased. The transitions of the fluctuations, quantified using the largest Lyapunov exponent, have been corroborated by Hurst exponent and the Shannon entropy. The Shannon entropy is high for quasiperiodic and low for chaotic oscillations.
Periodic thermodynamics of open quantum systems.
Brandner, Kay; Seifert, Udo
2016-06-01
The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and the second law are formulated consistently. In the linear response regime, entropy production becomes a quadratic form in the affinities. Specializing to Lindblad dynamics, we identify the corresponding kinetic coefficients in terms of correlation functions of the unperturbed dynamics. Reciprocity relations follow from symmetries with respect to time reversal. The kinetic coefficients can be split into a classical and a quantum contribution subject to an additional constraint, which follows from a natural detailed balance condition. This constraint implies universal bounds on efficiency and power of quantum heat engines. In particular, we show that Carnot efficiency cannot be reached whenever quantum coherence effects are present, i.e., when the Hamiltonian used for work extraction does not commute with the bare system Hamiltonian. For illustration, we specialize our universal results to a driven two-level system in contact with a heat bath of sinusoidally modulated temperature.
Edge reconstructions in fractional quantum Hall systems.
NASA Astrophysics Data System (ADS)
Joglekar, Yogesh; Nguyen, Hoang; Murthy, Ganpathy
2003-03-01
Two dimensional electron systems exhibiting fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations are possible [1]. We present a microscopic calculation of these egde-states at filling factors ν=1/3 and ν=2/5 using the Hamiltonian theory of the fractional quantum Hall effect [2]. We find that the quantum Hall egde undergoes a reconstruction as the confining potential, produced by the background charge density, softens [3,4]. Our results have implications to the tunneling experiments into the edge of a fractional quantum Hall system [5]. 1: X. G.Wen, Phys. Rev. Lett. 64, 2206 (1990). 2: R. Shankar and G. Murthy, Phys. Rev. Lett. 79, 4437 (1997). 3: C. de C. Chamon and X. G. Wen, Phys. Rev. B 49, 8227 (1994). 4: X. Wan, K. Yang, and E. H. Razayi, Phys. Rev. Lett. 88, 056802 (2002). 5: A.M.Chang et al., Phys. Rev. Lett. 86, 143 (2000).
Periodic thermodynamics of open quantum systems
NASA Astrophysics Data System (ADS)
Brandner, Kay; Seifert, Udo
2016-06-01
The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and the second law are formulated consistently. In the linear response regime, entropy production becomes a quadratic form in the affinities. Specializing to Lindblad dynamics, we identify the corresponding kinetic coefficients in terms of correlation functions of the unperturbed dynamics. Reciprocity relations follow from symmetries with respect to time reversal. The kinetic coefficients can be split into a classical and a quantum contribution subject to an additional constraint, which follows from a natural detailed balance condition. This constraint implies universal bounds on efficiency and power of quantum heat engines. In particular, we show that Carnot efficiency cannot be reached whenever quantum coherence effects are present, i.e., when the Hamiltonian used for work extraction does not commute with the bare system Hamiltonian. For illustration, we specialize our universal results to a driven two-level system in contact with a heat bath of sinusoidally modulated temperature.
Uchida, A; Sato, T; Kannari, F
1998-03-15
Suppression of chaotic instability arising in a Nd:YVO(4) microchip laser subject to frequency-shifted optical feedback is accomplished by injection of one of the periodic orbits into the bifurcation region of another chaotic system driven by pump modulation. Various periodic patterns, which do not exist in the original chaotic attractor, can be extracted from the chaotic oscillation by use of this nonfeedback chaos-control technique.
Powerlaw Decays and Thermalization in Isolated Many-Body Quantum Systems
NASA Astrophysics Data System (ADS)
Tavora, Marco; Torres-Herrera, E. J.; Santos, Lea
2016-05-01
We propose a new criterion for thermalization in isolated many-body quantum systems. It is based on the powerlaw behavior of the survival probability at long times. The value of the powerlaw exponent depends on the shape and filling of the energy distribution of the initial state. Exponents larger than or equal to 2 correspond to ergodic filling and consequent thermalization. We show that the algebraic behavior, which occurs in both integrable and chaotic systems, may be caused by bounds in the spectrum or by the presence of correlations between the eigenstates of the Hamiltonian. Numerical and analytical results as well as comparisons with existing rigorous mathematical derivations are presented. Our focus are on initial states that can be prepared experimentally using cold atoms in optical lattices. NSF Grant No. DMR-1147430.
Ergodicity in randomly perturbed quantum systems
NASA Astrophysics Data System (ADS)
Gherardini, Stefano; Lovecchio, Cosimo; Müller, Matthias M.; Lombardi, Pietro; Caruso, Filippo; Saverio Cataliotti, Francesco
2017-03-01
The theoretical cornerstone of statistical mechanics is the ergodic assumption, i.e. the assumption that the time average of an observable equals its ensemble average. Here, we show how such a property is present when an open quantum system is continuously perturbed by an external environment effectively observing the system at random times while the system dynamics approaches the quantum Zeno regime. In this context, by large deviation theory we analytically show how the most probable value of the probability for the system to be in a given state eventually deviates from the non-stochastic case when the Zeno condition is not satisfied. We experimentally test our results with ultra-cold atoms prepared on an atom chip.
Li, Chun-Ta; Lee, Cheng-Chi; Weng, Chi-Yao; Chen, Song-Jhih
2016-11-01
Secure user authentication schemes in many e-Healthcare applications try to prevent unauthorized users from intruding the e-Healthcare systems and a remote user and a medical server can establish session keys for securing the subsequent communications. However, many schemes does not mask the users' identity information while constructing a login session between two or more parties, even though personal privacy of users is a significant topic for e-Healthcare systems. In order to preserve personal privacy of users, dynamic identity based authentication schemes are hiding user's real identity during the process of network communications and only the medical server knows login user's identity. In addition, most of the existing dynamic identity based authentication schemes ignore the inputs verification during login condition and this flaw may subject to inefficiency in the case of incorrect inputs in the login phase. Regarding the use of secure authentication mechanisms for e-Healthcare systems, this paper presents a new dynamic identity and chaotic maps based authentication scheme and a secure data protection approach is employed in every session to prevent illegal intrusions. The proposed scheme can not only quickly detect incorrect inputs during the phases of login and password change but also can invalidate the future use of a lost/stolen smart card. Compared the functionality and efficiency with other authentication schemes recently, the proposed scheme satisfies desirable security attributes and maintains acceptable efficiency in terms of the computational overheads for e-Healthcare systems.
Some Theoretical Studies of Disordered Quantum Systems.
NASA Astrophysics Data System (ADS)
Dobrosavljevic, Vladimir
1988-12-01
In the first part of the thesis, two examples of disordered electronic systems are considered. I first investigate the role of conformational disorder relevant to the electronic structure of conjugated polymers such as polydiacetylene. Both in a solid and in solution the polymer undergoes a conformational transition accompanied by color changes as the temperature is increased. A simple statistical mechanical model for the transition is presented and solved, with the result defining the effective distribution of disorder for the electronic system. Renormalization group methods are then used to calculate the density of states and localization length for the model. Next, I study the fate of a hydrogenic atom in a hard sphere fluid. In this case, the disorder comes from the distribution of open spaces in the fluid accommodating the electron on its way around the nucleus. Simplified models for the electronic propagation in limits of small and large orbitals are presented. Simple variational methods can then be used to calculate the shift and broadening of spectral lines as a function of solvent density. In the second part, I examine the effects of quantum fluctuations on phase transitions in disordered systems. An example where such effects are manifestly important is the proton glass--a random mixture of a ferroelectric and an antiferroelectric component. The system can be described using a quantum mechanical Ising spin glass model, and the mean-field theory is solved using a novel combination of discretized path integral methods and replica techniques. The results show that the glassy phase is more susceptible to destruction by tunneling than are the ordered phases. Finally, I also consider the role of randomness in the size of quantum fluctuations, on the example of an Ising model with randomly mixed classical and quantum spins. For this model, the existence of a critical concentration of quantum spins is demonstrated, below which tunneling cannot destroy the ordered
Chaotic Behaviour in Quantum Dynamics
1991-09-01
is in some sense an approximation for the real Schrodinger equation . This is by no means obvious: the connection between the discrete time defined by...but even by the numerical solution of the Schrodinger equation (Figs.l), thus fully supporting the validity of the Kepler Map approach also for the...confirmed by extensive numerical simulations of the time-dependeut Schrodinger equation since 19842. In addition to that the Kepler map yields an
Uncertainty relation for non-Hamiltonian quantum systems
Tarasov, Vasily E.
2013-01-15
General forms of uncertainty relations for quantum observables of non-Hamiltonian quantum systems are considered. Special cases of uncertainty relations are discussed. The uncertainty relations for non-Hamiltonian quantum systems are considered in the Schroedinger-Robertson form since it allows us to take into account Lie-Jordan algebra of quantum observables. In uncertainty relations, the time dependence of quantum observables and the properties of this dependence are discussed. We take into account that a time evolution of observables of a non-Hamiltonian quantum system is not an endomorphism with respect to Lie, Jordan, and associative multiplications.
He, Lewei; Wang, Wen-Ge
2014-02-01
We study the problem of the basis of an open quantum system, under a quantum chaotic environment, which is preferred in view of its stationary reduced density matrix (RDM), that is, the basis in which the stationary RDM is diagonal. It is shown that, under an initial condition composed of sufficiently many energy eigenstates of the total system, such a basis is given by the eigenbasis of a renormalized self-Hamiltonian of the system, in the limit of large Hilbert space of the environment. Here, the renormalized self-Hamiltonian is given by the unperturbed self-Hamiltonian plus a certain average of the interaction Hamiltonian over the environmental degrees of freedom. Numerical simulations performed in two models, both with the kicked rotor as the environment, give results consistent with the above analytical predictions.
Zaks, Michael A; Goldobin, Denis S
2010-01-01
A recent paper claims that mean characteristics of chaotic orbits differ from the corresponding values averaged over the set of unstable periodic orbits, embedded in the chaotic attractor. We demonstrate that the alleged discrepancy is an artifact of the improper averaging. Since the natural measure is nonuniformly distributed over the attractor, different periodic orbits make different contributions into the time averages. As soon as the corresponding weights are accounted for, the discrepancy disappears.
Observable measure of quantum coherence in finite dimensional systems.
Girolami, Davide
2014-10-24
Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology, and cryptography. Yet, there is no universally efficient method for quantifying coherence either in theoretical or in experimental practice. I introduce a framework for measuring quantum coherence in finite dimensional systems. I define a theoretical measure which satisfies the reliability criteria established in the context of quantum resource theories. Then, I present an experimental scheme implementable with current technology which evaluates the quantum coherence of an unknown state of a d-dimensional system by performing two programmable measurements on an ancillary qubit, in place of the O(d2) direct measurements required by full state reconstruction. The result yields a benchmark for monitoring quantum effects in complex systems, e.g., certifying nonclassicality in quantum protocols and probing the quantum behavior of biological complexes.
NASA Astrophysics Data System (ADS)
Sui, Liansheng; Xu, Minjie; Tian, Ailing
2017-04-01
A novel optical image encryption scheme is proposed based on quick response code and high dimension chaotic system, where only the intensity distribution of encoded information is recorded as ciphertext. Initially, the quick response code is engendered from the plain image and placed in the input plane of the double random phase encoding architecture. Then, the code is encrypted to the ciphertext with noise-like distribution by using two cascaded gyrator transforms. In the process of encryption, the parameters such as rotation angles and random phase masks are generated as interim variables and functions based on Chen system. A new phase retrieval algorithm is designed to reconstruct the initial quick response code in the process of decryption, in which a priori information such as three position detection patterns is used as the support constraint. The original image can be obtained without any energy loss by scanning the decrypted code with mobile devices. The ciphertext image is the real-valued function which is more convenient for storing and transmitting. Meanwhile, the security of the proposed scheme is enhanced greatly due to high sensitivity of initial values of Chen system. Extensive cryptanalysis and simulation have performed to demonstrate the feasibility and effectiveness of the proposed scheme.
Lee, Tian-Fu
2014-12-01
Telecare medicine information systems provide a communicating platform for accessing remote medical resources through public networks, and help health care workers and medical personnel to rapidly making correct clinical decisions and treatments. An authentication scheme for data exchange in telecare medicine information systems enables legal users in hospitals and medical institutes to establish a secure channel and exchange electronic medical records or electronic health records securely and efficiently. This investigation develops an efficient and secure verified-based three-party authentication scheme by using extended chaotic maps for data exchange in telecare medicine information systems. The proposed scheme does not require server's public keys and avoids time-consuming modular exponential computations and scalar multiplications on elliptic curve used in previous related approaches. Additionally, the proposed scheme is proven secure in the random oracle model, and realizes the lower bounds of messages and rounds in communications. Compared to related verified-based approaches, the proposed scheme not only possesses higher security, but also has lower computational cost and fewer transmissions.
Multiple-state quantum Otto engine, 1D box system
NASA Astrophysics Data System (ADS)
Latifah, E.; Purwanto, A.
2014-03-01
Quantum heat engines produce work using quantum matter as their working substance. We studied adiabatic and isochoric processes and defined the general force according to quantum system. The processes and general force are used to evaluate a quantum Otto engine based on multiple-state of one dimensional box system and calculate the efficiency. As a result, the efficiency depends on the ratio of initial and final width of system under adiabatic processes.
Multiple-state quantum Otto engine, 1D box system
Latifah, E.; Purwanto, A.
2014-03-24
Quantum heat engines produce work using quantum matter as their working substance. We studied adiabatic and isochoric processes and defined the general force according to quantum system. The processes and general force are used to evaluate a quantum Otto engine based on multiple-state of one dimensional box system and calculate the efficiency. As a result, the efficiency depends on the ratio of initial and final width of system under adiabatic processes.
Thermalization of field driven quantum systems
Fotso, H.; Mikelsons, K.; Freericks, J. K.
2014-01-01
There is much interest in how quantum systems thermalize after a sudden change, because unitary evolution should preclude thermalization. The eigenstate thermalization hypothesis resolves this because all observables for quantum states in a small energy window have essentially the same value; it is violated for integrable systems due to the infinite number of conserved quantities. Here, we show that when a system is driven by a DC electric field there are five generic behaviors: (i) monotonic or (ii) oscillatory approach to an infinite-temperature steady state; (iii) monotonic or (iv) oscillatory approach to a nonthermal steady state; or (v) evolution to an oscillatory state. Examining the Hubbard model (which thermalizes under a quench) and the Falicov-Kimball model (which does not), we find both exhibit scenarios (i–iv), while only Hubbard shows scenario (v). This shows richer behavior than in interaction quenches and integrability in the absence of a field plays no role. PMID:24736404
Simple driven chaotic oscillators with complex variables.
Marshall, Delmar; Sprott, J C
2009-03-01
Despite a search, no chaotic driven complex-variable oscillators of the form z+f(z)=e(iOmegat) or z+f(z)=e(iOmegat) are found, where f is a polynomial with real coefficients. It is shown that, for analytic functions f(z), driven complex-variable oscillators of the form z+f(z)=e(iOmegat) cannot have chaotic solutions. Seven simple driven chaotic oscillators of the form z+f(z,z)=e(iOmegat) with polynomial f(z,z) are given. Their chaotic attractors are displayed, and Lyapunov spectra are calculated. Attractors for two of the cases have symmetry across the x=-y line. The systems' behavior with Omega as a control parameter in the range of Omega=0.1-2.0 is examined, revealing cases of period doubling, intermittency, chaotic transients, and period adding as routes to chaos. Numerous cases of coexisting attractors are also observed.
Mesoscopic systems: classical irreversibility and quantum coherence.
Barbara, Bernard
2012-09-28
Mesoscopic physics is a sub-discipline of condensed-matter physics that focuses on the properties of solids in a size range intermediate between bulk matter and individual atoms. In particular, it is characteristic of a domain where a certain number of interacting objects can easily be tuned between classical and quantum regimes, thus enabling studies at the border of the two. In magnetism, such a tuning was first realized with large-spin magnetic molecules called single-molecule magnets (SMMs) with archetype Mn(12)-ac. In general, the mesoscopic scale can be relatively large (e.g. micrometre-sized superconducting circuits), but, in magnetism, it is much smaller and can reach the atomic scale with rare earth (RE) ions. In all cases, it is shown how quantum relaxation can drastically reduce classical irreversibility. Taking the example of mesoscopic spin systems, the origin of irreversibility is discussed on the basis of the Landau-Zener model. A classical counterpart of this model is described enabling, in particular, intuitive understanding of most aspects of quantum spin dynamics. The spin dynamics of mesoscopic spin systems (SMM or RE systems) becomes coherent if they are well isolated. The study of the damping of their Rabi oscillations gives access to most relevant decoherence mechanisms by different environmental baths, including the electromagnetic bath of microwave excitation. This type of decoherence, clearly seen with spin systems, is easily recovered in quantum simulations. It is also observed with other types of qubits such as a single spin in a quantum dot or a superconducting loop, despite the presence of other competitive decoherence mechanisms. As in the molecular magnet V(15), the leading decoherence terms of superconducting qubits seem to be associated with a non-Markovian channel in which short-living entanglements with distributions of two-level systems (nuclear spins, impurity spins and/or charges) leading to 1/f noise induce τ(1)-like
Chaotic dynamics, fluctuations, nonequilibrium ensembles.
Gallavotti, Giovanni
1998-06-01
The ideas and the conceptual steps leading from the ergodic hypothesis for equilibrium statistical mechanics to the chaotic hypothesis for equilibrium and nonequilibrium statistical mechanics are illustrated. The fluctuation theorem linear law and universal slope prediction for reversible systems is briefly derived. Applications to fluids are briefly alluded to. (c) 1998 American Institute of Physics.
Electron Dynamics in Finite Quantum Systems
NASA Astrophysics Data System (ADS)
McDonald, Christopher R.
The multiconfiguration time-dependent Hartree-Fock (MCTDHF) and multiconfiguration time-dependent Hartree (MCTDH) methods are employed to investigate nonperturbative multielectron dynamics in finite quantum systems. MCTDHF is a powerful tool that allows for the investigation of multielectron dynamics in strongly perturbed quantum systems. We have developed an MCTDHF code that is capable of treating problems involving three dimensional (3D) atoms and molecules exposed to strong laser fields. This code will allow for the theoretical treatment of multielectron phenomena in attosecond science that were previously inaccessible. These problems include complex ionization processes in pump-probe experiments on noble gas atoms, the nonlinear effects that have been observed in Ne atoms in the presence of an x-ray free-electron laser (XFEL) and the molecular rearrangement of cations after ionization. An implementation of MCTDH that is optimized for two electrons, each moving in two dimensions (2D), is also presented. This implementation of MCTDH allows for the efficient treatment of 2D spin-free systems involving two electrons; however, it does not scale well to 3D or to systems containing more that two electrons. Both MCTDHF and MCTDH were used to treat 2D problems in nanophysics and attosecond science. MCTDHF is used to investigate plasmon dynamics and the quantum breathing mode for several electrons in finite lateral quantum dots. MCTDHF is also used to study the effects of manipulating the potential of a double lateral quantum dot containing two electrons; applications to quantum computing are discussed. MCTDH is used to examine a diatomic model molecular system exposed to a strong laser field; nonsequential double ionization and high harmonic generation are studied and new processes identified and explained. An implementation of MCTDHF is developed for nonuniform tensor product grids; this will allow for the full 3D implementation of MCTDHF and will provide a means to
Vibrational modes in the quantum Hall system
NASA Astrophysics Data System (ADS)
Wooten, Rachel; Yan, Bin; Daily, Kevin; Greene, Chris H.
The hyperspherical adiabatic technique is more familiar to atomic and nuclear few-body systems, but can also be applied with high accuracy to the many-body quantum Hall problem. This technique reformulates the Schrödinger equation for N electrons into hyperspherical coordinates, which, after extracting the trivial center of mass, describes the system in terms of a single global size coordinate known as the hyperradius R, and 2 N - 3 remaining internal angular coordinates. The solutions are approximately separable in the hyperradial coordinate, and solutions in the system are found by treating the hyperradius as an adiabatic coordinate. The approximate separability of the wave functions in this coordinate suggests the presence of hyperradial vibrational modes which are not described in conventional theories. The vibrationally excited states share the internal geometry of their quantum Hall ground states, and their excitation frequencies may vary with the number of participating particles or the strength of the confinement. We plan to discuss the features of these vibrational modes and their possible detection in quantum Hall systems. NSF.
On Mathematical Modeling Of Quantum Systems
Achuthan, P.; Narayanankutty, Karuppath
2009-07-02
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.
On Mathematical Modeling Of Quantum Systems
NASA Astrophysics Data System (ADS)
Achuthan, P.; Narayanankutty, Karuppath
2009-07-01
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.
Chaotic Map Construction from Common Nonlinearities and Microcontroller Implementations
NASA Astrophysics Data System (ADS)
Ablay, Günyaz
2016-06-01
This work presents novel discrete-time chaotic systems with some known physical system nonlinearities. Dynamic behaviors of the models are examined with numerical methods and Arduino microcontroller-based experimental studies. Many new chaotic maps are generated in the form of x(k + 1) = rx(k) + f(x(k)) and high-dimensional chaotic systems are obtained by weak coupling or cross-coupling the same or different chaotic maps. An application of the chaotic maps is realized with Arduino for chaotic pulse width modulation to drive electrical machines. It is expected that the new chaotic maps and their microcontroller implementations will facilitate practical chaos-based applications in different fields.
Artificial quantum thermal bath: Engineering temperature for a many-body quantum system
NASA Astrophysics Data System (ADS)
Shabani, Alireza; Neven, Hartmut
2016-11-01
Temperature determines the relative probability of observing a physical system in an energy state when that system is energetically in equilibrium with its environment. In this paper we present a theory for engineering the temperature of a quantum system different from its ambient temperature. We define criteria for an engineered quantum bath that, when coupled to a quantum system with Hamiltonian H , drives the system to the equilibrium state e/-H/TTr (e-H /T) with a tunable parameter T . This is basically an analog counterpart of the digital quantum metropolis algorithm. For a system of superconducting qubits, we propose a circuit-QED approximate realization of such an engineered thermal bath consisting of driven lossy resonators. Our proposal opens the path to simulate thermodynamical properties of many-body quantum systems of size not accessible to classical simulations. Also we discuss how an artificial thermal bath can serve as a temperature knob for a hybrid quantum-thermal annealer.
NASA Astrophysics Data System (ADS)
Li, Jun; Lu, Dawei; Luo, Zhihuang; Laflamme, Raymond; Peng, Xinhua; Du, Jiangfeng
2016-07-01
Precisely characterizing and controlling realistic quantum systems under noises is a challenging frontier in quantum sciences and technologies. In developing reliable controls for open quantum systems, one is often confronted with the problem of the lack of knowledge on the system controllability. The purpose of this paper is to give a numerical approach to this problem, that is, to approximately compute the reachable set of states for coherently controlled quantum Markovian systems. The approximation consists of setting both upper and lower bounds for system's reachable region of states. Furthermore, we apply our reachability analysis to the control of the relaxation dynamics of a two-qubit nuclear magnetic resonance spin system. We implement some experimental tasks of quantum state engineering in this open system at a near optimal performance in view of purity: e.g., increasing polarization and preparing pseudopure states. These results demonstrate the usefulness of our theory and show interesting and promising applications of environment-assisted quantum dynamics.
Isochronous classical systems and quantum systems with equally spaced spectra
NASA Astrophysics Data System (ADS)
Cariñena, J. F.; Perelomov, A. M.; Rañada, M. F.
2007-11-01
We study isoperiodic classical systems, what allows us to find the classical isochronous systems, i.e. having a period independent of the energy. The corresponding quantum analog, systems with an equally spaced spectrum are analysed by looking for possible creation-like differential operators. The harmonic oscillator and the isotonic oscillator are the two main essentially unique examples of such situation.
Measuring entanglement entropy in a quantum many-body system
NASA Astrophysics Data System (ADS)
Rispoli, Matthew; Preiss, Philipp; Tai, Eric; Lukin, Alex; Schittko, Robert; Kaufman, Adam; Ma, Ruichao; Islam, Rajibul; Greiner, Markus
2016-05-01
The presence of large-scale entanglement is a defining characteristic of exotic quantum phases of matter. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. However, measuring entanglement remains a challenge. This is especially true in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. We demonstrate a novel approach to the measurement of entanglement entropy of any bosonic system, using a quantum gas microscope with tailored potential landscapes. This protocol enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. In general, these experiments exemplify a method enabling the measurement and characterization of quantum phase transitions and in particular would be apt for studying systems such as magnetic ordering within the quantum Ising model.
Dynamical systems and quantum bicrossproduct algebras
NASA Astrophysics Data System (ADS)
Arratia, Oscar; del Olmo, Mariano A.
2002-06-01
We present a unified study of some aspects of quantum bicrossproduct algebras of inhomogeneous Lie algebras, such as Poincaré, Galilei and Euclidean in N dimensions. The action associated with the bicrossproduct structure allows us to obtain a nonlinear action over a new group linked to the translations. This new nonlinear action associates a dynamical system with each generator which is the object of our study.