Dynamics Of Maps Research Articles

A Single-Averaged Model for the Solar Radiation Pressure Applied to Space Debris Mitigation Using a Solar Sail

Several non-functional objects are orbiting around the Earth and they are called space debris. In this work, we investigate the process of space debris mitigation from the GEO region using a solar sail. The acceleration induced by the solar radiation pressure (SRP) is the most relevant perturbation for objects in orbit around the Earth with a high area-to-mass ratio (A/m). We consider the single-averaged SRP model with the Sun in an elliptical and inclined orbit. In addition to the SRP effect, the orbital evolution of space debris is analyzed considering the perturbations due to the Earth’s flattening and third-body perturbations in the dynamical system. The idea is to use the solar sail as a propulsion system using the Sun itself as a clean and abundant energy source so that it can remove space debris from the geostationary orbit and also contribute to the sustainability of space exploration. Using averaged dynamical maps as a tool, the numerical simulations show that the solar sail contributes strongly to exciting the eccentricity of the space debris, causing its reentry into Earth’s atmosphere. To perform the numerical simulations, we consider data from real space debris. We also show that the solar sail can be used to remove space debris for a graveyard orbit. In this way, the solar sail can work as a clean and sustainable space-debris-removal mechanism. Finally, we show that the convenient choice of the argument of perigee and the longitude of the ascending node might contribute to amplify the growth of eccentricity. It is also shown that solar radiation pressure destroys the symmetry of the orbits that can be observed in keplerian orbits, so all the orbits will be asymmetric when considering the presence of this force.

Improving classical capacity of qubit dynamical maps through stationary state manipulation

We analyze the evolution of Holevo and entanglement-assisted classical capacities for two classes of phase-covariant channels. In particular, we show that these capacities can be improved by changing the stationary state of the channel, which is closely related to its non-unitality degree. The more non-unital the channel, the greater its capacity. The channel parameters are engineered through mixtures on the level of dynamical maps, time-local generators, and memory kernels, for which we propose construction methods. For highly non-unital maps, we achieve a temporary increase in the classical capacity that exceeds the entanglement-assisted classical capacity of the unital map. This shows that non-unitality can become a better quantum resource for information transition purposes than quantum entanglement.

The Open Systems View and the Everett Interpretation

It is argued that those who defend the Everett, or ‘many-worlds’, interpretation of quantum mechanics should embrace what we call the general quantum theory of open systems (GT) as the proper framework in which to conduct foundational and philosophical investigations in quantum physics. GT is a wider dynamical framework than its alternative, standard quantum theory (ST). This is true even though GT makes no modifications to the quantum formalism. GT rather takes a different view, what we call the open systems view, of the formalism; i.e., in GT, the dynamics of systems whose physical states are fundamentally represented by density operators are represented as fundamentally open as specified by an in general non-unitary dynamical map. This includes, in principle, the dynamics of the universe as a whole. We argue that the more general dynamics describable in GT can be physically motivated, that there is as much prima facie empirical support for GT as there is for ST, and that GT could be fully in the spirit of the Everett interpretation—that there might, in short, be little reason for an Everettian not to embrace the more general theoretical landscape that GT allows one to explore.

A Dynamical Survey of the Trans-Neptunian Region. I. Mean-motion Resonances with Neptune

In this paper, we present a large-scale dynamical survey of the trans-Neptunian region, with particular attention to mean-motion resonances (MMRs). We study a set of 4121 trans-Neptunian objects (TNOs), a sample far larger than in previous works. We perform direct long-term numerical integrations that enable us to examine the overall dynamics of the individual TNOs as well as to identify all MMRs. For the latter purpose, we apply an own-developed FAIR method that allows the semi-automatic identification of even very high-order MMRs. Apart from searching for the more frequent eccentricity-type resonances that previous studies concentrated on, we set our method to allow the identification of inclination-type MMRs, too. Furthermore, we distinguish between TNOs that are locked in a given MMR throughout the whole integration time span (108 yr) and those that are only temporarily captured in resonances. For a more detailed dynamical analysis of the trans-Neptunian space, we also construct dynamical maps using test particles. Observing the fine structure of the 34–80 au region underlines the stabilizing role of the MMRs, with the regular regions coinciding with the positions of real TNOs.

Invertibility as a Witness of Markovianity of the Quantum Dynamical Maps

Markovianity of the quantum open system processes is a topic of the considerable current interest. Typically, invertibility is assumed to be non-essential for Markovianity of the open quantum system dynamical maps. Nevertheless, in this paper we distinguish a class of physically important dynamical maps (processes) for which invertibility is a necessary condition for Markovianity. Since every quantum state tomography directly provides information on invertibility of the map, no optimization procedure is necessary for determining non-Markovianity regarding the considered class of dynamical processes. On this basis we are able to provide a systematic insight and to distinguish mutual relations of the various approaches to quantum Markovianity. Notably, for the processes out of the considered class of dynamical maps, various relations are allowed between divisibility, invertibility and Markovianity of the dynamical maps.

Information backflow may not indicate quantum memory

We analyze recent approaches to quantum Markovianity and how they relate to the proper definition of quantum memory. We show that the well-known criterion of information backflow does not report a distinction between the quantum or classical character of observed memory effects. Therefore, as a complement to the current description, we propose a definition of a quantum backflow based on the concept of component dynamical maps and convexity arguments. In particular, for a natural choice of component maps, we provide a practical characterization of quantum memory in terms of the new concept of quantum memory witness. In particular, we give a full description of such witnesses in a qubit case. Finally, we discuss a potential generalization of component maps that should capture certain classical features of information backflow.

Bounds on the breaking time for entanglement-breaking channels

Entanglement-breaking channels are quantum channels transforming entangled states to separable states. Despite a detailed discussion of their operational structure, to be found in the literature, studies on dynamical characteristics of this type of maps are yet limited. We consider one of the basic questions: for Lindblad-type dynamics, when does a given channel break entanglement? We discuss the finite-dimensional case where the quantification of entanglement via entanglement witnesses is utilized. For the general setup, we use the method of quantum speed limit to derive lower bounds on entanglement breaking times in terms of an input state, the dynamical map and the witness operator. Then, with a particular choice of the input state and the entanglement witness, the bounds for the breaking time are turned to solely reflect the characteristics of the dynamics.

Quantum Dynamics is Not Strictly Bidivisible.

We address the question of the existence of quantum channels that are divisible in two quantum channels but not in three or, more generally, channels divisible in n but not in n+1 parts. We show that for the qubit those channels do not exist, whereas for general finite-dimensional quantum channels the same holds at least for full Kraus rank channels. To prove these results, we introduce a novel decomposition of quantum channels which separates them into a boundary and Markovian part, and it holds for any finite dimension. Additionally, the introduced decomposition amounts to the well-known connection between divisibility classes and implementation types of quantum dynamical maps and can be used to implement quantum channels using smaller quantum registers.

Classifying the non-time-local and entangling dynamics of an open qubit system

We study families of dynamical maps generated from interactions with varying degrees of symmetry. For a family of time-independent Hamiltonians, we demonstrate the relationship between symmetry, strong-coupling, perfect entanglers, non-Markovian features, and non-time-locality. We show that by perturbing the initial environment state, effective time-local descriptions can be obtained that are non-singular yet capture essential non-unitary features of the reduced dynamics. We then consider a time-dependent Hamiltonian that changes the degree of symmetry by activating a dormant degree of freedom. In this example we find that the one-qubit reduced dynamics changes dramatically. These results can inform the construction of effective theories of open systems when the larger system dynamics is unknown.

Non-Markovianity through entropy-based quantum thermodynamics

We introduce a generalized approach to characterize the non-Markovianity of quantum dynamical maps via breakdown of monotonicity of thermodynamic functions. By adopting an entropy-based formulation of quantum thermodynamics, we use the relationship between heat and entropy to propose a measure of non-Markovianity based on the heat flow for single-qubit quantum evolutions. This measure can be applied for unital dynamical maps that do not invert the sign of the internal energy. Under certain conditions, it can also be extended for other thermodynamic functions, such as internal energy and work flows. In this context, a natural connection between heat and quantum coherence can be identified for dynamical maps that are both unital and incoherent. As applications, we explore dissipative and non-dissipative quantum dynamical processes, illustrating the compatibility between our thermodynamic quantifiers and the well-establish measure defined via quantum coherence.

Quantum State Tomography in Nonequilibrium Environments

We generalize an approach to studying the quantum state tomography (QST) of open systems in terms of the dynamical map in Kraus representation within the framework of dynamic generation of informationally complete positive operator-valued measures. As applications, we use the generalized approach to theoretically study the QST of qubit systems in the presence of nonequilibrium environments which exhibit nonstationary and non-Markovian random telegraph noise statistical properties. We derive the time-dependent measurement operators for the quantum state reconstruction of the single qubit and two-qubit systems in terms of the polarization operator basis. It is shown that the behavior of the time-dependent measurement operators is closely associated with the dynamical map of the qubit systems.

A Fractional-Order Improved Quantum Logistic Map: Chaos, 0-1 Testing, Complexity, and Control

Based on a quantum logistic map and a Caputo-like delta difference operator, a fractional-order improved quantum logistic map, which has hidden attractors, was constructed. Its dynamical behaviors are investigated by employing phase portraits, bifurcation diagrams, Lyapunov spectra, dynamical mapping, and 0-1 testing. It is shown that the proposed fractional-order map is influenced by both the parameters and the fractional order. Then, the complexity of the map is explored through spectral entropy and approximate entropy. The results show that the fractional-order improved quantum logistic map has stronger robustness within chaos and higher complexity, so it is more suitable for engineering applications. In addition, the fractional-order chaotic map can be controlled for different periodic orbits by the improved nonlinear mapping on the wavelet function.

Effective master equations for two accelerated qubits

We revisit the problem involving two constantly accelerating Unruh-DeWitt detectors using Open Effective Field Theory methods. We study the time evolution of the joint detector state using a Markovian approximation which differs from the standard one taken in the literature. We show that this Markovian limit already implies the complete positivity of the dynamical evolution map without invoking the rotating wave approximation (RWA), in contrast to standard derivations of open system master equations. By calculating explicitly the domain of validity of this Markovian approximation, we argue that the lack of complete positivity in the usual microscopic derivation stems from the (subtle) fact that the Redfield equation is used outside its domain of validity. We give two well-known cases studied in the literature that violate the validity of the Markovian approximation: (i) the ``stacked trajectory'' limit (when detector trajectories are taken to be on top of one another), and (ii) large gap-to-acceleration ratio. Since Markovian dynamics with or without RWA can lead to different qualitative predictions for entanglement dynamics, our work emphasizes the need to properly track the regime of validity of all approximations.

New Insights Into Chaos Based Image Encryption & Its Application

Nowadays the whole world is upgrading with different innovative technologies. We need to resist any attack during data transfer over insecure networks. Random nature & sensitivity to initial conditions in dynamical maps are highly useful to secure cryptography algorithms. In this paper, structure of different chaotic maps have been reviewed, basis of chaos-based image encryption has mentioned. Finally a new encryption scheme has been proposed using tent & logistic map. Performance analysis of proposed scheme has been discussed. Different coupling of chaotic maps, aspects of elliptical curve can be considered for compressed image, video or audio encryption as future work.

Spatially heterogenous dynamics in colloidal gels during syneresis.

Syneresis, the compaction of a material accompanied by fluid expulsion, is a typical mechanical instability which exists among colloidal gel based materials and that negatively affects the quality of relevant applications. We shed light onto the internal dynamics of model colloidal gels undergoing syneresis using Laser Speckle Imaging (LSI). The resulting dynamical maps capture the distinct differences in spatial and temporal relaxation patterns between colloidal gels comprising solid and liquid particles. This indicates different mechanisms of syneresis between the two systems and highlights the importance of the constituent particles and their mobile or restrictive interfaces in the mechanical relaxation of the colloidal gels during syneresis.

Multipartite entanglement and purity dynamics in channels influenced by fractional Gaussian noise

The dynamical map of entanglement, coherence and mixedness in four-qubit maximally entangled GHZ-class state paired with classical channels driven by fractional Gaussian noise is investigated. The qubit-channel coupling is assumed in four distinct ways: common, bipartite, tripartite, and independent local channel-qubit configurations comprising single, double, triple, or independent noisy sources. Using entanglement witness, negativity, purity and von Neumann entropy, except for the independent configuration, we show that indefinite entanglement, coherence, and purity preservation may be simulated in multipartite GHZ-like states. Quantum correlations and purity decrease exponentially in four qubits, and exact fluctuating local field behavior, as well as entanglement sudden death and birth revivals, are completely suppressed. Entanglement, coherence, and purity preservation are affected by noise and the number of independent channels utilized. The Hurst parameter of fractional Gaussian noise was discovered in the four qubits to improve entanglement, coherence and avoid mixedness.

Construction and Local Equivalence of Dual-Unitary Operators: From Dynamical Maps to Quantum Combinatorial Designs

While quantum circuits built from two-particle dual-unitary (maximally entangled) operators serve as minimal models of typically nonintegrable many-body systems, the construction and characterization of dual-unitary operators themselves are only partially understood. A nonlinear map on the space of unitary operators was proposed in PRL.~125, 070501 (2020) that results in operators being arbitrarily close to dual unitaries. Here we study the map analytically for the two-qubit case describing the basins of attraction, fixed points, and rates of approach to dual unitaries. A subset of dual-unitary operators having maximum entangling power are 2-unitary operators or perfect tensors, and are equivalent to four-party absolutely maximally entangled states. It is known that they only exist if the local dimension is larger than $d=2$. We use the nonlinear map, and introduce stochastic variants of it, to construct explicit examples of new dual and 2-unitary operators. A necessary criterion for their local unitary equivalence to distinguish classes is also introduced and used to display various concrete results and a conjecture in $d=3$. It is known that orthogonal Latin squares provide a ``classical combinatorial design" for constructing permutations that are 2-unitary. We extend the underlying design from classical to genuine quantum ones for general dual-unitary operators and give an example of what might be the smallest sized genuinely quantum design of a 2-unitary in $d=4$.

Time inhomogeneous quantum dynamical maps.

We discuss a wide class of time inhomogeneous quantum evolution which is represented by two-parameter family of completely positive trace-preserving maps. These dynamical maps are constructed as infinite series of jump processes. It is shown that such dynamical maps satisfy time inhomogeneous memory kernel master equation which provides a generalization of the master equation involving the standard convolution. Time-local (time convolution-less) approach is discussed as well. Finally, the comparative analysis of traditional time homogeneous versus time inhomogeneous scenario is provided.

Initial correlations in open quantum systems: constructing linear dynamical maps and master equations

We investigate the dynamics of open quantum systems which are initially correlated with their environment. The strategy of our approach is to analyze how given, fixed initial correlations modify the evolution of the open system with respect to the corresponding uncorrelated dynamical behavior with the same fixed initial environmental state, described by a completely positive dynamical map. We show that, for any predetermined initial correlations, one can introduce a linear dynamical map on the space of operators of the open system which acts like the proper dynamical map on the set of physical states and represents its unique linear extension. Furthermore, we demonstrate that this construction leads to a linear, time-local quantum master equation with generalized Lindblad structure involving time-dependent, possibly negative transition rates. Thus, the general non-Markovian dynamics of an open quantum system can be described by means of a time-local master equation even in the case of arbitrary, fixed initial system–environment correlations. We present some illustrative examples and explain the relation of our approach to several other approaches proposed in the literature.

On the retrograde planar co-orbital asteroid motion with Jupiter

AbstractWe study the motion of an asteroid being in retrograde 1/1 resonance with Jupiter (co-orbital motion). We consider the planar case (i=180°) and Jupiter is on a circular or elliptic orbit (e′ = 0.048). In the cirular model we compute families of symmetric periodic orbits and their stability type. In the elliptic model we have isolated periodic orbits which affect the orbital modes of motion as it is shown by the FLI dynamical maps.